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Robust image processing algorithms, involving tools from digital geometry and mathematical morphology

This document summarizes a seminar presentation about robust image processing algorithms involving tools from digital geometry and mathematical morphology. The presentation introduces the speaker and their background and research interests. It then discusses the need for a formal definition of robustness for image processing algorithms. Such a definition is proposed, involving evaluating algorithms over multiple noise scales and ensuring quality measures respect Lipschitz continuity as noise increases. Examples are given of algorithms from mathematical morphology and digital geometry that have been evaluated for robustness based on this definition. The talk concludes by discussing applications of these techniques to biomedical image analysis tasks.

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ROBUST IMAGE PROCESSING ALGORITHMS, INVOLVING TOOLS FROM DIGITAL GEOMETRY AND MATHEMATICAL MORPHOLOGY CBA SEMINAR 2018 ANTOINE VACAVANT, PHD, HDR, ASSOCIATE PROFESSOR INSTITUT PASCAL, UMR6602 UCA / SIGMA / CNRS, LE PUY-EN-VELAY www.linkedin.com/in/antoinevacavant twitter.com/antoinevacavant antoine.vacavant@uca.fr antoine-vacavant.eu
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 1 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 2 / 55
Me in one slide / Université Clermont Auvergne 2010 - now: Associate prof. in computer science, Institut Pascal, IUT Le Puy-en-Velay Researches in IGT / Image Guided Therapies 2010 - 2015: Head of bachelor degree in computer graphics 2017 - now: Responsible of tech transfer in IGT 2017 - now: Scientific head of Embolization research team Computer vision Image processing Spatial data structures Digital geometry Medical appli- cations Antoine Vacavant 3 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 4 / 55
Introduction / Image processing in a nutshell Image processing is a central task for computer image analysis For various contexts: Remote satellite image interpretation Biomedical imagery Surveillance and security, etc. Followed by high-level interpretation Methodological contributions: Image processing Medical applications: Computer vision Sensor Input: Acquisition, sampling, quantification Pre-processing: enhancement, denoising, etc. Processing: segmenta- tion, feature extraction, etc. Machine learning: classification, recognition, etc. User decision Antoine Vacavant 5 / 55
Introduction / Image processing in a nutshell Image processing is a central task for computer image analysis For various contexts: Remote satellite image interpretation Biomedical imagery Surveillance and security, etc. Followed by high-level interpretation Methodological contributions: Image processing Medical applications: Computer visionMedical applications with Computer vision Sensor Input: Acquisition, sampling, quantification Pre-processing: enhancement, denoising, etc. Processing: segmenta- tion, feature extraction, etc. Machine learning: classification, recognition, etc. User decision Antoine Vacavant 5 / 55
Introduction / Image processing in a nutshell Image processing is a central task for computer image analysis For various contexts: Remote satellite image interpretation Biomedical imagery Surveillance and security, etc. Followed by high-level interpretation Methodological contributions: Image processing Medical applications: Computer vision Methodological contributions in Image processing Medical applications with Computer vision Sensor Input: Acquisition, sampling, quantification Pre-processing: enhancement, denoising, etc. Processing: segmenta- tion, feature extraction, etc. Machine learning: classification, recognition, etc. User decision Antoine Vacavant 5 / 55
Introduction / Image processing in a nutshell Image processing is a central task for computer image analysis For various contexts: Remote satellite image interpretation Biomedical imagery Surveillance and security, etc. Followed by high-level interpretation Problem revealed by experience in image processing Methodological contributions: Image processing Medical applications: Computer vision Methodological contributions in Image processing Novel definition of Robustness Sensor Input: Acquisition, sampling, quantification Pre-processing: enhancement, denoising, etc. Processing: segmenta- tion, feature extraction, etc. Machine learning: classification, recognition, etc. User decision Antoine Vacavant 5 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 6 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 7 / 55
Definition of robustness / Noise and robustness Image processing (IP), noise Common issue in IP: uncontrolled and destructive perturbation of the image Coming from diverse sources Artefacts in medical images Videos jittered by the camera, etc. Antoine Vacavant 8 / 55
Definition of robustness / Noise and robustness Image processing (IP), noise Common issue in IP: uncontrolled and destructive perturbation of the image Coming from diverse sources Artefacts in medical images Videos jittered by the camera, etc. Designed as noise Antoine Vacavant 8 / 55
Definition of robustness / Noise and robustness Image processing (IP), noise Common issue in IP: uncontrolled and destructive perturbation of the image Coming from diverse sources Artefacts in medical images Videos jittered by the camera, etc. Designed as noise Robustness Is seen as the ability of an algorithm to resist to this noise Ensures that the developed algorithm satisfies the final user of the application Antoine Vacavant 8 / 55
Definition of robustness / Noise and robustness Image processing (IP), noise Common issue in IP: uncontrolled and destructive perturbation of the image Coming from diverse sources Artefacts in medical images Videos jittered by the camera, etc. Designed as noise Robustness Is seen as the ability of an algorithm to resist to this noise Ensures that the developed algorithm satisfies the final user of the application But is mixed up with terms as efficiency, quality, performance Without any formal definition for image processing Antoine Vacavant 8 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 9 / 55
Definition of robustness / Robustness for image processing Contribution Propose a definition of robustness for IP algorithms In parallel of what has been done in CV Antoine Vacavant 10 / 55
Definition of robustness / Robustness for image processing Contribution Propose a definition of robustness for IP algorithms In parallel of what has been done in CV Presented at CBA in 2016 Antoine Vacavant 10 / 55
Definition of robustness / Robustness for image processing Contribution Propose a definition of robustness for IP algorithms In parallel of what has been done in CV Presented at CBA in 2016 Input noise model We suppose that the input data is altered with an additive noise, with similar notations as [Meer, 2001] yi y0 i + δyi , yi ∈ Rq , i 1, . . . , n also shortened as Y Y0 + δY Antoine Vacavant 10 / 55
Definition of robustness / Robustness for image processing Contribution Propose a definition of robustness for IP algorithms In parallel of what has been done in CV Presented at CBA in 2016 Input noise model We suppose that the input data is altered with an additive noise, with similar notations as [Meer, 2001] yi y0 i + δyi , yi ∈ Rq , i 1, . . . , n also shortened as Y Y0 + δY With Y: measurements Y0: true (and generally unknown) value δY: corruption by the noise We can suppose wlog an iid noise as δyi GI(0, σ2Cy)Antoine Vacavant 10 / 55
Definition of robustness / Robustness for image processing Robustness model for IP Robustness should be measured with multiple scales of noise Study limitations of an algorithm, how to make it fail Antoine Vacavant 11 / 55
