Centerline detection of cardiac vessels in ct images martin korevaar
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Centerline detection of (cardiac) vessels in CT images Martin Korevaar. Supervisors: Shengjun Wang Han van Triest Yan Kang Bart ter Haar Romenij. Overview. Introduction Method Feature space Minimal Cost Path (MCP) search Results Conclusion Discussion. Introduction.

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Centerline detection of cardiac vessels in ct images martin korevaar

Centerline detection of (cardiac) vessels in CT imagesMartin Korevaar

Supervisors:

Shengjun Wang

Han van Triest

Yan Kang

Bart ter Haar Romenij


Overview
Overview

  • Introduction

  • Method

    • Feature space

    • Minimal Cost Path (MCP) search

  • Results

  • Conclusion

  • Discussion


Introduction
Introduction

  • Coronary artery and heart diseases are one of the main causes of death in Western world

  • Therefore improvement of diagnosis, prevention and treatment is needed

  • Diagnosis is improved by techniques like CTA and MRA

  • CAD is needed to analyze huge amount of data


Introduction1
Introduction

  • Centerline of vessel is interesting feature for CAD

  • Needed e.g. for CPR and lumen size measurements

  • Should be

    • Independent of vessel segmentation

    • Robust with respect to image degradations.


CPR

  • Visualization method

Images from: Armin Kanitsar in IEEE Viz. 2002 Okt


CPR

  • Visualization method

  • Maps 3D path on 2D image

Images adapted from: Armin Kanitsar in IEEE Viz. 2002 Okt


CPR

  • Visualization method

  • Maps 3D path on 2D image

  • Artery can be investigated from just 1 image


CPR

  • Visualization method

  • Maps 3D path on 2D image

  • Artery can be investigated from just 1 image

  • Centerline needs to be correct

Images from: Armin Kanitsar in IEEE Viz. 2002 Okt


Algorithm
Algorithm

Create feature space

Feature space with:

  • Center of vessel lower value then peripheryof vessel

  • Vessel lower value then background

Find Minimum Cost Path with Dijkstra’s algorithm


Feature space
Feature space

  • Filter based on eigenvalues of Hessian


Hessian 1

Dxx*G(x,y,)

G(x,y,)

Dyy*G(x,y,)

Dxy*G(x,y,)

Hessian (1)

  • Matrix with all second order derivatives2D Hessian:

  • Derivative of image:Convolve derivative of Gaussian with image

  • Gaussian:


Hessian 2 eigenvectors values

1v1

2v2

Hessian (2)Eigenvectors / -values

  • 1< 2(<3)

  • measure of curvature

  • i relates to vi

  • v2 points to max. curvature

  • v1 points to min. curvature, perpendicular to v1

  • Rate of change of intensity is curvature of an image


Hessian 2 eigenvectors values1
Hessian (2)Eigenvectors / -values

3v3

Eigenvalue of Hessian of a pixel gives information about the local structure (e.g. tube)

2v2

1v1


Tubular structure filter
Tubular structure filter

Frangi

Distinguishes blob-like structures, cannot distinguish between plate and line-like structures

Distinguishes between line and plate-like structures

Filters noise.


Tubular structure filters
Tubular structure filters

Frangi

Wink et al. α = β = 0.5 and c = 0.25 Max[Greyvalue]

Olabarriagaet al. α = 1, β = 0.1 and c > 100

=> better discrimination center / periphery vessel

Chapman et al. α = 0.5, β = ∞ and c > 0.25 Max[Greyvalue]

=> drops RB-term

=> better discrimination vessel / background


Tubular structure filters1
Tubular structure filters

HessDiff

Better discrimination background / vessel


Tubular structure filters2
Tubular structure filters

  • Hessian is calculated at multiscale (2.6    18.6)

  • Scale with highest response is scale of a voxel

  • Highest response is in center vessel

  • Hessian is scaled with 2


Algorithm1
Algorithm

Create feature space

Feature space with:

  • Center of vessel lower value then peripheryof vessel

  • Vessel lower value then background

Find Minimum Cost Path with Dijkstra’s algorithm


Invert pixel values 1 pixelvalue
Invert pixel values(1/pixelvalue)

  • Response highest at center of the vessel.

  • Minimal cost path needs lowest

  • Pixel values are inverted

1 / I


Minimal cost path
Minimal cost path

  • Select start and end point

  • Find minimal cost path in between

  • Dijkstra’s algorithm to find that minimal cost path


Dijkstra 2a
Dijkstra 2a

4

5

5

2

End

7

6

3

7

7

6

1

Begin

7

5

6

10

20

3


Dijkstra 2b
Dijkstra 2b

Find min neighbours (green)

Add it to investigated nodes (red).

Remember predecessor

.

4

5

5

2 (1) [6]

.

.

7

6

3

7

7

6

1

7

5 (1) [7]

.

6

8

20

3 (1) [8]


Dijkstra 2c
Dijkstra 2c

Add neighbours (green)

Remember predecessor

.

.

4

4 (2) [11]

4

5

5

2 (1) [6]

2 (1)

.

7

6

3

3

7

7

7

6

1

7

5

5 (1) [7]

.

6

8

20

3 (1) [8]


Dijkstra 2d
Dijkstra 2d

Find min neighbours (green)

Add it to investigated nodes (red).

Remember predecessor

.

.

4 (2) [11]

4

5

5

2 (1) [6]

2 (1)

.

7

6

3

3

7

7

7

1

6

7

5 (1) [7]

.

6

8

20

3 (1) [8]


Dijkstra 2e
Dijkstra 2e

  • Add neighbours (green)

  • Remember predecessor

    Update predecessor and cost if node already in neighbours

.

