The document discusses local and non-metric similarities between images. It outlines that local similarities are needed to compare images and detect small differences. The document proposes using a local dissimilarity map (LDM) approach to quantify local differences between images. The LDM approach involves calculating a distance measure, such as the Hausdorff distance, within a sliding window over the images to identify localized regions of difference. This localized comparison approach could be useful for applications like analyzing ancient printings.
nternational Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Presented at SIGGRAPH 2004 in Los Angeles on Tuesday, August 10th during the "Real-Time Shadowing Techniques" course. Jan Kautz and Marc Stamminger organized the course. The presentation covers robust shadow volume rendering techniques for GPUs.
nternational Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Presented at SIGGRAPH 2004 in Los Angeles on Tuesday, August 10th during the "Real-Time Shadowing Techniques" course. Jan Kautz and Marc Stamminger organized the course. The presentation covers robust shadow volume rendering techniques for GPUs.
The objective of this work is to propose an image
denoising technique and compare it with image denoising
using ridgelets. The proposed method uses slantlet transform
instead of wavelets in ridgelet transform. Experimental result
shows that the proposed method is more effective than ridgelets
in noise removal. The proposed method is effective in
compressing images while preserving edges.
A DIGITAL COLOR IMAGE WATERMARKING SYSTEM USING BLIND SOURCE SEPARATIONcsandit
An attempt is made to implement a digital color image-adaptive watermarking scheme in
spatial domain and hybrid domain i.e host image in wavelet domain and watermark in spatial
domain. Blind Source Separation (BSS) is used to extract the watermark The novelty of the
presented scheme lies in determining the mixing matrix for BSS model using BFGS (Broyden–
Fletcher–Goldfarb–Shanno) optimization technique. This method is based on the smooth and
textured portions of the image. Texture analysis is carried based on energy content of the
image (using GLCM) which makes the method image adaptive to embed color watermark.
The performance evaluation is carried for hybrid domain of various color spaces like YIQ, HSI
and YCbCr and the feasibility of optimization algorithm for finding mixing matrix is also
checked for these color spaces. Three ICA (Independent Component Analysis)/BSS algorithms
are used in extraction procedure ,through which the watermark can be retrieved efficiently . An
effort is taken to find out the best suited color space to embed the watermark which satisfies the
condition of imperceptibility and robustness against various attacks.
DeepLab V3+: Encoder-Decoder with Atrous Separable Convolution for Semantic I...Joonhyung Lee
A presentation introducting DeepLab V3+, the state-of-the-art architecture for semantic segmentation. It also includes detailed descriptions of how 2D multi-channel convolutions function, as well as giving a detailed explanation of depth-wise separable convolutions.
This paper presents a new approach for the enhancement of Synthetic Radar Imagery using Discrete Wavelet Transform and its variants. Some of the approaches like nonlocal filtering (NLF) techniques, and multiscale iterative reconstruction (e.g., the BM3D method) do not solve the RE/SR imaging inverse problems in descriptive settings imposing some structured regularization constraints and exploits the sparsity of the desired image representations for resolution enhancement (RE) and superresolution (SR) of coherent remote sensing (RS). Such approaches are not properly adapted to the SR recovery of the speckle-corrupted low resolution (LR) coherent radar imagery. These pitfalls are eradicated by using DWT approach wherein the despeckled/deblurred HR image is recovered from the LR speckle/blurry corrupted radar image by applying some of the descriptive-experiment-design-regularization (DEDR) based re-constructive steps. Next, the multistage RE is consequently performed in each scaled refined SR frame via the iterative reconstruction of the upscaled radar images, followed by the discrete-wavelet-transform-based sparsity promoting denoising with guaranteed consistency preservation in each resolution frame. The performance of the method proposed is compared in terms of the number of iterations taken by it with other techniques existing in the literature.
Practical and Robust Stenciled Shadow Volumes for Hardware-Accelerated RenderingMark Kilgard
Twenty-five years ago, Crow published the shadow volume approach for determining shadowed regions in a scene. A decade ago, Heidmann described a hardware-accelerated stencil bufferbased shadow volume algorithm. However, hardware-accelerated stenciled shadow volume techniques have not been widely adopted by 3D games and applications due in large part to the lack of robustness of described techniques. This situation persists despite widely available hardware support. Specifically what has been lacking is a technique that robustly handles various "hard" situations created by near or far plane clipping of shadow volumes. We describe a robust, artifact-free technique for hardwareaccelerated rendering of stenciled shadow volumes. Assuming existing hardware, we resolve the issues otherwise caused by shadow volume near and far plane clipping through a combination of (1) placing the conventional far clip plane “at infinity”, (2) rasterization with infinite shadow volume polygons via homogeneous coordinates, and (3) adopting a zfail stencil-testing scheme. Depth clamping, a new rasterization feature provided by NVIDIA's GeForce3 & GeForce4 Ti GPUs, preserves existing depth precision by not requiring the far plane to be placed at infinity. We also propose two-sided stencil testing to improve the efficiency of rendering stenciled shadow volumes.
March 12, 2002.
This was submitted to the SIGGRAPH 2002 papers committee but was rejected.
Kernel Estimation of Videodeblurringalgorithm and Motion Compensation of Resi...IJERA Editor
This paper presents a videodeblurring algorithm utilizing the high resolution information of adjacent unblurredframes.First, two motion-compensated predictors of a blurred frame are derived from its neighboring unblurred frames via bidirectional motion compensation. Then, an accurate blur kernel, which is difficult to directly obtain from the blurred frame itself, is computed between the predictors and the blurred frame. Next, a residual deconvolution is employed to reduce the ringing artifacts inherently caused by conventional deconvolution. The blur kernel estimation and deconvolution processes are iteratively performed for the deblurred frame. Experimental results show that the proposed algorithm provides sharper details and smaller artifacts than the state-of-the-art algorithms.
A technical deep dive into the DX11 rendering in Battlefield 3, the first title to use the new Frostbite 2 Engine. Topics covered include DX11 optimization techniques, efficient deferred shading, high-quality rendering and resource streaming for creating large and highly-detailed dynamic environments on modern PCs.