Definition of robustness / Robustness for image processing Robustness model for IP Robustness should be measured with multiple scales of noise Study limitations of an algorithm, how to make it fail Definition of robustness for IP A: algorithm designed for a given IP application X {xi }i 1,n: output of A N: additive noise specific to this application {σk }k 1,m: set of scales of N Q(Xk, Y0 k ): measure of the quality of A for the scale k of N A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 11 / 55
Definition of robustness / Robustness for image processing Robustness model for IP Robustness should be measured with multiple scales of noise Study limitations of an algorithm, how to make it fail Definition of robustness for IP A: algorithm designed for a given IP application X {xi }i 1,n: output of A N: additive noise specific to this application {σk }k 1,m: set of scales of N Q(Xk, Y0 k ): measure of the quality of A for the scale k of N A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 11 / 55
Definition of robustness / Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
Definition of robustness / Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
Definition of robustness / Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
Definition of robustness / Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
Definition of robustness / Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
Definition of robustness / Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
Definition of robustness / Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
Definition of robustness / Robustness for image processing Synthetic example 1st way to assess robustness: graphically 2nd way to assess robustness: numerically Algorithm 1: α 0.30 Algorithm 2: α 0.18 Algorithm 3: α 0.05 Algorithm 4: α 0.02 Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 13 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 14 / 55
MM / Context and motivation Image denoising filtering A lot of contributions since 70’s [Lebrun et al., 2012] Linear, popular, simple filters: Gaussian, average, median, bilateral, etc. Non-local strategies: NL-means, BM3D, total variation, etc. PDE schemes: anisotropic diffusion, coherence, etc. Antoine Vacavant 15 / 55
MM / Context and motivation Image denoising filtering A lot of contributions since 70’s [Lebrun et al., 2012] Linear, popular, simple filters: Gaussian, average, median, bilateral, etc. Non-local strategies: NL-means, BM3D, total variation, etc. PDE schemes: anisotropic diffusion, coherence, etc. Shock filtering Shock filter iteratively produces local segmentations in inflection zones: ∆ f t−1(pi , qj) < 0 ⇒ f t(pi , qj) f t−1(pi , qj) ⊕ D ; ∆ f t−1(pi , qj) > 0 ⇒ f t(pi , qj) f t−1(pi , qj) D Antoine Vacavant 15 / 55
MM / Context and motivation Image denoising filtering A lot of contributions since 70’s [Lebrun et al., 2012] Linear, popular, simple filters: Gaussian, average, median, bilateral, etc. Non-local strategies: NL-means, BM3D, total variation, etc. PDE schemes: anisotropic diffusion, coherence, etc. Shock filtering Shock filter iteratively produces local segmentations in inflection zones: ∆ f t−1(pi , qj) < 0 ⇒ f t(pi , qj) f t−1(pi , qj) ⊕ D ; ∆ f t−1(pi , qj) > 0 ⇒ f t(pi , qj) f t−1(pi , qj) D Smoothed shock filtering Enhance contours by creating smoothed ruptures PDE scheme with smoothed ⊕, operators A. Vacavant, A. Albouy-Kissi, P.-Y. Menguy, J. Solomon: Fast smoothed shock filtering. In IEEE ICPR 2012, Tsukuba, Japan, 2012. Antoine Vacavant 15 / 55
MM / Context and motivation Smoothed shock filtering examples Results with a photo and a complete CT slice Different values of ρ parameter (impact of shock) Algorithm iterated 10, 20, 30 times (PDE) Result of a simple segmentation algorithm afterwards Antoine Vacavant 16 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 17 / 55
MM / Test of robustness Material and methods 13 classic images / Y0 Altered with additive white Gaussian noise / Y With increasing std / scales {σk }k 1,5 {5, 10, 15, 20, 25} Antoine Vacavant 18 / 55
MM / Test of robustness Material and methods 13 classic images / Y0 Altered with additive white Gaussian noise / Y With increasing std / scales {σk }k 1,5 {5, 10, 15, 20, 25} From state of the art Shock-based methods Classic algorithms Median-based methods Algorithm Reference Median [Huang et al., 1979] Coherence [Weickert, 2003] OriginalShock [Osher and Rudin, 1990] EnhancedShock [Alvarez and Mazorra, 1994] ComplexShock [Gilboa et al., 2004] Bilateral [Tomasi and Manduchi, 1998] SmoothedMedian [Kass and Solomon, 2010] SmoothedShock [Vacavant et al., 2012] Antoine Vacavant 18 / 55
MM / Test of robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
MM / Test of robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
MM / Test of robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
MM / Test of robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
MM / Test of robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
MM / Test of robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
MM / Test of robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness Numerical evaluation of robustness Algorithm α Median 0.15 Coherence 0.15 OriginalShock 0.14 EnhancedShock 0.14 ComplexShock 0.12 Bilateral 0.11 SmoothedMedian 0.05 SmoothedShock 0.04 A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 20 / 55
MM / Improvement of machine learning tasks Texture recognition We have proposed to improve texture classification by a scale-space approach For a given dataset: Brodatz, Vistex, Usptex or Outex Select a feature: LBP, GLCM, GLDM, SFTA, CLBP or LBPV Select a classifier: KNN or Naive Bayes Determine the best scales to be used in improving the classification rates Same is done for 2 other filters: Anisotropic diffusion (PM) and Gaussian filtering (G) M.B. Neiva, A. Vacavant, O.M. Bruno: Improving Texture Extraction and Classification using Smoothed Morphological Operators. Digital signal processing, 2018. Antoine Vacavant 21 / 55
MM / Improvement of machine learning tasks Evaluation of accuracy for all datasets With KNN Dataset Best rate (feat.) Best SSF (feat.) Iterations Best G (feat.) Iterations Best PM (feat.) Iterations Outex 75.59 (LBPV) 84.78 (GLDM) {2, 4 . . . 18} 83.01 (CLBP) {9} 82.94 (CLBP) {19} Brodatz 97.6 (CLBP) 98.11 (CLBP) {6} 97.20 (CLBP) {2} 97.84 (CLBP) {11, 14} Usptex 83.1 (CLBP) 88.66 (CLBP) {1, 8} 85.21 (CLBP) {1} 88.57 (CLBP) {1, 3 . . . 17} Vistex 98.96 (CLBP) 99.31 (CLBP) {2} 98.96 (CLBP) {2, 3} 99.54 (CLBP) {14} With Naive Bayes Dataset Best rate (feat.) Best SSF (feat.) Iterations Best G (feat.) Iterations Best PM (feat.) Iterations Outex 80.81 (LBP) 86.47 (LBP) {2, 7 . . . 17} 83.01 (LBP) {8} 85.15 (CLBP) {4} Brodatz 96.6 (CLBP) 98.02 (CLBP) {2} 96.85 (CLBP) {1} 97.47 (CLBP) {15} Usptex 85.77 (CLBP) 91.49 (CLBP) {1, 3, 5} 86.43 (CLBP) {1, 3} 89.66 (CLBP) {8, 11 . . . 20} Vistex 97.33 (CLBP) 98.50 (CLBP) {2, 3} 98.50 (CLBP) {1, 3, 5} 97.92 (CLBP) {1, 8} Antoine Vacavant 22 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 23 / 55
MM / Discussion Smoothed shock filtering Original contribution: robust image denoising algorithm Approved by applying definition of robustness Antoine Vacavant 24 / 55
MM / Discussion Smoothed shock filtering Original contribution: robust image denoising algorithm Approved by applying definition of robustness Several parameters modulate algorithm’s behavior Shock impact Number of iterations Improves segmentation and machine learning tasks (e.g. fMRI classification) Antoine Vacavant 24 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 25 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 26 / 55
DG / Context and motivation Notion of Reeb graph Reeb graph is discrete structure representing both geometry and topology of an object Edges: object’s branches Vertices: branches’ junctions Calculated on a compact manifold wrt. definition of a given h function Note Critical points of h are graph vertices Definition of h is important for a correct graph construction Antoine Vacavant 27 / 55
