texture texture

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

• The first step in medical image interpretation is to detect

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:

• Computerized texture analysis is proposed to assist clinicians in

image interpretation tasks.

2. Multiscale steerable Riesz filterbanks

• The components of the 𝑁th-order Riesz transform 𝓡 of a two-

dimensional signal 𝑓(𝑥) are defined in the Fourier domain as:

𝓡 𝑛1,𝑛2 𝑓 𝝎 =𝑛1+𝑛2

𝑛1!𝑛2!

−𝑗𝜔1𝑛1 −𝑗𝜔2

𝑛2

𝝎 𝑛1+𝑛2𝑓 𝝎 , (1)

for all combinations of (𝑛1, 𝑛2) with 𝑛1 + 𝑛2 = 𝑁 and 𝑛1,2 ∈ ℕ.

• It yields steerable filterbanks when convolved with Gaussian

kernels 𝐺:

𝑁 = 1 , 𝑁 = 2 ,

𝑁 = 3 .

• Multiscale filterbanks 𝑠1, … , 𝑠4 are obtained by coupling the

Riesz transform with Simoncelli’s multi-resolution framework.

2. Texture signature learning

• A texture signature 𝛤𝑐𝑁 of the class 𝑐 is built from a linear

combination of the multiscale Riesz components as:

𝛤𝑐𝑁 = 𝑤1 𝐺 ∗ 𝓡𝑁,0

𝑠1+ 𝑤2 𝐺 ∗ 𝓡𝑁−1,1

𝑠1+ ⋯ + 𝑤4𝑁+4 𝐺 ∗ 𝓡0,𝑁

𝑠4, (2)

• Support vector machines (SVM) are used to determine the

weights 𝒘 in Eq. (2) for a given texture discrimination task:

3. Results

• Signatures from artificial textures

– 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%

and 2.3%, 3.9%, 14%, 79.8% , respectively.

– Rotation covariance is demonstrated with oriented stripes in the 3rd and 4th columns

of Fig. 4.

• Lung texture signatures

– 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.

– Comparison with optimized state-of-the-art approaches:

• 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):

orientations 𝜃 = 0,𝜋

4,𝜋

2,3𝜋

4, distances 𝑑 = 1: 5 and grey-levels 𝑙 = 8, 16, 32.

– 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

Hounsfield Units.

– The Riesz transform outperforms the other approaches for all classes but

emphysema 𝑝 < 10−19 .

3. Conclusions and future work

• Texture analysis enabling scale and rotation covariance with

infinitesimal precision is introduced.

• The learned signatures allows checking for the visual relevance of the

information modeled by the proposed approach.

• Future work will maximize the local orientation of the signatures for

enhanced texture characterization.

• The framework has already been extended to three dimensions:

Contact and more information: adrien.depeursinge@hevs.ch, http://medgift.hevs.ch/

healthy emphysema ground glass fibrosis micronodules

Figure 1. Steerable filterbanks derived from the Riesz transform with 𝑵 = 𝟏, 𝟐, 𝟑.

𝐺 ∗ 𝓡1,0 𝐺 ∗ 𝓡0,1 𝐺 ∗ 𝓡2,0 𝐺 ∗ 𝓡1,1 𝐺 ∗ 𝓡0,2

𝐺 ∗ 𝓡3,0 𝐺 ∗ 𝓡2,1 𝐺 ∗ 𝓡1,2 𝐺 ∗ 𝓡0,3

⋯

S

Riesz

filterbank

(𝑁 = 8)

𝑤2= 1.7 𝑤𝑁−1= -0.1 𝑤3= -0.8 𝑤𝑁= -4.2

texture to learn:

associated

texture

signature

𝑤1= 2.9

𝒘 =2.9

1.7

versus

Figure 2. Construction of the texture signature 𝜞𝒄𝑵

.

Figure 3. Weight learning using SVMs.

Figure 4. Lower row: multiscale texture signatures 𝜞𝒄𝟖 of the upper row for 𝑵 = 𝟖.

healthy micronodules fibrosis ground glass emphysema

𝜞𝒉𝒆𝒂𝒍𝒕𝒉𝒚 𝜞𝒆𝒎𝒑𝒉𝒚𝒔𝒆𝒎𝒂 𝜞𝒈𝒓𝒐𝒖𝒏𝒅 𝒈𝒍𝒂𝒔𝒔 𝜞𝒇𝒊𝒃𝒓𝒐𝒔𝒊𝒔 𝜞𝒎𝒊𝒄𝒓𝒐𝒏𝒐𝒅𝒖𝒍𝒆𝒔 𝟒 𝟒 𝟒 𝟒 𝟒

3011 blocks,

7 patients. 2226 blocks,

32 patients.

407 blocks,

6 patients.

2962 blocks,

37 patients. 5988 blocks,

16 patients.

Figure 5. Distributions of the texture classes and visual appearance of the class-wise lung texture signatures 𝜞𝒄𝟒 .

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.

healthy emphysema ground glass fibrosis micronodules

False positive rate False positive rate False positive rate False positive rate False positive rate

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