Performance Analysis of Image Enhancement Using Dual-Tree Complex Wavelet Tra...IJERD Editor
Resolution enhancement (RE) schemes which are not based on wavelets has one of the major
drawbacks of losing high frequency contents which results in blurring. The discrete wavelet- transform-based
(DWT) Resolution Enhancement scheme generates artifacts (due to a DWT shift-variant property). A wavelet-
Domain approach based on dual-tree complex wavelet transform (DT-CWT) & nonlocal means (NLM) is
proposed for RE of the satellite images. A satellite input image is decomposed by DT-CWT (which is nearly
shift invariant) to obtain high-frequency sub bands. Here the Lanczos interpolator is used to interpolate the highfrequency
sub bands & the low-resolution (LR) input image. The high frequency sub bands are passed through
an NLM filter to cater for the artifacts generated by DT-CWT (despite of it’s nearly shift invariance). The
filtered high-frequency sub bands and the LR input image are combined by using inverse DTCWT to obtain a
resolution-enhanced image. Objective and subjective analyses show superiority of the new proposed technique
over the conventional and state-of-the-art RE techniques.
The objective of this work is to propose an image
denoising technique and compare it with image denoising
using ridgelets. The proposed method uses slantlet transform
instead of wavelets in ridgelet transform. Experimental result
shows that the proposed method is more effective than ridgelets
in noise removal. The proposed method is effective in
compressing images while preserving edges.
A DIGITAL COLOR IMAGE WATERMARKING SYSTEM USING BLIND SOURCE SEPARATIONcsandit
An attempt is made to implement a digital color image-adaptive watermarking scheme in
spatial domain and hybrid domain i.e host image in wavelet domain and watermark in spatial
domain. Blind Source Separation (BSS) is used to extract the watermark The novelty of the
presented scheme lies in determining the mixing matrix for BSS model using BFGS (Broyden–
Fletcher–Goldfarb–Shanno) optimization technique. This method is based on the smooth and
textured portions of the image. Texture analysis is carried based on energy content of the
image (using GLCM) which makes the method image adaptive to embed color watermark.
The performance evaluation is carried for hybrid domain of various color spaces like YIQ, HSI
and YCbCr and the feasibility of optimization algorithm for finding mixing matrix is also
checked for these color spaces. Three ICA (Independent Component Analysis)/BSS algorithms
are used in extraction procedure ,through which the watermark can be retrieved efficiently . An
effort is taken to find out the best suited color space to embed the watermark which satisfies the
condition of imperceptibility and robustness against various attacks.
DeepLab V3+: Encoder-Decoder with Atrous Separable Convolution for Semantic I...Joonhyung Lee
A presentation introducting DeepLab V3+, the state-of-the-art architecture for semantic segmentation. It also includes detailed descriptions of how 2D multi-channel convolutions function, as well as giving a detailed explanation of depth-wise separable convolutions.
This paper presents a new approach for the enhancement of Synthetic Radar Imagery using Discrete Wavelet Transform and its variants. Some of the approaches like nonlocal filtering (NLF) techniques, and multiscale iterative reconstruction (e.g., the BM3D method) do not solve the RE/SR imaging inverse problems in descriptive settings imposing some structured regularization constraints and exploits the sparsity of the desired image representations for resolution enhancement (RE) and superresolution (SR) of coherent remote sensing (RS). Such approaches are not properly adapted to the SR recovery of the speckle-corrupted low resolution (LR) coherent radar imagery. These pitfalls are eradicated by using DWT approach wherein the despeckled/deblurred HR image is recovered from the LR speckle/blurry corrupted radar image by applying some of the descriptive-experiment-design-regularization (DEDR) based re-constructive steps. Next, the multistage RE is consequently performed in each scaled refined SR frame via the iterative reconstruction of the upscaled radar images, followed by the discrete-wavelet-transform-based sparsity promoting denoising with guaranteed consistency preservation in each resolution frame. The performance of the method proposed is compared in terms of the number of iterations taken by it with other techniques existing in the literature.
Practical and Robust Stenciled Shadow Volumes for Hardware-Accelerated RenderingMark Kilgard
Twenty-five years ago, Crow published the shadow volume approach for determining shadowed regions in a scene. A decade ago, Heidmann described a hardware-accelerated stencil bufferbased shadow volume algorithm. However, hardware-accelerated stenciled shadow volume techniques have not been widely adopted by 3D games and applications due in large part to the lack of robustness of described techniques. This situation persists despite widely available hardware support. Specifically what has been lacking is a technique that robustly handles various "hard" situations created by near or far plane clipping of shadow volumes. We describe a robust, artifact-free technique for hardwareaccelerated rendering of stenciled shadow volumes. Assuming existing hardware, we resolve the issues otherwise caused by shadow volume near and far plane clipping through a combination of (1) placing the conventional far clip plane “at infinity”, (2) rasterization with infinite shadow volume polygons via homogeneous coordinates, and (3) adopting a zfail stencil-testing scheme. Depth clamping, a new rasterization feature provided by NVIDIA's GeForce3 & GeForce4 Ti GPUs, preserves existing depth precision by not requiring the far plane to be placed at infinity. We also propose two-sided stencil testing to improve the efficiency of rendering stenciled shadow volumes.
March 12, 2002.
This was submitted to the SIGGRAPH 2002 papers committee but was rejected.
Kernel Estimation of Videodeblurringalgorithm and Motion Compensation of Resi...IJERA Editor
This paper presents a videodeblurring algorithm utilizing the high resolution information of adjacent unblurredframes.First, two motion-compensated predictors of a blurred frame are derived from its neighboring unblurred frames via bidirectional motion compensation. Then, an accurate blur kernel, which is difficult to directly obtain from the blurred frame itself, is computed between the predictors and the blurred frame. Next, a residual deconvolution is employed to reduce the ringing artifacts inherently caused by conventional deconvolution. The blur kernel estimation and deconvolution processes are iteratively performed for the deblurred frame. Experimental results show that the proposed algorithm provides sharper details and smaller artifacts than the state-of-the-art algorithms.
A technical deep dive into the DX11 rendering in Battlefield 3, the first title to use the new Frostbite 2 Engine. Topics covered include DX11 optimization techniques, efficient deferred shading, high-quality rendering and resource streaming for creating large and highly-detailed dynamic environments on modern PCs.
Performance Analysis of Image Enhancement Using Dual-Tree Complex Wavelet Tra...IJERD Editor
Resolution enhancement (RE) schemes which are not based on wavelets has one of the major
drawbacks of losing high frequency contents which results in blurring. The discrete wavelet- transform-based
(DWT) Resolution Enhancement scheme generates artifacts (due to a DWT shift-variant property). A wavelet-
Domain approach based on dual-tree complex wavelet transform (DT-CWT) & nonlocal means (NLM) is
proposed for RE of the satellite images. A satellite input image is decomposed by DT-CWT (which is nearly
shift invariant) to obtain high-frequency sub bands. Here the Lanczos interpolator is used to interpolate the highfrequency
sub bands & the low-resolution (LR) input image. The high frequency sub bands are passed through
an NLM filter to cater for the artifacts generated by DT-CWT (despite of it’s nearly shift invariance). The
filtered high-frequency sub bands and the LR input image are combined by using inverse DTCWT to obtain a
resolution-enhanced image. Objective and subjective analyses show superiority of the new proposed technique
over the conventional and state-of-the-art RE techniques.