DG / Context and motivation Reeb graphs in literature A lot of attention on its construction for 3-D meshes [Biasotti et al., 2008; Harvey et al., 2010] Generally, h is a height function (along an axis) Appropriate for many objects, but not for all! Can be calculated with other functions (e.g. geodesic) [Tierny, 2006] Antoine Vacavant 28 / 55
DG / Context and motivation Reeb graphs in literature A lot of attention on its construction for 3-D meshes [Biasotti et al., 2008; Harvey et al., 2010] Generally, h is a height function (along an axis) Appropriate for many objects, but not for all! Can be calculated with other functions (e.g. geodesic) [Tierny, 2006] Skeletons, medial axes and other 1-pixel-wide centered structures capture topology [Arcelli et al., 2010; Bertrand et al., 2014] Strategy: Compute Reeb graph from such structures [Janusch et al., 2015; Pascucci et al., 2007] Antoine Vacavant 28 / 55
DG / Context and motivation Reeb graphs in literature A lot of attention on its construction for 3-D meshes [Biasotti et al., 2008; Harvey et al., 2010] Generally, h is a height function (along an axis) Appropriate for many objects, but not for all! Can be calculated with other functions (e.g. geodesic) [Tierny, 2006] Skeletons, medial axes and other 1-pixel-wide centered structures capture topology [Arcelli et al., 2010; Bertrand et al., 2014] Strategy: Compute Reeb graph from such structures [Janusch et al., 2015; Pascucci et al., 2007] But they can be very sensitive to noise! Linking them to Reeb graph is not trivial Antoine Vacavant 28 / 55
DG / Context and motivation Our contribution Compute Reeb graphs of 2-D binary shapes Use a robust skeletonization scheme Capable of using several h functions Applications in robust image analysis A. Vacavant, A. Leborgne: Robust computations of reeb graphs in 2-D binary images. In CTIC 2016, LNCS 9667, pages 204–215, Marseille, France, 2016. Antoine Vacavant 29 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 30 / 55
DG / Reeb graph computations by skeleton extraction DECS algorithm DECS: Discrete Euclidean Connected Skeleton [Leborgne et al., 2015] Resist to noise, compared to other algorithms Antoine Vacavant 31 / 55
DG / Reeb graph computations by skeleton extraction DECS algorithm DECS: Discrete Euclidean Connected Skeleton [Leborgne et al., 2015] Resist to noise, compared to other algorithms Algorithm: From a binary image I Euclidean distance map EDTI Reduced medial axis RDMAI Laplacian-of-Gaussian filtering of EDTI as RDGI Combine RDGI and RDMAI to calculate a coarse skeleton SI Thin and prune SI to obtain S∗ I EDTI RDMAI RDGI SI S∗ I Antoine Vacavant 31 / 55
DG / Reeb graph computations by skeleton extraction The definition Definition (Reeb graph) Let h be a continuous function defined on a compact variety M, h : M → R. The Reeb graph of M, denoted by G(h), is the quotient space defined by the equivalence relation p ∼ q ⇔ (p, h(p)) ∼ (q, h(q)) s.t.: h(p) h(q), p, q belongs to the same connected component of h−1(h(p)). Antoine Vacavant 32 / 55
DG / Reeb graph computations by skeleton extraction Properties of Reeb graph G(h) is constructed by a level-sets approach wrt. h Points in the same con. component are associated to a level of h Reeb graph brings together topology and geometry (h defined on M) Key items G(h) is constructed by a level-sets approach wrt. h Antoine Vacavant 33 / 55
DG / Reeb graph computations by skeleton extraction Properties of Reeb graph G(h) (V, E) represents M through h Edges: object’s branches (points belonging to the same con. component) Vertices: Critical points of h: begin, end, merge, split Key items G(h) is constructed by a level-sets approach wrt. h G(h) represents M through h Antoine Vacavant 33 / 55
DG / Reeb graph computations by skeleton extraction Properties of Reeb graph Discrete G(h) (V, E) is built by an iterative process All notions hold in the discrete case Finite number of h level-sets Key items G(h) is constructed by a level-sets approach wrt. h G(h) represents M through h Discrete G(h) is built by an iterative process Antoine Vacavant 33 / 55
DG / Reeb graph computations by skeleton extraction Properties of Reeb graph Key items G(h) is constructed by a level-sets approach wrt. h G(h) represents M through h Discrete G(h) is built by an iterative process Use DECS to build Reeb graphs of binary object Antoine Vacavant 33 / 55
DG / Reeb graph computations by skeleton extraction Our algorithm From a binary image I, compute DECS S∗ I , select a starting point pS in S∗ I Breadth-first construction of GI(h) by adding points of S∗ I Increase level-set by assigning increasing h values to points treated Antoine Vacavant 34 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 35 / 55
DG / Experimental evaluation Reeb graph obtained for noisy vascular image Antoine Vacavant 36 / 55
DG / Experimental evaluation With synthetic images nit 0 nit 1 Antoine Vacavant 37 / 55
DG / Experimental evaluation With synthetic images nit 0 nit 5 Antoine Vacavant 37 / 55
DG / Experimental evaluation With synthetic images nit 0 nit 50 Antoine Vacavant 37 / 55
DG / Experimental evaluation With synthetic images nit 0 nit 100 Antoine Vacavant 37 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 38 / 55
DG / Discussion Reeb graphs of noisy binary shapes Possibility to choose a relevant h function h may be chosen for further pattern recognition issues (descriptor encoding) Robustness may be assessed by means of our formalism Antoine Vacavant 39 / 55
DG / Discussion Reeb graphs of noisy binary shapes Possibility to choose a relevant h function h may be chosen for further pattern recognition issues (descriptor encoding) Robustness may be assessed by means of our formalism Other works Irregular isothetic grids for vectorization Quadtree complexity theorem Vectorization of grayscale images A. Vacavant, B. Kerautret, T. Roussillon, F. Feschet: Reconstructions of noisy digital contours with maximal primitives based on multi-scale/irregular geometric representation and generalized linear programming. In DGCI 2017, LNCS 10502, pages 291–303, Vienna, Austria, 2017. Y. Gerard, A. Vacavant, J.-M. Favreau: Tight bounds in the quadtree complexity theorem and the maximal number of pixels crossed by a curve of given length. Theoretical Computer Science, 624:41–55, 2016. B. Kerautret, P. Ngo, Y. Kenmochi, A. Vacavant: Greyscale image vectorization from geometric digital contour representations. In DGCI 2017, LNCS 10502, pages 319–331, Vienne, Autriche, 2017. Antoine Vacavant 39 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 40 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 41 / 55
MM & DG for the liver / Context and motivation Our research group Inside IGT research axis CaVITI (Cardio-Vascular Interventional Therapy and Imaging) 3 research groups Theme 1: Endoprothesis Theme 2: Embolization Theme 3: Myocardial function Antoine Vacavant 42 / 55
MM & DG for the liver / Context and motivation Our research group Inside IGT research axis CaVITI (Cardio-Vascular Interventional Therapy and Imaging) 3 research groups Theme 1: Endoprothesis Theme 2: Embolization Theme 3: Myocardial function Research targets Quantitatively assess hepatic tumoral response by medical image analysis Innovative tools devoted to tumoral tissue quantification Personalized numerical simulation of treatments Link with clinical activities: chemo-embolization, surgery, biopsy, etc. Target cancer: HCC (Hepato-Cellular Carcinoma) Antoine Vacavant 42 / 55
