centerline detection of cardiac vessels in ct images martin korevaar n.
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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.
slide5
CPR
  • Visualization method

Images from: Armin Kanitsar in IEEE Viz. 2002 Okt

slide6
CPR
  • Visualization method
  • Maps 3D path on 2D image

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

slide7
CPR
  • Visualization method
  • Maps 3D path on 2D image
  • Artery can be investigated from just 1 image
slide8
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

slide38

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 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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