SUITES ET SÉRIES NUMÉRIQUES
VARIATION DES SUITES
CONVERGENCE DES SÉRIES NUMÉRIQUES
SÉRIES DE FONCTIONS
SÉRIES ENTIÈRES
Développement en séries entières
Matrices, opérations élémentaires (addition, produit, transposition), déterminant, inverse, méthodes d'inversion, lien avec les systèmes d'équations linéaires, résolution des systèmes d'équations linéaires, système de Cramer
Séries de Fourier complexes, Transformées de Fourier, Spectres d’amplitude et de phases, Relation d’indéterminatoin d’Heisenberg-Gabor, Produit de convolution, Théorème de convolution, Impulsion de Dirac, Éléments sur les distributions
Ce cours est développé dans le cadre de la formation d'ingénieurs en génie des procédés et de l'environnement de la faculté des sciences et techniques de l'université Hassan II de Casablanca.
Je serai ravi d'échanger avec des collègues et étudiants pour son enrichissement.
1 introduction générale à l'automatique slideshareKheddioui
Ce cours est développé dans le cadre de la formation de la filière d'ingénieurs en génie des procédés et de l'environnement de la faculté des sciences et techniques de l'université Hassan II de Casablanca.
Je serai ravi d'échanger avec des collègues et étudiants pour son enrichissement.
Secrets of CryENGINE 3 Graphics TechnologyTiago Sousa
In this talk, the authors will describe an overview of a different method for deferred lighting approach used in CryENGINE 3, along with an in-depth description of the many techniques used. Original file and videos at http://crytek.com/cryengine/presentations
International Journal of Engineering Research and Development (IJERD)IJERD Editor
We would send hard copy of Journal by speed post to the address of correspondence author after online publication of paper.
We will dispatched hard copy to the author within 7 days of date of publication
This presentation is meant to discuss the basics of video compression like DCT, Color space conversion, Motion Compensation etc. It also discusses the standards like H.264, MPEG2, MPEG4 etc.
Similar to 2012.09.25 - Local and non-metric similarities between images - why, how and what for ? (20)
Maruthi Prithivirajan, Head of ASEAN & IN Solution Architecture, Neo4j
Get an inside look at the latest Neo4j innovations that enable relationship-driven intelligence at scale. Learn more about the newest cloud integrations and product enhancements that make Neo4j an essential choice for developers building apps with interconnected data and generative AI.
Dr. Sean Tan, Head of Data Science, Changi Airport Group
Discover how Changi Airport Group (CAG) leverages graph technologies and generative AI to revolutionize their search capabilities. This session delves into the unique search needs of CAG’s diverse passengers and customers, showcasing how graph data structures enhance the accuracy and relevance of AI-generated search results, mitigating the risk of “hallucinations” and improving the overall customer journey.
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
Generative AI Deep Dive: Advancing from Proof of Concept to ProductionAggregage
Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
Sudheer Mechineni, Head of Application Frameworks, Standard Chartered Bank
Discover how Standard Chartered Bank harnessed the power of Neo4j to transform complex data access challenges into a dynamic, scalable graph database solution. This keynote will cover their journey from initial adoption to deploying a fully automated, enterprise-grade causal cluster, highlighting key strategies for modelling organisational changes and ensuring robust disaster recovery. Learn how these innovations have not only enhanced Standard Chartered Bank’s data infrastructure but also positioned them as pioneers in the banking sector’s adoption of graph technology.
Pushing the limits of ePRTC: 100ns holdover for 100 daysAdtran
At WSTS 2024, Alon Stern explored the topic of parametric holdover and explained how recent research findings can be implemented in real-world PNT networks to achieve 100 nanoseconds of accuracy for up to 100 days.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
Challenges: The hurdles in monetizing open-source projects and measuring user engagement.
Development Practices: Best practices for creating, maintaining, and scaling open-source libraries, including code hygiene, CI/CD, and fast iteration.
Community Building: Strategies for making adoption easy, iterating quickly, and fostering a vibrant, engaged community.
Marketing: Both online and offline marketing tactics, focusing on real, impactful interactions and collaborations.
Mental Health: Maintaining balance and not feeling pressured by user demands.
Key insights include the importance of automation, making the adoption process seamless, and leveraging offline interactions for marketing. The presentation also emphasizes the need for continuous small improvements and building a friendly, inclusive community that contributes to the project's growth.
Vladimir Iglovikov brings his extensive experience as a Kaggle Grandmaster, ex-Staff ML Engineer at Lyft, sharing valuable lessons and practical advice for anyone looking to enhance the adoption of their open-source projects.
Explore more about Albumentations and join the community at:
GitHub: https://github.com/albumentations-team/albumentations
Website: https://albumentations.ai/
LinkedIn: https://www.linkedin.com/company/100504475
Twitter: https://x.com/albumentations
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024Neo4j
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
8. 3D Acquisition : An Example
ANALYSIS AND CONSERVATION OF ANCIENT WOODEN STAMPS
ANALYSIS AND CONSERVATION OF ANCIENT WOODEN STAMPS 115
7 Range image (‘Pisces’ stamp) computed from projec-
6 3D View of acquired points of ‘Pisces’ stamp: point tion of point cloud
cloud acquired with Minolta scanner
Else t5Mzk*s (M.m and the neigh-
a stamp, the printing zones are high elevation ones;
7 Range image (‘Pisces’ stamp) computed
bourhood is in a low zone)
6 3D View of acquired points of ‘Pisces’range imagespoint
the high grey-level pixels in the stamp: have to tion of point cloud
End if
be binarized as black (pixel50). The non-printing If pixel.t Then pixel50
cloud acquired with Minolta scanner
zones must therefore be binarized as white (pixel51). Else pixel51
Stamp 3D model Range Image
A modified Niblack’s algorithm is used to binarize End if Else t5Mzk*s (M.m an
range images.11,12 The main task is to adapt the End Do
a stamp, the printing zones are high elevation ones;
threshold over the image. The threshold is deter- bourhood is in a low zone
The local threshold computing can be summarized
the high grey-level pixels from the local meanimageslocal standard
mined in the range and the have to End if
by equation (1)
deviation, computed on a restricted neighbourhood t~max(M,m)zk às (1)
be binarized as blackeach pixel.
for
(pixel50). The non-printing If pixel.t Then pixel50
By modifying the k parameter, it is possible to
zones must therefore be binarized as white (pixel51).