MM & DG for the liver / Context and motivation Our research group Inside IGT research axis CaVITI (Cardio-Vascular Interventional Therapy and Imaging) 3 research groups Theme 1: Endoprothesis Theme 2: Embolization Theme 3: Myocardial function Research targets Quantitatively assess hepatic tumoral response by medical image analysis Innovative tools devoted to tumoral tissue quantification Personalized numerical simulation of treatments Link with clinical activities: chemo-embolization, surgery, biopsy, etc. Target cancer: HCC (Hepato-Cellular Carcinoma) More details tomor- row at CoSy seminar! Antoine Vacavant 42 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 43 / 55
MM & DG for the liver / HCC segmentation Segmentation of HCC within MRI ROI Enhance patches by smoothed shock filtering Segmentation by a fuzzy approach Input MRI ROI SSF Output Segmentation by fuzzification/defuzzification First calculate a fuzzy clustering by FCMVC (with variable compactness) JFCMVC n j 1 c i 1 ˆµij(xj − vi)2pi , ˆµij (xj − vi)−2pi c i 1 (xj − vi)−2pi Then calculate a binary segmentation by sequential feature selection Including geometrical and fuzzy features Antoine Vacavant 44 / 55
MM & DG for the liver / HCC segmentation Some segmentation results Our approach also compared with methods from state-of-the-art Positive impact of smoothed shock filter ROI SSF GT Output A. Vacavant, A.-R. Ali, M. Grand-Brochier, A. Albouy-Kissi, J.-Y. Boire, A. Alfidja et P. Chabrot: Smoothed shock filtered defuzzification with Zernike moments for liver tumor extraction in MR images. In IEEE IPTA 2015, Orléans, France, Nov. 2015. Antoine Vacavant 45 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 46 / 55
MM & DG for the liver / Hepatic vascular network segmentation Our pipeline for segmenting liver vessels From a CT or MRI volume, I Extract the liver and use it as a bounding box Multi-scale vessel detection with Hessian matrix IS [Sato et al., 1994] Partial skeletonization and reconnection S in IS [Homann et al., 2007] Calculate the RORPO vesselness filter IR [Merveille et al., 2018] Use S as initialization for fast marching segmentation within IR M.-A. Lebre, A. Vacavant, M. Grand-Brochier, O. Merveille, A. Abergel, P. Chabrot, B. Magnin: Automatic 3-D Skeleton-based Segmentation of Liver Vessels From MRI and CT for Couinaud Representation. In IEEE ICIP 2018, Athens, Greece, Antoine Vacavant 47 / 55
MM & DG for the liver / Hepatic vascular network segmentation Numerical results with IRCAD dataset (CT) ACC SPE SEN PRE FPR FNR Ours 0.97±0.01 0.98±0.01 0.69±0.10 0.61±0.07 0.01±0.01 0.32±0.09 RORPO 0.90±0.02 0.97±0.01 0.20±0.06 0.41±0.09 0.02±0.01 0.80±0.06 Sato 0.89±0.03 0.97±0.02 0.24±0.10 0.46±0.17 0.03±0.01 0.75±0.10 Numerical results with MRI for Couinaud representation Sketon-based metric (first branches) Overlap rate M0 and mean distance Md Hepatic vein M0 (%) Md (mm) Ours 95.46 8 RORPO 55.57 33 Portal vein M0 (%) Md (mm) Ours 100.0 7 RORPO 72.17 33 Antoine Vacavant 48 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 49 / 55
MM & DG for the liver / Robustness with shape variability for liver segmentation Novel measurement of robustness Based on a more general input uncertainty model Y Y0 δY Suppose we can measure difference between uncertain data vs. perfect ideal data Can be applied to classic additive Gaussian model Antoine Vacavant 50 / 55
MM & DG for the liver / Robustness with shape variability for liver segmentation Novel measurement of robustness Based on a more general input uncertainty model Y Y0 δY Suppose we can measure difference between uncertain data vs. perfect ideal data Can be applied to classic additive Gaussian model We study here complex shape variability Liver volume segmentation We measure the variability of liver data (IRCAD + SLIVER07 datasets) Construct a bounding box (BB) with standard dimensions of the liver Measure the variability of a given binary image by σ #(L BB) #(L) × 100 With L: set of pixels belonging to the liver in the binary segmentation Antoine Vacavant 50 / 55
MM & DG for the liver / Robustness with shape variability for liver segmentation Evaluation of robustness for liver segmentation We compare our model-based method (MultiVarSeg) with SmartPaint Natural extension of our definition of robustness We also keep the scale of uncertainty (σ) where α value is reached M.-A. Lebre, A. Vacavant, M.-A. Lebre, H. Rositi, M. Grand-Brochier, R. Strand: New Definition of Image Processing Robustness with Generalized Uncertainty Modeling, Applied to Denoising and Segmentation. Guest paper submitted to IEEE RRPR@ICPR 2018, Beijing, China Antoine Vacavant 51 / 55
MM & DG for the liver / Robustness with shape variability for liver segmentation Evaluation of robustness for liver segmentation We compare our model-based method (MultiVarSeg) with SmartPaint Natural extension of our definition of robustness We also keep the scale of uncertainty (σ) where α value is reached 0 2 4 6 8 Variability scale 75 80 85 90 95 Dice MultiVarSeg SmartPaint Algorithm (α, σ) MultiVarSeg (19.4,5.49) SmartPaint (38.9,4.71) M.-A. Lebre, A. Vacavant, M.-A. Lebre, H. Rositi, M. Grand-Brochier, R. Strand: New Definition of Image Processing Robustness with Generalized Uncertainty Modeling, Applied to Denoising and Segmentation. Guest paper submitted to IEEE RRPR@ICPR 2018, Beijing, China Antoine Vacavant 51 / 55
Outline 1. Me in one slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 52 / 55
Conclusion, future works As a summary Original contributions w/ other (young) researchers & MDs Different (multi-scale) approaches for image analysis Image enhancement and denoising employing mathematical morphology Tools from digital geometry / topology for representing graphical objects Machine learning and numerical simulation: important topics for computer-aided liver cancer diagnosis Antoine Vacavant 53 / 55
Conclusion, future works As a summary Original contributions w/ other (young) researchers & MDs Different (multi-scale) approaches for image analysis Image enhancement and denoising employing mathematical morphology Tools from digital geometry / topology for representing graphical objects Machine learning and numerical simulation: important topics for computer-aided liver cancer diagnosis Robustness Original & foundational definitions for image processing algorithms With 2 main applications: image denoising and liver segmentation Related to benchmarking and big data issues Antoine Vacavant 53 / 55
Conclusion, future works R-VESSEL-X project ANR Project 2019-2022 (42 months) Robust vascular network extraction and understanding within hepatic biomedical images Segment liver vessels from MRI volumes Extend vessels by machine learning from Human CT data Animal µ-MRI/synchrotron registration Validation by numerical simulation of hepatic perfusion Antoine Vacavant 54 / 55
The end... Questions? Antoine Vacavant 55 / 55

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Robust image processing algorithms, involving tools from digital geometry and mathematical morphology

  • 1.
    ROBUST IMAGE PROCESSINGALGORITHMS, INVOLVING TOOLS FROM DIGITAL GEOMETRY AND MATHEMATICAL MORPHOLOGY CBA SEMINAR 2018 ANTOINE VACAVANT, PHD, HDR, ASSOCIATE PROFESSOR INSTITUT PASCAL, UMR6602 UCA / SIGMA / CNRS, LE PUY-EN-VELAY www.linkedin.com/in/antoinevacavant twitter.com/antoinevacavant antoine.vacavant@uca.fr antoine-vacavant.eu
  • 2.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 1 / 55
  • 3.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 2 / 55
  • 4.
    Me in oneslide / Université Clermont Auvergne 2010 - now: Associate prof. in computer science, Institut Pascal, IUT Le Puy-en-Velay Researches in IGT / Image Guided Therapies 2010 - 2015: Head of bachelor degree in computer graphics 2017 - now: Responsible of tech transfer in IGT 2017 - now: Scientific head of Embolization research team Computer vision Image processing Spatial data structures Digital geometry Medical appli- cations Antoine Vacavant 3 / 55
  • 5.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 4 / 55
  • 6.
