Texture–based computerized analysis of high–resolution computed tomography images from patients with interstitial lung diseases is introduced to assist radiologists in image interpretation. The cornerstone of our approach is to learn lung texture signatures using a linear combination of N–th order Riesz templates at multiple scales. The weights of the linear combination are derived from one–versus–all support vector machines. Steerability and multiscale properties of Riesz wavelets allow for scale and rotation covariance of the texture descriptors with infinitesimal precision. Orientations are normalized among texture instances by locally aligning the Riesz templates, which is carried out analytically. The proposed approach is compared with state–of–the–art texture attributes and shows significant improvement in classification performance with an average area under receiver operating characteristic curves of 0.94 for five lung tissue classes. The derived lung texture signatures illustrate optimal class–wise discriminative properties.

1. Multiscale Lung Texture Signature Learning
Using The Riesz Transform
Adrien Depeursinge¹, Antonio Foncubierta¹, Dimitri Van de Ville², Henning Müller¹
¹University of Applied Sciences Western Switzerland, Sierre (HES-SO)
²Ecole Polytechnique Fédérale de Lausanne, Switzerland (EPFL)
1. Introduction 3. Results
• The first step in medical image interpretation is to detect • Signatures from artificial textures
abnormal image patterns and is related to visual perception.
• Visual perception strongly relies on texture properties, which
are essential for the characterization of biomedical tissue.
– Healthy and pathological lung parenchyma in high-resolution computed
tomography (HRCT) from patients with interstitial lung diseases (ILD)
can only be described in terms of texture properties:
Figure 4. Lower row: multiscale texture signatures 𝜞 𝒄 𝟖 of the upper row for 𝑵 = 𝟖.
– The first two columns on Fig. 4 demonstrate the scale covariance of the signatures.
The distributions of the weights 𝒘 for scales 𝑠1 , … , 𝑠4 are 0.1%, 18.5%, 81.1%, 0.3%
healthy emphysema ground glass fibrosis micronodules
and 2.3%, 3.9%, 14%, 79.8% , respectively.
• Computerized texture analysis is proposed to assist clinicians in – Rotation covariance is demonstrated with oriented stripes in the 3rd and 4th columns
image interpretation tasks. of Fig. 4.
2. Multiscale steerable Riesz filterbanks • Lung texture signatures
• The components of the 𝑁th-order Riesz transform 𝓡 of a two- healthy emphysema ground glass fibrosis micronodules
dimensional signal 𝑓(𝑥) are defined in the Fourier domain as:
𝑛1 ,𝑛2 𝑛1 +𝑛2 −𝑗𝜔1 𝑛1 −𝑗𝜔2 𝑛2
𝓡 𝑓 𝝎 = 𝑓 𝝎 , (1) 𝟒 𝟒 𝟒 𝟒 𝟒
𝑛1 !𝑛2 ! 𝝎 𝑛1 +𝑛2 𝜞 𝒉𝒆𝒂𝒍𝒕𝒉𝒚 𝜞 𝒆𝒎𝒑𝒉𝒚𝒔𝒆𝒎𝒂 𝜞 𝒈𝒓𝒐𝒖𝒏𝒅 𝒈𝒍𝒂𝒔𝒔 𝜞 𝒇𝒊𝒃𝒓𝒐𝒔𝒊𝒔 𝜞 𝒎𝒊𝒄𝒓𝒐𝒏𝒐𝒅𝒖𝒍𝒆𝒔
for all combinations of (𝑛1 , 𝑛2 ) with 𝑛1 + 𝑛2 = 𝑁 and 𝑛1,2 ∈ ℕ.
• It yields steerable filterbanks when convolved with Gaussian
kernels 𝐺:
𝐺 ∗ 𝓡1,0 𝐺 ∗ 𝓡0,1 𝐺 ∗ 𝓡2,0 𝐺 ∗ 𝓡1,1 𝐺 ∗ 𝓡0,2
3011 blocks, 407 blocks, 2226 blocks, 2962 blocks, 5988 blocks,
𝑁=1 , 𝑁=2 , 7 patients. 6 patients. 32 patients. 37 patients. 16 patients.
Figure 5. Distributions of the texture classes and visual appearance of the class-wise lung texture signatures 𝜞 𝒄 𝟒 .
𝐺 ∗ 𝓡3,0 𝐺 ∗ 𝓡2,1 𝐺 ∗ 𝓡1,2 𝐺 ∗ 𝓡0,3 – The proposed methods are evaluated on 14,594 32x32 overlapping blocks from
manually drawn regions in 85 cases with a leave-one-patient-out cross-validation.
𝑁=3 .
– Comparison with optimized state-of-the-art approaches:
Figure 1. Steerable filterbanks derived from the Riesz transform with 𝑵 = 𝟏, 𝟐, 𝟑.
• Local binary patterns (LBP): radius 𝑅 = 1,2 pixels and number of samples 𝑃 = 8,16.
• Grey-level co-occurrence matrices (GLCM) combined with run-length matrices (RLE):
• Multiscale filterbanks 𝑠1 , … , 𝑠4 are obtained by coupling the 𝜋 𝜋 3𝜋
orientations 𝜃 = 0, , , , distances 𝑑 = 1: 5 and grey-levels 𝑙 = 8, 16, 32.
4 2 4
Riesz transform with Simoncelli’s multi-resolution framework. – One versus all SVMs are used to learn the weights 𝒘 in Eq. (2).
– All approaches are combined with 22 grey-level histograms bins in −1050; 600
2. Texture signature learning Hounsfield Units.
𝑁
• A texture signature 𝛤𝑐 of the class 𝑐 is built from a linear
True positive rate
combination of the multiscale Riesz components as: healthy emphysema ground glass fibrosis micronodules
𝛤𝑐 𝑁 = 𝑤1 𝐺 ∗ 𝓡 𝑁,0 𝑠1 + 𝑤2 𝐺 ∗ 𝓡 𝑁−1,1 𝑠1 + ⋯ + 𝑤4𝑁+4 𝐺 ∗ 𝓡0,𝑁 𝑠4 , (2)
False positive rate False positive rate False positive rate False positive rate False positive rate
Riesz
filterbank
(𝑁 = 8)
⋯ Figure 6. Receiver operator characteristic (ROC) analysis for the various texture analysis approaches. 𝑵 = 𝟒 for all
Riesz features. Area under ROC curves are shown in the subfigures.
𝑤1 = 2.9 𝑤2 = 1.7 𝑤3 = -0.8 𝑤 𝑁−1 = -0.1 𝑤 𝑁 = -4.2
– The Riesz transform outperforms the other approaches for all classes but
emphysema 𝑝 < 10−19 .
S
texture to learn:
3. Conclusions and future work
associated
texture
signature • Texture analysis enabling scale and rotation covariance with
infinitesimal precision is introduced.
• The learned signatures allows checking for the visual relevance of the
𝑵 information modeled by the proposed approach.
Figure 2. Construction of the texture signature 𝜞𝒄 .
• Future work will maximize the local orientation of the signatures for
• Support vector machines (SVM) are used to determine the
enhanced texture characterization.
weights 𝒘 in Eq. (2) for a given texture discrimination task:
• The framework has already been extended to three dimensions:
versus 2.9
𝒘=
1.7
texture texture
Figure 3. Weight learning using SVMs.
Contact and more information: adrien.depeursinge@hevs.ch, http://medgift.hevs.ch/