Define: Else pixel51
simulate the inking and printing process for various
m the local mean computed on a [w6w]
8
A modified Niblack’s algorithm is used to binarize
neighbourhood End if
conditions (ink quantity, paper quality or humidity,
11,12 ink fluidity, exerted pressure etc.). Figure 8 shows the
9. 3D Acquisition ➙ Virtual Printing
RVATION OF ANCIENT WOODEN STAMPS 115
local threshold
7 Range image (‘Pisces’ stamp) computed from projec-
point tion of point cloud
Else t5Mzk*s (M.m and the neigh-
ones; bourhood is in a low zone)
ave to End if
inting If pixel.t Then pixel50
el51). Else pixel51
narize End if
pt the End Do
deter- The local threshold computing can be summarized
ndard by equation (1)
rhood t~max(M,m)zk às (1)
By modifying the k parameter, it is possible to
simulate the inking and printing process for various
w6w]
conditions (ink quantity, paper quality or humidity,
ink fluidity, exerted pressure etc.). Figure 8 shows the
mplete
same range image as that used in Fig. 7, binarized for
k50.1–0.8. Note the ‘inking’ variations produced by
d on a
the k value modification.
3.3 Comparison between virtual and real stamping
In order to test the proposed method, the results of 9
virtual printing were compared with real ones. For
10. 3D : Virtual vs. Real Fidelity ?
Virtual Resolution ! Real
10
16. Local Dissimilarity Map (LDM)
Φ( , )
Which measure ?
Which size ?
e 7.4 – Comparaison de deux groupes de lettres. L’image de la CDL indique clai
CDL indique cla
lisations des dissimilarités. La comparaison est également quantifiée.
quantifiée.
LDM
on de deux groupes de lettres. L’image de la CDL indique clairement
n de deux L’image de la CDL indique clairement
milarités. La comparaison est également16quantifiée.
milarités. également quantifiée.
17. Local Dissimilarity Map
Which measure
between small
images ?
• MSE - PSNR?
➡ pixel to pixel diffs
A
dA,B (p) = |A(p) B(p)|
|A(p) B(p)|
➡ low information
and
hard to interpret B
17
18. Local Dissimilarity Map
Which measure
between small
images ? DH(A, B) = max (h(A, B), h(B, A))
✓ ◆
• Binary image = set of h(A, B) = max min d(a, b)
pixels (foreground) a2A b2B
h(B, A)
➡ Hausdorff distance DH(A, B)
[Huttenlocher 1993]
DH(A, Tv A) = kvk
➡ numerous variations, A
including partial HD
ieme
B
hK (A, B) = Ka2A d(a, B)
18
19. Local Dissimilarity Map
Which size for the sliding
window ?
➡ adaptative
➡ must encompass
the «diffs» but no
more
A B
(a) (a) (b) (b) (c
➡ increase until the
Figure 7.2 – Illustration de la notion de dissimilarité locale. Les Les imag
Figure 7.2 – Illustration de la notion de dissimilarité locale. image A
measure equals itsdissimilaires. Les Les fenêtrescentrepetite et AetetABetcar carc), petites.perme
dissimilaires. fenêtres de taille
de taille petitemoyenne (en (en ne permetten
la dissimilarité locale au centre des des images
la dissimilarité locale au images
moyenne
B trop
c), ne
trop petites.
theoretical max ⇒ stopping criterion
Nous pouvons donner uneune idée générale. les pixels situés dans la
Nous pouvons donner idée générale. Si Si les pixels situés dans
partiennent à des des traits grossiers,fenêtre doitdoit avoir une taille su⇥
partiennent à traits grossiers, la la fenêtre avoir une taille su⇥san
écarts résultant de la comparaison de ces ces traits. les traits sont fins,
écarts résultant de la comparaison de traits. Si Si les traits sont fi
fenêtre soitsoit trop grande. Dans le cas contraire, des écarts qui sont plu
fenêtre trop grande. Dans le cas contraire, des écarts qui ne ne sont
19
20. rmax = max r|DHW (p,r) (A, B) = r . (7.27)
r>0
Local Dissimilarity Map
En pratique ce théorème indique que tant que la distance de Hausdor locale est égale au
rayon de la fenêtre, la mesure optimale n’est pas atteinte.
In the Hausdorff distancedissimilarités locales
7.1.4.4 Définition de la carte des
case :
La carte des dissimilarités locales est définie maintenant aisément. Elle regroupe l’ensemble
des mesures de dissimilarités locales réalisés pour di érentes positions. L’algorithme général
lorsque la distance locale est basée sur la distance de Hausdor est le suivant :
Algorithme 7.1 Algorithme itératif de calcul de la carte des dissimilarités locales (CDL)
entre deux images binaires A et B. W (p, n) désigne la fenêtre carrée centrée au pixel p et de
rayon n.
Pour chaque pixel p, faire
1. n ⇤ 1
2. tant que DHW (p,n) (A, B) = n et n ⇥ DH(A, B), faire
n⇤n+1
3. CDLA,B (p) = DHW (p,n 1) (A, B) =n 1
84
20
21. Local Dissimilarity Map
With the Hausdorff distance : fast computation
CDLA,B (p) = |A(p) B(p)| max (d(p, A), d(p, B))
Distance transform (or function) based
TDA (p) = d(p, A)
(distance to the nearest foreground pixel : very fast with a chamfer distance)
⇒ linear expression (binary images) :
CDLA,B = A.TDB + B.TDA
[Baudrier PhD - Pattern Recognition 2008]
21
22. Local Dissimilarity Map : Toy Examples
CDLa,b
Figure 7.3 – Comportement de la CDL avec des motifs simp
comparer. d est la CDL entre a et b, e est la CDL entre b et c e
CDL de
le niveau b,c gris est foncé, plus grande est la valeur locale de la
FigureFigure 7.3 – Comportement de la CDL avec des simples ; a,b,c sont lessont les images à
7.3 – Comportement de la CDL avec des motifs motifs simples ; a,b,c images à
comparer. d est la d est la CDL et b, e est b, e est la CDL entreet fet cCDL la CDL entre Plus c. Plus
comparer. CDL entre a entre a et la CDL entre b et c b la et f entre a et c. a et
le niveau de gris est foncé, plus grande est la valeur locale de la mesure.mesure.