    Introduction / Image processingin a nutshell Image processing is a central task for computer image analysis For various contexts: Remote satellite image interpretation Biomedical imagery Surveillance and security, etc. Followed by high-level interpretation Methodological contributions: Image processing Medical applications: Computer vision Sensor Input: Acquisition, sampling, quantification Pre-processing: enhancement, denoising, etc. Processing: segmenta- tion, feature extraction, etc. Machine learning: classification, recognition, etc. User decision Antoine Vacavant 5 / 55
  • 7.
    Introduction / Image processingin a nutshell Image processing is a central task for computer image analysis For various contexts: Remote satellite image interpretation Biomedical imagery Surveillance and security, etc. Followed by high-level interpretation Methodological contributions: Image processing Medical applications: Computer visionMedical applications with Computer vision Sensor Input: Acquisition, sampling, quantification Pre-processing: enhancement, denoising, etc. Processing: segmenta- tion, feature extraction, etc. Machine learning: classification, recognition, etc. User decision Antoine Vacavant 5 / 55
  • 8.
    Introduction / Image processingin a nutshell Image processing is a central task for computer image analysis For various contexts: Remote satellite image interpretation Biomedical imagery Surveillance and security, etc. Followed by high-level interpretation Methodological contributions: Image processing Medical applications: Computer vision Methodological contributions in Image processing Medical applications with Computer vision Sensor Input: Acquisition, sampling, quantification Pre-processing: enhancement, denoising, etc. Processing: segmenta- tion, feature extraction, etc. Machine learning: classification, recognition, etc. User decision Antoine Vacavant 5 / 55
  • 9.
    Introduction / Image processingin a nutshell Image processing is a central task for computer image analysis For various contexts: Remote satellite image interpretation Biomedical imagery Surveillance and security, etc. Followed by high-level interpretation Problem revealed by experience in image processing Methodological contributions: Image processing Medical applications: Computer vision Methodological contributions in Image processing Novel definition of Robustness Sensor Input: Acquisition, sampling, quantification Pre-processing: enhancement, denoising, etc. Processing: segmenta- tion, feature extraction, etc. Machine learning: classification, recognition, etc. User decision Antoine Vacavant 5 / 55
  • 10.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 6 / 55
  • 11.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 7 / 55
  • 12.
    Definition of robustness/ Noise and robustness Image processing (IP), noise Common issue in IP: uncontrolled and destructive perturbation of the image Coming from diverse sources Artefacts in medical images Videos jittered by the camera, etc. Antoine Vacavant 8 / 55
  • 13.
    Definition of robustness/ Noise and robustness Image processing (IP), noise Common issue in IP: uncontrolled and destructive perturbation of the image Coming from diverse sources Artefacts in medical images Videos jittered by the camera, etc. Designed as noise Antoine Vacavant 8 / 55
  • 14.
    Definition of robustness/ Noise and robustness Image processing (IP), noise Common issue in IP: uncontrolled and destructive perturbation of the image Coming from diverse sources Artefacts in medical images Videos jittered by the camera, etc. Designed as noise Robustness Is seen as the ability of an algorithm to resist to this noise Ensures that the developed algorithm satisfies the final user of the application Antoine Vacavant 8 / 55
  • 15.
    Definition of robustness/ Noise and robustness Image processing (IP), noise Common issue in IP: uncontrolled and destructive perturbation of the image Coming from diverse sources Artefacts in medical images Videos jittered by the camera, etc. Designed as noise Robustness Is seen as the ability of an algorithm to resist to this noise Ensures that the developed algorithm satisfies the final user of the application But is mixed up with terms as efficiency, quality, performance Without any formal definition for image processing Antoine Vacavant 8 / 55
  • 16.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 9 / 55
  • 17.
    Definition of robustness/ Robustness for image processing Contribution Propose a definition of robustness for IP algorithms In parallel of what has been done in CV Antoine Vacavant 10 / 55
  • 18.
    Definition of robustness/ Robustness for image processing Contribution Propose a definition of robustness for IP algorithms In parallel of what has been done in CV Presented at CBA in 2016 Antoine Vacavant 10 / 55
  • 19.
    Definition of robustness/ Robustness for image processing Contribution Propose a definition of robustness for IP algorithms In parallel of what has been done in CV Presented at CBA in 2016 Input noise model We suppose that the input data is altered with an additive noise, with similar notations as [Meer, 2001] yi y0 i + δyi , yi ∈ Rq , i 1, . . . , n also shortened as Y Y0 + δY Antoine Vacavant 10 / 55
  • 20.
    Definition of robustness/ Robustness for image processing Contribution Propose a definition of robustness for IP algorithms In parallel of what has been done in CV Presented at CBA in 2016 Input noise model We suppose that the input data is altered with an additive noise, with similar notations as [Meer, 2001] yi y0 i + δyi , yi ∈ Rq , i 1, . . . , n also shortened as Y Y0 + δY With Y: measurements Y0: true (and generally unknown) value δY: corruption by the noise We can suppose wlog an iid noise as δyi GI(0, σ2Cy)Antoine Vacavant 10 / 55
  • 21.
    Definition of robustness/ Robustness for image processing Robustness model for IP Robustness should be measured with multiple scales of noise Study limitations of an algorithm, how to make it fail Antoine Vacavant 11 / 55
  • 22.
    Definition of robustness/ Robustness for image processing Robustness model for IP Robustness should be measured with multiple scales of noise Study limitations of an algorithm, how to make it fail Definition of robustness for IP A: algorithm designed for a given IP application X {xi }i 1,n: output of A N: additive noise specific to this application {σk }k 1,m: set of scales of N Q(Xk, Y0 k ): measure of the quality of A for the scale k of N A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 11 / 55
  • 23.
    Definition of robustness/ Robustness for image processing Robustness model for IP Robustness should be measured with multiple scales of noise Study limitations of an algorithm, how to make it fail Definition of robustness for IP A: algorithm designed for a given IP application X {xi }i 1,n: output of A N: additive noise specific to this application {σk }k 1,m: set of scales of N Q(Xk, Y0 k ): measure of the quality of A for the scale k of N A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 11 / 55
  • 24.
    Definition of robustness/ Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
  • 25.
    Definition of robustness/ Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
  • 26.
    Definition of robustness/ Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
  • 27.
    Definition of robustness/ Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
  • 28.
    Definition of robustness/ Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
  • 29.
    Definition of robustness/ Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
  • 30.
    Definition of robustness/ Robustness for image processing Synthetic example 1st way to assess robustness: graphically Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
  • 31.
    Definition of robustness/ Robustness for image processing Synthetic example 1st way to assess robustness: graphically 2nd way to assess robustness: numerically Algorithm 1: α 0.30 Algorithm 2: α 0.18 Algorithm 3: α 0.05 Algorithm 4: α 0.02 Definition of robustness for IP A is robust if Q respects a Lipschitz continuity under α: dY Q(Xk, Y0 k ), Q(Xk+1, Y0 k+1 ) ≤ αdX(σk+1 − σk), 1 ≤ k ≤ m A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 12 / 55
  • 32.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 13 / 55
  • 33.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 14 / 55
  • 34.
    MM / Contextand motivation Image denoising filtering A lot of contributions since 70’s [Lebrun et al., 2012] Linear, popular, simple filters: Gaussian, average, median, bilateral, etc. Non-local strategies: NL-means, BM3D, total variation, etc. PDE schemes: anisotropic diffusion, coherence, etc. Antoine Vacavant 15 / 55
  • 35.
