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.

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

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 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

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 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. 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

49. 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

50. 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

51. 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

52. MM / Discussion
Smoothed shock filtering
Original contribution: robust
image denoising algorithm
Approved by applying
definition of robustness
Antoine Vacavant 24 / 55

53. 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

54. 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

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

56. 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

57. 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

58. 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

59. 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

60. 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

61. 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

62. 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

63. 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

64. 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

65. 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

66. 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

67. 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

68. 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

69. 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

70. 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

71. DG / Experimental evaluation
Reeb graph obtained for noisy vascular image
Antoine Vacavant 36 / 55

72. DG / Experimental evaluation
With synthetic images
nit 0
nit 1
Antoine Vacavant 37 / 55

73. DG / Experimental evaluation
With synthetic images
nit 0
nit 5
Antoine Vacavant 37 / 55

74. DG / Experimental evaluation
With synthetic images
nit 0
nit 50
Antoine Vacavant 37 / 55

75. DG / Experimental evaluation
With synthetic images
nit 0
nit 100
Antoine Vacavant 37 / 55

76. 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

77. 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

78. 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

79. 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

80. 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

81. 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

82. 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

83. 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

84. 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

85. 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

86. 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

87. 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

88. 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

89. 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

90. 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

91. 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

92. 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

93. 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

94. 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

95. 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

96. 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

97. 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

98. 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

99. The end...
Questions?
Antoine Vacavant 55 / 55