.

.

4 (5) [10]

4

5

5

2 (1) [6]

2 (1)

.

7 (5) [13]

7

6

3

3

7

7

7

1

6

7

5

5 (1)

5 (1) [7]

.

6

8

20

3 (1) [8]


Dijkstra 2f
Dijkstra 2f

Find min neighbours (green)

Add it to investigated nodes (red).

Remember predecessor

.

.

.

4 (5) [10]

4

5

5

2 (1) [6]

2 (1)

.

7 (5) [13]

7

5

3

3

7

7

7

1

6

7

5

5 (1)

5 (1) [7]

.

6

8

20

3 (1) [8]


Dijkstra 2g
Dijkstra 2g

Add neighbours (green)

Remember predecessor

.

.

.

4 (5) [10]

4

5

5

2 (1) [6]

2 (1)

.

7 (5) [13]

7

6

3

3

7

7

.

7

1

6

7

5 (1) [7]

5

5 (1)

.

6 (3) [28]

8

20

3 (1) [8]


Dijkstra 2h
Dijkstra 2h

Find min neighbours (green)

Add it to investigated nodes (red).

Remember predecessor

.

.

.

4 (5) [10]

4

5

5

2 (1) [6]

2 (1)

.

7 (5) [13]

6

3

3

7

7

.

7

1

6

7

5 (1) [7]

5

5 (1)

.

6 (3) [28]

8

20

3

3 (1) [8]


Dijkstra 2i
Dijkstra 2i

.

Goal!

.

.

4 (5) [10]

4 (5)

5

5

2 (1) [6]

2 (1)

.

7

7 (5) [13]

6

3

3

7

7

.

7

1

6

7

5 (1) [7]

5

5 (1)

.

6 (4) [17]

8

20

3 (1) [8]

3


Dijkstra 2i1
Dijkstra 2i

.

Backtrack: 7 => 5 => 1

.

.

4 (5) [10]

4 (5)

5

5

2 (1) [6]

2 (1)

.

.

7

7 (5) [13]

6

3

3

7

7

.

7

1

6

7

5

5 (1) [7]

5 (1)

.

6 (4) [17]

8

20

3

3 (1) [8]


Minimal cost path1
Minimal cost path

Defined cost:

V(i) is the voxel value

a is weight factor

i is ith voxel of the path


Minimal cost path2
Minimal cost path

Defined cost:

V(i) is the voxel value

a is weight factor

i is ith voxel of the path

Higher values of a

=> Relative difference between

center and surrounding increases

=> Will follow minimum better instead of shortest path


Algorithm2
Algorithm

Calculate response to (Frangi’s) filter

Get Eigenvalues of the Hessian Matrix

Invert pixel values (1/pixelvalue)

Find minimum cost path with dijkstra’s algorithm


Experiments
Experiments

  • Original method on different datasets

  • On worst performing dataset

    • a = 1

    • a = 5

  • Different filters

    • Frangi with different parameters

      • Wink

      • Olabarriaga

      • Chapman

    • HessDiff


Result cpr
Result (CPR)

3 Datasets

(1) LAD (2) RCx (3) LAD


Different filters and cost functions cpr proximal part
Different filters and cost functions (CPR) Proximal part

Wink a=1

Wink a=5

Chapman a=1

Chapman a=5


Different filters and cost functions cpr proximal part1
Different filters and cost functions (CPR) Proximal part

Olabarriagaa=5

Olabarriaga a=1


Olabarriaga (a=5)

Wink (a=5)

Different filters: Wink and Olabarriaga

Sagittal slice at the stenosis

Frangi’s filter with

Wink’s constants

Frangi’s filter with

Olabarriaga‘s constants


Different filters: Wink and Olabarriaga

Sagittal slice heart wall


Different filters and cost functions cpr proximal part2
Different filters and cost functions (CPR) Proximal part

HessDiff a=1


Different filters h essdiff
Different filters: HessDiff

Low response at stenosis

Lot of false positives

Strong false positives at the heart wall

Response

CT


Different filters and cost functions
Different filters and cost functions

Distal part

a=1 a= 5

a=1 a= 5

a=1 a= 5

a=1 a= 5

Chapman

Wink

Olabarriaga

HessDiff


Different filters
Different filters

Doesn’t follow vessel at heart wall

Wink

Grey

Olabarriaga

Chapman

HessDiff


Multiscale wink
Multiscale Wink

  • Vessel response at low scale

  • Heart wall response at high scale

  • Heart wall response is stronger

σ= 2.6

σ= 6

σ= 10

σ= 16

σ= All

Grey value


Different cost function
Different cost function

a=1 and a=5

a=1

  • α = 5 vs. α =1

  • Investigates nodes in smaller area

    • Less computations

    • More able to follow local minima

    • Less able to pass local maxima (stenosis)


Discussion
Discussion

  • Used scales were high (2.6    18.6)

    • High responses of the heart wall => bad centerline extraction

  • HessDiff and Olabarriaga track the centerline badly:

    • Low response at stenosis.

    • HessDiff lot of false positive response

  • Wink and Chapman track the centerline excellent.


Conclusion
Conclusion

  • The centerline is tracked in most cases (more or less) accurate

  • Wink and Chapman are best filters.

  • They can even coop with a stenosis.

  • It returns to the center even if it gets outside the vessel (robust)

  • Different cost functions yield different results:

    • High power more precise in details and faster.

    • Low power more robust and slower.


Further research
Further research

  • Smaller scales might improve results

  • Use Wink’s constants



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