    MM / Contextand motivation Image denoising filtering A lot of contributions since 70’s [Lebrun et al., 2012] Linear, popular, simple filters: Gaussian, average, median, bilateral, etc. Non-local strategies: NL-means, BM3D, total variation, etc. PDE schemes: anisotropic diffusion, coherence, etc. Shock filtering Shock filter iteratively produces local segmentations in inflection zones: ∆ f t−1(pi , qj) < 0 ⇒ f t(pi , qj) f t−1(pi , qj) ⊕ D ; ∆ f t−1(pi , qj) > 0 ⇒ f t(pi , qj) f t−1(pi , qj) D Antoine Vacavant 15 / 55
  • 36.
    MM / Contextand motivation Image denoising filtering A lot of contributions since 70’s [Lebrun et al., 2012] Linear, popular, simple filters: Gaussian, average, median, bilateral, etc. Non-local strategies: NL-means, BM3D, total variation, etc. PDE schemes: anisotropic diffusion, coherence, etc. Shock filtering Shock filter iteratively produces local segmentations in inflection zones: ∆ f t−1(pi , qj) < 0 ⇒ f t(pi , qj) f t−1(pi , qj) ⊕ D ; ∆ f t−1(pi , qj) > 0 ⇒ f t(pi , qj) f t−1(pi , qj) D Smoothed shock filtering Enhance contours by creating smoothed ruptures PDE scheme with smoothed ⊕, operators A. Vacavant, A. Albouy-Kissi, P.-Y. Menguy, J. Solomon: Fast smoothed shock filtering. In IEEE ICPR 2012, Tsukuba, Japan, 2012. Antoine Vacavant 15 / 55
  • 37.
    MM / Contextand motivation Smoothed shock filtering examples Results with a photo and a complete CT slice Different values of ρ parameter (impact of shock) Algorithm iterated 10, 20, 30 times (PDE) Result of a simple segmentation algorithm afterwards Antoine Vacavant 16 / 55
  • 38.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 17 / 55
  • 39.
    MM / Testof robustness Material and methods 13 classic images / Y0 Altered with additive white Gaussian noise / Y With increasing std / scales {σk }k 1,5 {5, 10, 15, 20, 25} Antoine Vacavant 18 / 55
  • 40.
    MM / Testof robustness Material and methods 13 classic images / Y0 Altered with additive white Gaussian noise / Y With increasing std / scales {σk }k 1,5 {5, 10, 15, 20, 25} From state of the art Shock-based methods Classic algorithms Median-based methods Algorithm Reference Median [Huang et al., 1979] Coherence [Weickert, 2003] OriginalShock [Osher and Rudin, 1990] EnhancedShock [Alvarez and Mazorra, 1994] ComplexShock [Gilboa et al., 2004] Bilateral [Tomasi and Manduchi, 1998] SmoothedMedian [Kass and Solomon, 2010] SmoothedShock [Vacavant et al., 2012] Antoine Vacavant 18 / 55
  • 41.
    MM / Testof robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
  • 42.
    MM / Testof robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
  • 43.
    MM / Testof robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
  • 44.
    MM / Testof robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
  • 45.
    MM / Testof robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
  • 46.
    MM / Testof robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
  • 47.
    MM / Testof robustness Experimental results Quality measure: SSIM / Structural similarity [Wang et al., 2004] Graphical evaluation of robustness Numerical evaluation of robustness Algorithm α Median 0.15 Coherence 0.15 OriginalShock 0.14 EnhancedShock 0.14 ComplexShock 0.12 Bilateral 0.11 SmoothedMedian 0.05 SmoothedShock 0.04 A. Vacavant: A novel definition of robustness for image processing algorithms. In IEEE RRPR@ICPR 2016, LNCS 10214, pages 75–87, Cancún, Mexico, 2016. Antoine Vacavant 19 / 55
  • 48.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 20 / 55
  • 49.
    MM / Improvementof machine learning tasks Texture recognition We have proposed to improve texture classification by a scale-space approach For a given dataset: Brodatz, Vistex, Usptex or Outex Select a feature: LBP, GLCM, GLDM, SFTA, CLBP or LBPV Select a classifier: KNN or Naive Bayes Determine the best scales to be used in improving the classification rates Same is done for 2 other filters: Anisotropic diffusion (PM) and Gaussian filtering (G) M.B. Neiva, A. Vacavant, O.M. Bruno: Improving Texture Extraction and Classification using Smoothed Morphological Operators. Digital signal processing, 2018. Antoine Vacavant 21 / 55
  • 50.
    MM / Improvementof machine learning tasks Evaluation of accuracy for all datasets With KNN Dataset Best rate (feat.) Best SSF (feat.) Iterations Best G (feat.) Iterations Best PM (feat.) Iterations Outex 75.59 (LBPV) 84.78 (GLDM) {2, 4 . . . 18} 83.01 (CLBP) {9} 82.94 (CLBP) {19} Brodatz 97.6 (CLBP) 98.11 (CLBP) {6} 97.20 (CLBP) {2} 97.84 (CLBP) {11, 14} Usptex 83.1 (CLBP) 88.66 (CLBP) {1, 8} 85.21 (CLBP) {1} 88.57 (CLBP) {1, 3 . . . 17} Vistex 98.96 (CLBP) 99.31 (CLBP) {2} 98.96 (CLBP) {2, 3} 99.54 (CLBP) {14} With Naive Bayes Dataset Best rate (feat.) Best SSF (feat.) Iterations Best G (feat.) Iterations Best PM (feat.) Iterations Outex 80.81 (LBP) 86.47 (LBP) {2, 7 . . . 17} 83.01 (LBP) {8} 85.15 (CLBP) {4} Brodatz 96.6 (CLBP) 98.02 (CLBP) {2} 96.85 (CLBP) {1} 97.47 (CLBP) {15} Usptex 85.77 (CLBP) 91.49 (CLBP) {1, 3, 5} 86.43 (CLBP) {1, 3} 89.66 (CLBP) {8, 11 . . . 20} Vistex 97.33 (CLBP) 98.50 (CLBP) {2, 3} 98.50 (CLBP) {1, 3, 5} 97.92 (CLBP) {1, 8} Antoine Vacavant 22 / 55
  • 51.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 23 / 55
  • 52.
    MM / Discussion Smoothedshock filtering Original contribution: robust image denoising algorithm Approved by applying definition of robustness Antoine Vacavant 24 / 55
  • 53.
    MM / Discussion Smoothedshock filtering Original contribution: robust image denoising algorithm Approved by applying definition of robustness Several parameters modulate algorithm’s behavior Shock impact Number of iterations Improves segmentation and machine learning tasks (e.g. fMRI classification) Antoine Vacavant 24 / 55
  • 54.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 25 / 55
  • 55.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 26 / 55
  • 56.
    DG / Contextand motivation Notion of Reeb graph Reeb graph is discrete structure representing both geometry and topology of an object Edges: object’s branches Vertices: branches’ junctions Calculated on a compact manifold wrt. definition of a given h function Note Critical points of h are graph vertices Definition of h is important for a correct graph construction Antoine Vacavant 27 / 55
  • 57.
    DG / Contextand motivation Reeb graphs in literature A lot of attention on its construction for 3-D meshes [Biasotti et al., 2008; Harvey et al., 2010] Generally, h is a height function (along an axis) Appropriate for many objects, but not for all! Can be calculated with other functions (e.g. geodesic) [Tierny, 2006] Antoine Vacavant 28 / 55
  • 58.