le niveau de gris est foncé, plus grande est la valeur locale de la
Cet algorithme est coûteux en temps de calcul car itératif. En
Figure 7.3 – Comportement de la CDL avec des motifs simples ; a,b,c sont le
est en O(m4 ) pour deux images composées deet f⇥ m pixels. No
comparer. d est la CDL entre a et b, e est la CDL entre b et c m la CDL entre
A quantified and localized information
le niveau de gris est distance de grandeEn elaet, la complexité de mesure.
la foncé, plus Hausdor est utilisée dans de mesure locale de dis
locale la la calcul
Cet algorithme est coûteuxcoûteux en temps de calcul car itératif.valeur et, la complexité de calcul
en temps de calcul car itératif. est
7.3 – Comportement de algorithme est des motifs simples ; a,b,c sont les imagese à
Cet la CDL avec très rapide. En
. d est laest en entreen et b, 4 ) est la deux images composées de m ⇥ m pixels.c. Plus avons montré que lorsque
4 ) pour deux images composées de m ⇥ m pixels. Nous avons montré que lorsque
CDL O(m a O(m e pour CDL entre b et c et f la CDL entre a et Nous
est
de gris est distancedistance deest estvaleur locale Théorème mesure locale dedes dissimilaritéscalcul peut être
la foncé,la de grande Hausdor est dansde la mesure.
plus Hausdor la utilisée utilisée dans la locale La dissimilarité, le calcul peut être entre deux
la mesure 7.8. de carte dissimilarité, le locales
22
27. Ancients Printings
É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 1471
É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478
É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 1471
É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 16
20 16
20 16
18
20 1614
18
20 14
16
18
16 14
12
18 14
12
14
16
14 12
16 12
1010
12
14
12
14 10
10
12
10
12 88
10
810
10
8 88
66
68
86
É. Baudrier et al. 46 /4Pattern Recognition 41 (2008) 1461 – 1478 66
44
É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 6 1471
24
42 44
22
É. Baudrier et al. 0 Pattern Recognition 41 (2008) 1461 – 1478
02/ 22
00
É. Baudrier et al. / Pattern Recognition 41 (2008) 1461 – 1478 2 1471
20 0 16
0
16 00
20
16
20 18
16 18
18 14
20 18 14 1616
18 1614
16 16
18
18 12
18 14 16
12 16
1416
16 1412
14 14
16 12 14
16
16
14 10
14 12 10 14
1214
12
14 12
10 12
14
14
12
12 10
10 10 8 8 12
10
12 10
12 12
10
10 88
88 12
10 6
10 6
8 10
8810
88 666 810
10
6 44
6 88
66
66 4
44
4 68
8
22
4 66
44
44 2 2 46
6
2 02
20 00
2 4
24
2 24
4 2
00 00 0
2 2
02
2
0 0
1818 0 0
0 16
16 0
18
18 Fig. 8. Medieval impressions and their LDMaps. Here are four medieval impressions. Imp. 1, Imp. 2 and Imp. 3 illustrate the same scene with a di
1616 and their LDMaps. Here are four medieval impressions. Imp. 1, Imp. 2 and Imp. 3 illustrate the same scene with a
Fig. 8. Medieval impressions16 16
16
16 kind 8. Medieval impressions Imp. their LDMaps. Here aare four medieval 14
Comparaison d’illustrations 12
14
14
Figure 20 – 14 Imp. their LDMaps. Here aare four 16 anciennes.Imp. 1, Imp. 22 and Imp. 3illustrate the same16 scene with a
Fig. of grass and helmets in and 3. Imp. 4 illustrates distinct scene. impressions. Imp. 1, images a, b3et c représentent la a di
7.9 14 and 3. Imp. 4 illustrates distinct medieval impressions. Les Imp. and Imp. illustrate the same with m scene
kind 8. Medieval impressions
Fig. of grass and helmets in 14in Imp. 3. Imp. 4 illustrates a distinct 16
scene. 20 16
kindFigure 18CDL Imp.(f) CDL d’illustrations anciennes. Les images a, b et cde scènes dissimila
of grass and 7.9 –12 Comparaison ; (g) CDLscene. (h) CDL . La comparaison représentent la m
14
14 kind of grass and helmets
20 12 12 20
18 14
scène. (e)18 10 helmets12 ; 3. Imp. 4 illustrates a distinct14
in
12 scene. ; 10
14 18 14
12
12 a,b
10 a,c a,d 10 16 c,d 12
10
10 scène. (e)methods are (f) CDLa,c ; (g)réparties; sur CDLc,d .the measure result is h).image comparaison
produit 14
16
CDLa,b ; importantes ones12a,d (h) whether La comparaison de scènes dissimila
8
10
8 8 16
comparisondes valeurscompared with the CDLobtained 8 toute l’image (en g et an La (case of the LD
16 10 12 14
14
12
10
comparison methods86are compared with the ones 10obtained 6 whether LSDMap) or aresultvalue (case of(case ofof the L
comparisonThe five classification methods réparties sur toute l’image (en result is h).image comparaison
14
ones obtained6
methods are compared with the are the follo-
8 10 whether the measure realet is an image 10 HD and LD
12 the the measure an (case the its
88
produit 10 valeurs importantes
manually. des 12 and
10 faible measure g
12
scènes methods66 produit with the ones 8obtained 4 and the LSDMap) or a real value ou très8the HD and i
12
manually. The10 five 64classification des valeurs importanteswhetherLSDMap) or a resultvalue(case of 8(case of is itsL
comparison similaires classificationmethods are the follo-4 La the
en the In the first case,(en is an (case of method the
the nombrereal e) image the HD and
the classification localisées
6 are compared methods are the follo- 8 10
6 wing ones: The five
manually. 4 and
ations). a
44 scènes similaires produit methods are the follo-2 2 ations). Inin Sectioncase, In theclassificationmethod is is
manually. The
wing ones:
wing ones: 6
8 five42classification des valeurs importantes enthe LSDMap) or a real valueou très6localisées
8
2 4 6 6 and 88 faible nombre (en e) (case of the HD and 6
described the first case, the classification 4 an empirica
ations).
66 first 6.2. the second case, method a
2 6 20 4
2 wing ones: 44 based on the LDMap,
• our method 02 4 4 0
0 describedforthe first case,In the second case, an empirica
ations). Inin each class C In and C
Section 6.2. the classification method is
described Section 6.2. sim the second is computed from
44
tribution case, an empiri
0 0 2
In and Cdissim 2 0
2 dissim
0 • ourthe so-calledbased on the LDMap,
• our method Local the LDMap,
method22 based on Simple Difference Map (LSDMap) us-
0 22 2
describedfor eachthe modes of the dissim isis computed fr
in each class Csim and C empirical distribution
Section 6.2. sim the second case, an empiri
tribution set. different C
Medieval impressions and their LDMaps. Here are four medieval on the LDMap, Imp. 2 and Imp. 30illustrate the same 0 learning a As class
tribution 0 computed fro
• and are four illustrateLocal SimpleImp. theasimple difference locallythe same0 scene set. eachthe modes of the empiricalcomputed f
ourImp. the medievalthe Simple with 1, Imp.Map (LSDMap) us-
• the the
• so-called
edieval impressions and their LDMaps.2Here ing so-called based impressions. Imp. 1, different (LSDMap) us-
impressions.
method00 Localmap, but Difference 2Map Imp. 316
distance same sceneDifference and
0illustrate
scene with
tribution with As the easy of the dissim 16 distribution
learning for a different Csim and C empirical distributi
class is
16
ure andimpressions. Imp. Imp.Imp.d’illustrations anciennes.(F, G)imagesdifferencelocally learning ladefined, anmodesand efficient classification me
f medieval impressions. Imp. 1, Imp. 2 and Imp.33 illustrate the same scene with a different b 16 c représentent
grass 7.9 – Comparaisonillustrates
4 20
medieval helmets Imp. 3. 3. 1, 4 illustrates a a distinctscene.
in Imp. scene. with
20Local Simple Difference Map a,
quite well
20
Les simple ∩ W − Get W |,us- learning set.mêmeanmodesand efficient classification m
• ing instead ofcthe HD: but with la = |F difference locally 20
ons anciennes. Les images a, bdistance map, H SD W the même (LSDMap)
ass and helmets in
t scene.
scene.
Imp. the ing the distance map, but with the simple
so-called
distinct
the et 18 représentent
18
18 14
14
∩ quite well defined, an easy method. empirical distributi
quite maximum likelihood and the
the
18
18
18 As the easy of efficient 14
is 18 well defined, 14
classification
16
e. (e) CDLa,b ; (f) CDLa,c ;insteadglobal the map,SD W (F, G)La=comparaisonW |, scènes16 well defined, an easymethod.
(g) CDL16 HD: H but with . G) |F difference W de
• instead of ; (h) CDL (F, simple W − G 12 |,
18
16
ingthe of theHD,HD: H SD Wc,dthe = |F ∩∩ W − G 12locally
the distance16
a,d 16
∩ ∩
16 16dissimilaires
quite maximum likelihood and efficient 14
16
is 14 maximum likelihood method.
is the
the
16
16
12
classification
12
La,d ; methods are c,d . La comparaison14HD, H SD W (F, G) =measure result1014 an image (case of the LDMap
(h) CDL compared withinsteadglobal HD: 14de scènes dissimilaires
16
arisondes valeurs importantes theones the sur whether the |F ∩ W g 14 W |, La comparaison likelihood method. 14 14
duitmethods are comparedmeasuretherépartiesimage touteof the LDMap − Get12h). imageis 12 maximum de
son
• of 14
• the global HD,
PHD,14 obtained
12
12 l’image 27 result10 an
(en ∩is 14
14
the
12 of the LDMap
10
12
10
12
rties sur toute l’image (enresult isobtained comparaison de
obtained whether the with the g et 10 La (case
ones h). an whether the measure 12is
8 (case
12
12
6.3.2. Results
10 8
28. Ancients Printings
• LDM classification
• similar
• dissimilar
➡ SVM
Bonne classification (en %) CDL DPP DH PHD MHD
pour Csim 98 90 60 83 77
pour Cdissim 97 92 75 81 83
Table 7.1 – Performances en classification d’images similaires issues de la base d’impressions
anciennes. CDL = carte des dissimilarités locales, DPP : di érence pixel à pixel, DH : distance
de Hausdor , PHD : distance de Hausdor partielle, MHD : distance de Hausdor modifiée
(voir 7.2.1.4).
[Baudrier PhD]
28
29. Tumor Evolution
t1 t2 t3
(a) (b) (c)
? ?
Fig. 2. Segmented MRI.
7.12 – Un exemple de la segmentation d’une tumeur. Seule une coupe d’u
représentée, à trois dates di érentes.
values in (f) do not reflect et al. 2007] in this case. As
[Nicolier the similarity
a short conclusion, the LDMap is a useful tool for non-
29
30. (S1) Coupes de la segmentation 1
A. Segmentation Method R ESULTS
III.
using SVM with RBF kernel.
(j)
Tumor Evolution
A. MRI images are acquired on a 1.5T GE (General
Segmentation Method
Electric Co.) machine using an axial1.5T IR (Inversion
on a 3D Slices 18 to 23 (a-f) of the Local Distance Volu
MRI images are acquired Fig. 5. GE (General
Recuperation) machine using an axialan axial FSE (Fast
Electric Co.) T1-weighted sequence, 3D IR (Inversion
Spin Echo) T2-weighted, ansequence, anPD-weighted 3) and 2 (fig 4). The distances are absolute
volumes 1 (fig se-
Recuperation) T1-weighted axial FSE axial FSE (Fast
quence and T2-weighted, an axial FSE examination, we distance histogram (logarithmic scale in g
Spin Echo) an axial FLAIR. eq. one PD-weighted se-
For (3). (j) is the (a) (b) (c)
have 24and an axial FLAIR.signals with a voxel size
quence slices of the four colormap of images (a-f).
For one examination, we
of 0.47 ⇥slices ⇥ 5.5 mm3. signals with a and all size
0.47 of the four All the slices voxel the (a) (b) (c)
have 24
examinations are⇥ 5.5 mm3. All SPM software. all the
of 0.47 ⇥ 0.47 registrated using the slices and
examinations are registrated using SPM software. using
We use the first examination for training SVM
RBF kernelthe first examination for training SVM using
We use [10]. The training set was obtained from one
(a) slice(b) using mouse to(c)
(c) RBF by choose ten pixels into the tumour
kernel [10]. The training set was obtained from one (d) (e) (f)
(a) and (b) outside. We perform theten pixels into the tumour
sliceten using mouse to choose first segmentation of this
by (c)
(c)
volume by usingWe perform the first segmentation of this Fig. 4. Segmentation of the de (e) volume (slices from(f) to 23, a-f)
and (b) outside. the SVM model obtained. So, we build using SVM with RBF kernel. second segmentation 18
(d) Coupes
(S2) la 2
(c) t1 (a) ten (c)hundred points into the tumour
automatically about one model obtained. So, we build Fig. 4. Segmentation of the second volume (slices from 18 to 23, a-f)
volume by using the SVM
his case. As and outside from all one hundred slices. into retraining a using SVM with RBF kernel.