    DG / Contextand motivation Reeb graphs in literature A lot of attention on its construction for 3-D meshes [Biasotti et al., 2008; Harvey et al., 2010] Generally, h is a height function (along an axis) Appropriate for many objects, but not for all! Can be calculated with other functions (e.g. geodesic) [Tierny, 2006] Skeletons, medial axes and other 1-pixel-wide centered structures capture topology [Arcelli et al., 2010; Bertrand et al., 2014] Strategy: Compute Reeb graph from such structures [Janusch et al., 2015; Pascucci et al., 2007] Antoine Vacavant 28 / 55
  • 59.
    DG / Contextand motivation Reeb graphs in literature A lot of attention on its construction for 3-D meshes [Biasotti et al., 2008; Harvey et al., 2010] Generally, h is a height function (along an axis) Appropriate for many objects, but not for all! Can be calculated with other functions (e.g. geodesic) [Tierny, 2006] Skeletons, medial axes and other 1-pixel-wide centered structures capture topology [Arcelli et al., 2010; Bertrand et al., 2014] Strategy: Compute Reeb graph from such structures [Janusch et al., 2015; Pascucci et al., 2007] But they can be very sensitive to noise! Linking them to Reeb graph is not trivial Antoine Vacavant 28 / 55
  • 60.
    DG / Contextand motivation Our contribution Compute Reeb graphs of 2-D binary shapes Use a robust skeletonization scheme Capable of using several h functions Applications in robust image analysis A. Vacavant, A. Leborgne: Robust computations of reeb graphs in 2-D binary images. In CTIC 2016, LNCS 9667, pages 204–215, Marseille, France, 2016. Antoine Vacavant 29 / 55
  • 61.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 30 / 55
  • 62.
    DG / Reebgraph computations by skeleton extraction DECS algorithm DECS: Discrete Euclidean Connected Skeleton [Leborgne et al., 2015] Resist to noise, compared to other algorithms Antoine Vacavant 31 / 55
  • 63.
    DG / Reebgraph computations by skeleton extraction DECS algorithm DECS: Discrete Euclidean Connected Skeleton [Leborgne et al., 2015] Resist to noise, compared to other algorithms Algorithm: From a binary image I Euclidean distance map EDTI Reduced medial axis RDMAI Laplacian-of-Gaussian filtering of EDTI as RDGI Combine RDGI and RDMAI to calculate a coarse skeleton SI Thin and prune SI to obtain S∗ I EDTI RDMAI RDGI SI S∗ I Antoine Vacavant 31 / 55
  • 64.
    DG / Reebgraph computations by skeleton extraction The definition Definition (Reeb graph) Let h be a continuous function defined on a compact variety M, h : M → R. The Reeb graph of M, denoted by G(h), is the quotient space defined by the equivalence relation p ∼ q ⇔ (p, h(p)) ∼ (q, h(q)) s.t.: h(p) h(q), p, q belongs to the same connected component of h−1(h(p)). Antoine Vacavant 32 / 55
  • 65.
    DG / Reebgraph computations by skeleton extraction Properties of Reeb graph G(h) is constructed by a level-sets approach wrt. h Points in the same con. component are associated to a level of h Reeb graph brings together topology and geometry (h defined on M) Key items G(h) is constructed by a level-sets approach wrt. h Antoine Vacavant 33 / 55
  • 66.
    DG / Reebgraph computations by skeleton extraction Properties of Reeb graph G(h) (V, E) represents M through h Edges: object’s branches (points belonging to the same con. component) Vertices: Critical points of h: begin, end, merge, split Key items G(h) is constructed by a level-sets approach wrt. h G(h) represents M through h Antoine Vacavant 33 / 55
  • 67.
    DG / Reebgraph computations by skeleton extraction Properties of Reeb graph Discrete G(h) (V, E) is built by an iterative process All notions hold in the discrete case Finite number of h level-sets Key items G(h) is constructed by a level-sets approach wrt. h G(h) represents M through h Discrete G(h) is built by an iterative process Antoine Vacavant 33 / 55
  • 68.
    DG / Reebgraph computations by skeleton extraction Properties of Reeb graph Key items G(h) is constructed by a level-sets approach wrt. h G(h) represents M through h Discrete G(h) is built by an iterative process Use DECS to build Reeb graphs of binary object Antoine Vacavant 33 / 55
  • 69.
    DG / Reebgraph computations by skeleton extraction Our algorithm From a binary image I, compute DECS S∗ I , select a starting point pS in S∗ I Breadth-first construction of GI(h) by adding points of S∗ I Increase level-set by assigning increasing h values to points treated Antoine Vacavant 34 / 55
  • 70.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 35 / 55
  • 71.
    DG / Experimentalevaluation Reeb graph obtained for noisy vascular image Antoine Vacavant 36 / 55
  • 72.
    DG / Experimentalevaluation With synthetic images nit 0 nit 1 Antoine Vacavant 37 / 55
  • 73.
    DG / Experimentalevaluation With synthetic images nit 0 nit 5 Antoine Vacavant 37 / 55
  • 74.
    DG / Experimentalevaluation With synthetic images nit 0 nit 50 Antoine Vacavant 37 / 55
  • 75.
    DG / Experimentalevaluation With synthetic images nit 0 nit 100 Antoine Vacavant 37 / 55
  • 76.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 38 / 55
  • 77.
    DG / Discussion Reebgraphs of noisy binary shapes Possibility to choose a relevant h function h may be chosen for further pattern recognition issues (descriptor encoding) Robustness may be assessed by means of our formalism Antoine Vacavant 39 / 55
  • 78.
    DG / Discussion Reebgraphs of noisy binary shapes Possibility to choose a relevant h function h may be chosen for further pattern recognition issues (descriptor encoding) Robustness may be assessed by means of our formalism Other works Irregular isothetic grids for vectorization Quadtree complexity theorem Vectorization of grayscale images A. Vacavant, B. Kerautret, T. Roussillon, F. Feschet: Reconstructions of noisy digital contours with maximal primitives based on multi-scale/irregular geometric representation and generalized linear programming. In DGCI 2017, LNCS 10502, pages 291–303, Vienna, Austria, 2017. Y. Gerard, A. Vacavant, J.-M. Favreau: Tight bounds in the quadtree complexity theorem and the maximal number of pixels crossed by a curve of given length. Theoretical Computer Science, 624:41–55, 2016. B. Kerautret, P. Ngo, Y. Kenmochi, A. Vacavant: Greyscale image vectorization from geometric digital contour representations. In DGCI 2017, LNCS 10502, pages 319–331, Vienne, Autriche, 2017. Antoine Vacavant 39 / 55
  • 79.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 40 / 55
  • 80.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 41 / 55
  • 81.
    MM & DGfor the liver / Context and motivation Our research group Inside IGT research axis CaVITI (Cardio-Vascular Interventional Therapy and Imaging) 3 research groups Theme 1: Endoprothesis Theme 2: Embolization Theme 3: Myocardial function Antoine Vacavant 42 / 55
  • 82.
    MM & DGfor the liver / Context and motivation Our research group Inside IGT research axis CaVITI (Cardio-Vascular Interventional Therapy and Imaging) 3 research groups Theme 1: Endoprothesis Theme 2: Embolization Theme 3: Myocardial function Research targets Quantitatively assess hepatic tumoral response by medical image analysis Innovative tools devoted to tumoral tissue quantification Personalized numerical simulation of treatments Link with clinical activities: chemo-embolization, surgery, biopsy, etc. Target cancer: HCC (Hepato-Cellular Carcinoma) Antoine Vacavant 42 / 55
  • 83.