automatically about the tumoral points We the tumour
second SVM fromuse it fortumoral slices. Wesegmentation (a) (b)
ol for non-
his case. As and outside and all the perform a second retraining a
for improve the first it for perform this last SVM model, As a true distance is used to compute the LDV, the
). It is non-
for thus
ol case. As (d) second SVM and use result. With a second segmentation
(e) (f)
his we perform the segmentationWith given scalar are true physical distance in mm. The given
). It is non-
thus (d) for improve the first result. of others examinations. At
Fig. 3. Segmentation of the first volume (slices from (f) to 23, a-f) this last SVM model,
(e) 18 As a true distance is used to compute the LDV, the
ol for using SVM with RBF kernel. eachperform the segmentation of others examinations. At given scalar are true physical there are mm. more low
we segmentation of examination, we use this 2 steps
distances histogram indicates distance inmuch The given
). It is thus (d) Coupesprocess for improve of examination, we use this 2 steps distances than (b) distances. This a coherent fact as non-
Fig. 3. Segmentation of thede (e) segmentation(f) to 23, Fig 2 contains an example
(S1) each la segmentation the 1
first volume (slices from 18 result. a-f) (a) distances histogram indicates there are much more low
high (c)
using SVM with RBF kernel. zero LDV values aredistances. in theaintersection of as non-
Fig. 3. Segmentation of thede la obtained segmentation. All the nine slices of two
the for (slices from result. a-f)
process segmentation18 distances high obtained This coherent fact the two
(S1) Coupesof first volumeimprove the 1 to 23, Fig 2 contains an example volumes. than intersection is locally filled with increasing
segmented volumes are given All the and slices of two zero LDVThe are obtained in the intersection of the two
using SVM with RBF kernel. the obtained segmentation. in figs 3 nine 4.
of values (d) (e)
E (General values, starting from zero locally filledmaximum local
segmented volumesDetails are given in figs 3 and 4. volumes. The intersection is up to the with increasing
E (Inversion B. Implementation distance starting from volumes. to the maximum 7. Us Fig.
(General
l FSE (Fast Fig. 6. a new mageJ is 15.56mm. This represent the higher straight distance
values, between the zero the The maximum tumor hasvo
A three-dimensional view of up LDV between re local
distance
E (Inversion
(General B. The computation DetailsLDV is done with
Implementation of the distance between the volumes. The maximum has progresse distance
leighted se-
FSE (Fast
R (Inversion
2.
plugin computation2GHz opteron, donecomparison mageJ between the two volumes. the higher straight directed dista
The [6]. With a of the LDV is the with a new of the is 15.56mm. This represent
(d) (e) (f) distance
t
weighted we 2
ination, se-
l voxel (Fast
FSE
(a) (b) ⇥ 512 ⇥ 9 volumes is done in 39 seconds.
plugin [6].
(c) The proposed Local Distance Volume can be used to
two 512 With a 2GHz opteron, the comparison of the between the two volumes. and 4). (b) is
(j)
ination, size
we (a)
(VDM) - coupes duprecisely the variations between two volumes. S
track more volume des dissimilarités can be used to
locales entre
weighted these-
and all size two (b) ⇥ (c)
C. Results 512 ⇥ 9 volumes is done in 39 seconds.
512 The proposed Local Distance Volume
voxel we
ination,
Fig. 5. Slices 18 to 23 (a-f) of the
The Hausdorff Distance in a window (eq. (3)) is defined as
track more precisely the variations between two2 volumes. ds
C.The LDV is computed between Figure 1 and – Exemple de volume des dissimilarités (j) is the distance histogram (l
volumes 7.13 2. The the maximum of two directed distance. In(3)) is Les deux
locales.
are.
and all size (a) (b) (c) volumes 1 (fig 3) and (fig 4). The
voxel the
SVM using
Results The Hausdorff Distance in a window (eq. the present case
eq. (3). defined as
are.
and all one results LDVpresented in betweenS2)the z-resolution is L’histogramme indique la useful information.(a-f). (A, B)
are is computed fig 5. As sont 1 and 2. The the maximum of two directed distance.of imagespresent case(e
comparées. the directed distances carry répartition des distances
clearly seen (by high negative distances). colormap hW
d from the
Local Dissimilary Volume
The volumes In the
SVM using
are. tumour slightly greather than the xfigy 5. As the (with a ratio of carry the information on voxels sont expriméesW (A, B)
results are presented in resolutions z-resolution is the directedniveaux de gris, present in vol. 1h ennot in
Les distances, traduites par des distances carry useful information. and mm.
(j)
the
d from one
SVMof this
using (d) 11.7), the obtained distance depends only(with a ratiothe vol. 2. SymmetricallyonW (B, A) carry in vol. 1 and not on
(e) (f) information h voxels Volume the information in
slightly greather than the x y resolutions lightly on of carry the (a-f) of the Local Distance present between
ationtumour
the Fig. 5. Slices 18 to 23
z-axis information. distance dependsobtained distance is voxels present indistances andabsolute accordinginformation B)
Only when the only lightly vol. 2. (fig 4). The vol. hWare not carry the to hW (A, on
2 (B, A) in vol. 1. So
o, from this
d we build
one (d) Coupesgreathersegmentation the z-information has beenon the(fig 3) and 2 Symmetricallytumor has regressed and h (B, A)
Fig. 4. Segmentation of the11.7), the obtained from(f) to 23, a-f)
(S2) de la 2 volumes 1
the of
ationtumour
the tumour using SVM with RBF kernel.
(e) than 11.7mm, 18
second volume (slices
Fig. 4. Segmentation of the de (e) volume (slices froma18 to 23, a-f)
IV. CONCLUSION
z-axis information. Only when the obtained distance (j) is the distance histogram the 2 and notinin vol. 1. the hW (A, B)
taken indicates where (logarithmic scale gray) and So W
eq. (3). is voxels present in vol.
ation build
o, weof this (d) Coupesinto account. Fig 6 is (f) z-information has been taken images (a-f). where the tumor has regressedillustrated(B, fig.