    MM & DGfor the liver / Context and motivation Our research group Inside IGT research axis CaVITI (Cardio-Vascular Interventional Therapy and Imaging) 3 research groups Theme 1: Endoprothesis Theme 2: Embolization Theme 3: Myocardial function Research targets Quantitatively assess hepatic tumoral response by medical image analysis Innovative tools devoted to tumoral tissue quantification Personalized numerical simulation of treatments Link with clinical activities: chemo-embolization, surgery, biopsy, etc. Target cancer: HCC (Hepato-Cellular Carcinoma) More details tomor- row at CoSy seminar! Antoine Vacavant 42 / 55
  • 84.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 43 / 55
  • 85.
    MM & DGfor the liver / HCC segmentation Segmentation of HCC within MRI ROI Enhance patches by smoothed shock filtering Segmentation by a fuzzy approach Input MRI ROI SSF Output Segmentation by fuzzification/defuzzification First calculate a fuzzy clustering by FCMVC (with variable compactness) JFCMVC n j 1 c i 1 ˆµij(xj − vi)2pi , ˆµij (xj − vi)−2pi c i 1 (xj − vi)−2pi Then calculate a binary segmentation by sequential feature selection Including geometrical and fuzzy features Antoine Vacavant 44 / 55
  • 86.
    MM & DGfor the liver / HCC segmentation Some segmentation results Our approach also compared with methods from state-of-the-art Positive impact of smoothed shock filter ROI SSF GT Output A. Vacavant, A.-R. Ali, M. Grand-Brochier, A. Albouy-Kissi, J.-Y. Boire, A. Alfidja et P. Chabrot: Smoothed shock filtered defuzzification with Zernike moments for liver tumor extraction in MR images. In IEEE IPTA 2015, Orléans, France, Nov. 2015. Antoine Vacavant 45 / 55
  • 87.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 46 / 55
  • 88.
    MM & DGfor the liver / Hepatic vascular network segmentation Our pipeline for segmenting liver vessels From a CT or MRI volume, I Extract the liver and use it as a bounding box Multi-scale vessel detection with Hessian matrix IS [Sato et al., 1994] Partial skeletonization and reconnection S in IS [Homann et al., 2007] Calculate the RORPO vesselness filter IR [Merveille et al., 2018] Use S as initialization for fast marching segmentation within IR M.-A. Lebre, A. Vacavant, M. Grand-Brochier, O. Merveille, A. Abergel, P. Chabrot, B. Magnin: Automatic 3-D Skeleton-based Segmentation of Liver Vessels From MRI and CT for Couinaud Representation. In IEEE ICIP 2018, Athens, Greece, Antoine Vacavant 47 / 55
  • 89.
    MM & DGfor the liver / Hepatic vascular network segmentation Numerical results with IRCAD dataset (CT) ACC SPE SEN PRE FPR FNR Ours 0.97±0.01 0.98±0.01 0.69±0.10 0.61±0.07 0.01±0.01 0.32±0.09 RORPO 0.90±0.02 0.97±0.01 0.20±0.06 0.41±0.09 0.02±0.01 0.80±0.06 Sato 0.89±0.03 0.97±0.02 0.24±0.10 0.46±0.17 0.03±0.01 0.75±0.10 Numerical results with MRI for Couinaud representation Sketon-based metric (first branches) Overlap rate M0 and mean distance Md Hepatic vein M0 (%) Md (mm) Ours 95.46 8 RORPO 55.57 33 Portal vein M0 (%) Md (mm) Ours 100.0 7 RORPO 72.17 33 Antoine Vacavant 48 / 55
  • 90.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 49 / 55
  • 91.
    MM & DGfor the liver / Robustness with shape variability for liver segmentation Novel measurement of robustness Based on a more general input uncertainty model Y Y0 δY Suppose we can measure difference between uncertain data vs. perfect ideal data Can be applied to classic additive Gaussian model Antoine Vacavant 50 / 55
  • 92.
    MM & DGfor the liver / Robustness with shape variability for liver segmentation Novel measurement of robustness Based on a more general input uncertainty model Y Y0 δY Suppose we can measure difference between uncertain data vs. perfect ideal data Can be applied to classic additive Gaussian model We study here complex shape variability Liver volume segmentation We measure the variability of liver data (IRCAD + SLIVER07 datasets) Construct a bounding box (BB) with standard dimensions of the liver Measure the variability of a given binary image by σ #(L BB) #(L) × 100 With L: set of pixels belonging to the liver in the binary segmentation Antoine Vacavant 50 / 55
  • 93.
    MM & DGfor the liver / Robustness with shape variability for liver segmentation Evaluation of robustness for liver segmentation We compare our model-based method (MultiVarSeg) with SmartPaint Natural extension of our definition of robustness We also keep the scale of uncertainty (σ) where α value is reached M.-A. Lebre, A. Vacavant, M.-A. Lebre, H. Rositi, M. Grand-Brochier, R. Strand: New Definition of Image Processing Robustness with Generalized Uncertainty Modeling, Applied to Denoising and Segmentation. Guest paper submitted to IEEE RRPR@ICPR 2018, Beijing, China Antoine Vacavant 51 / 55
  • 94.
    MM & DGfor the liver / Robustness with shape variability for liver segmentation Evaluation of robustness for liver segmentation We compare our model-based method (MultiVarSeg) with SmartPaint Natural extension of our definition of robustness We also keep the scale of uncertainty (σ) where α value is reached 0 2 4 6 8 Variability scale 75 80 85 90 95 Dice MultiVarSeg SmartPaint Algorithm (α, σ) MultiVarSeg (19.4,5.49) SmartPaint (38.9,4.71) M.-A. Lebre, A. Vacavant, M.-A. Lebre, H. Rositi, M. Grand-Brochier, R. Strand: New Definition of Image Processing Robustness with Generalized Uncertainty Modeling, Applied to Denoising and Segmentation. Guest paper submitted to IEEE RRPR@ICPR 2018, Beijing, China Antoine Vacavant 51 / 55
  • 95.
    Outline 1. Me inone slide 2. Introduction 3. Definition of robustness Noise and robustness Robustness for image processing 4. MM: Smoothed shock filtering Test of robustness Improvement of machine learning tasks Discussion 5. DG: Robust Reeb graph computations Reeb graph computations by skeleton extraction Experimental evaluation Discussion 6. MM & DG for biomedical image analysis HCC segmentation Hepatic vascular network segmentation Robustness with shape variability for liver segmentation 7. Conclusion, future works Antoine Vacavant 52 / 55
  • 96.
    Conclusion, future works Asa summary Original contributions w/ other (young) researchers & MDs Different (multi-scale) approaches for image analysis Image enhancement and denoising employing mathematical morphology Tools from digital geometry / topology for representing graphical objects Machine learning and numerical simulation: important topics for computer-aided liver cancer diagnosis Antoine Vacavant 53 / 55
  • 97.
    Conclusion, future works Asa summary Original contributions w/ other (young) researchers & MDs Different (multi-scale) approaches for image analysis Image enhancement and denoising employing mathematical morphology Tools from digital geometry / topology for representing graphical objects Machine learning and numerical simulation: important topics for computer-aided liver cancer diagnosis Robustness Original & foundational definitions for image processing algorithms With 2 main applications: image denoising and liver segmentation Related to benchmarking and big data issues Antoine Vacavant 53 / 55
  • 98.
    Conclusion, future works R-VESSEL-Xproject ANR Project 2019-2022 (42 months) Robust vascular network extraction and understanding within hepatic biomedical images Segment liver vessels from MRI volumes Extend vessels by machine learning from Human CT data Animal µ-MRI/synchrotron registration Validation by numerical simulation of hepatic perfusion Antoine Vacavant 54 / 55
  • 99.