(S2) second segmentation 2
la than 11.7mm, the
greather colormap of
three-dimensional representation where the tumor has progressed. This is and hW in A)
indicates
retraining a
the tumour using SVM with RBF kernel.
o, we build of the LDV. Fig is 18 to 23, a-f)
Fig. 4. Segmentation of theinto account. (slices6from a three-dimensional representation
second volume (a) (b) (c) 97
7 and fig. 8. The has progressed. This central occlusion is
where the tumor augmentation of the is illustrated in fig.
egmentation
retraining a
VM tumour
the model, using SVM with RBF kernel. the LDV.
of
As a true distance is used to compute the LDV, the A distance measure between volumes has
30
7 and fig. 8. The augmentation of the central occlusion is
32. Binary Pattern Localization
Local dissimilarities aggregation :
XX
MDGI,P = CDLI,P (k, l)
k l
with CDLI,P = I.TDP + P.TDI
) DI,P = TD2 P +I TD2
I P sum of two
oriented measures
Chamfer score [Borgefors,
1988]: how much
I looks like à P?
32
33. Binary Pattern Localization : Example
Fig. 2.Chamfer score MDG
In (c), image response by Borgefors chamfer matcher. – In (d), image
obtained with symmetric LDM-matcher. – A good match with the reference
pattern is reported by low values (with dark gray levels).
ce pattern, the ideal location in (a)
33
38. Brain Internal Structures Segmentation
Optimal transformation :
regularization
T ⇤ = argminT 2 {Esim (B, A T ) + Ereg (T )}
similarity measure
Classic solution :
1 2
Esim (B, A T ) = kB A Tk
2
Displacement field :
(A T B)(p)
u(p) = 2 rB(p)
(A T B)2 (p) + krB(p)k
38
39. representation of the corresponding structure in the deformed deformed shape map shapeaccording to the following p
representation of the corresponding structure in the unified unified MðpÞ map MðpÞ according to the
8
atlas after the transformation T. Under the constraint of the shape the shape > Fs ðpÞ
atlas after the transformation T. Under the constraint of 8
< i > Fsif Fsi ðpÞ Z0 Fsi ðpÞ Z0
< i
ðpÞ if
similarity term, the optimal transform would leadwould lead to the final maxðF ðpÞÞ maxðF ðpÞ o0if and ðpÞ o0F ðpÞÞj
similarity term, the optimal transform to the final
Brain Internal Structures Segmentation
MðpÞ ¼ MðpÞs¼
i
if Fssi ðpÞÞ
i
Fsi jmaxð and
si
segmented structure shape as closer as as closer asatlas.in the atlas. Therefore >
segmented structure shape that in the that Therefore :0 >
: 0 if F ðpÞ o0if and ðpÞ o0F ðpÞÞj
si Fsi jmaxð and
si
the above overall costoverall cost function can be modified as
the above function can be modified as
where e is the threshold, ethreshold, e ¼ Fsi ðpÞÞg. Ther
E ¼ Esim ðB; A3TÞ¼ Esim ðB; A3TÞ þ Ereg ðB; A3TÞ þ Eshape ðFS ðAÞ; Fshape ðFSþ Ereg ðTÞ
E þ Ereg ðTÞ ¼ Eintensity ðTÞ ¼ Eintensity ðB; A3TÞ þ ESSD
where e is the ¼ mini fmaxp ð mini fmaxp ðF
SSD SSD SSD S ðA3TÞÞ ðAÞ; FS ðA3TÞÞ þ Ereg ðTÞ
in Eqs. (7),in Eqs. (7), (8)should be should be rep
(8) and (10) and (10) replaced by M
ð8Þ ð8Þ
implementation procedure. procedure.
implementation
By extending the originalthe original Demons registration[25],
By extending Demons registration algorithm algorithm [25],
Shape constraint introduction :
an optimal an optimal solution can be obtained by the alternating strategy.
solution can be obtained by the alternating strategy.
The displacement vectors related to the intensity and the shape at
The displacement vectors related to the intensity and the shape at
3.2. Topology correction strategy
3.2. Topology correction strategy
the point p theinterest regions are regions are
of point p of interest
As is mentioned, mentioned, topology preservatio
As is topology preservation of a defor
ðA3TðpÞÀBðpÞÞðA3TðpÞÀBðpÞÞ is important in registration-segmentation method
is important in registration-segmentati
uintensity ðpÞ ¼ À
uintensity ðpÞ ¼ À 2 rBðpÞ rBðpÞ ð9Þ ð9Þ
8 ðA3TðpÞÀBðpÞÞ 22
ðA3TðpÞÀBðpÞÞ þ JrBðpÞJ þ JrBðpÞJ 2 brain case.brain case. bijectivity bijectivity and
Although Although and smoothing
adopted in optimizing the cost function like Eq. (4) l
adopted in optimizing the cost function o
>0
<
ushape ðpÞ ¼ À shape ðpÞ ¼ À
u
ðFS ðA3TðpÞÞÀFSSðA3TðpÞÞÀFS ðAðpÞÞÞ
ð F ðAðpÞÞÞ
2 2 2
p⇥C helpful for preventing topology change, it ischange, it
rFS ðAðpÞÞ 2 rFS ðAðpÞÞ helpful for preventing topology hard to b
ðFS ðA3TðpÞÞÀFSSðA3TðpÞÞÀFrFS ðAðpÞÞJ rFS ðAðpÞÞJ
ðF ðAðpÞÞÞ þJ S ðAðpÞÞÞ þJ theory. The topology preservation problem of t
theory. The topology preservation pro
S (p) = d(p, C) p⇥S
ð10Þ algorithm has been investigated in recent years [3
ð10Þ algorithm has been investigated in rece
cases without topology preservation using this metho
cases without topology preservation usin
>
:
The combined displacement vector is vector is
The combined displacement found in some published reliable experiments [3
found in some published reliable exp
d(p, C)
uðpÞ ¼ ð1ÀbuðpÞ ¼ ð1ÀbÞuintensityðpÞ þ bushape ðpÞ
Þuintensity ðpÞ þ bushape p ⇥ ¬S
ð11Þ experiments. By optimizing optimizing the cost fu
ð11Þ experiments. By the cost function over
diffeomorphism, a diffeomorphic Demons algorith
diffeomorphism, a diffeomorphic Demo
posed [36,37]. In this paper, a different simple topolog
posed [36,37]. In this paper, a different sim
method is proposedis proposed based onfield vector
method based on the vector the analys
Let T ¼ ðX; Y; ZÞ T ¼ ðX; Y; ZÞ deformation field, whe
Let denote the denote the deformatio
the new point p of point p ðx; y; zÞ afte
the new position of position ðx; y; zÞ after deformati
1 β1 β
0.5 0.5
− + − +
x
x0 x 0 x 0 x0 x 0 x 0
Fig. 1. An example of the shape representationrepresentation (a) (b) its shape (b) its shape
Fig. 1. An example of the shape (a) the putamen the putamen
S
distance representationrepresentation map.
distance map.
S Fig. 2. The function parameter b.
Fig. 2. The function of the balance of the balance
39