Perceptual Grouping: The Closure of Gapswithin Elongated Structures in Medical Images

Renske de BoerMarch 23rd, 2006

Committee:

prof. dr. ir. B.M. ter Haar Romenyprof. dr. ir. F.N. van de Vossedr. L.M.J. Florackdr. ir. R. Duitsir. E.M. Franken

Contents

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

1. Introduction2. Orientation scores

• Cake kernels

3. Linear operations• G-Convolution• Stochastic completion

kernel

4. Non-linear operations• Probability density

function• 5 non-linear operations

5. Experiments• Measures for gap filling• Non-linear operations• Noise robustness• Probability density

function• Examples artificial

images• Examples medical

images

6. Conclusion• Conclusions• Recommendations

Introduction

http://www.cps.utexas.edu/Research/Geisler/Projects/perceptualgrouping.html

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Introduction

Bosking et al., 1997Ts’o et al., 1990

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Orientation scores

2D image f(x,y) ‘2D + orientation’ score Uf(x,y,)

with position (x,y) and local orientation .

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Orientation scores

with and the rotation matrix:

Orientation score is obtained by wavelet transformation of image:

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Reconstruction of image is possible.

Orientation scores

Advantage: easy reconstruction of image.

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Different possibilities for kernel

For example cake kernels

Linear operations

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Normal convolution

G-convolution, where G is the Euclidean motion group

Linear operations

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Stochastic completion kernel creates probability density field for line continuation.

Linear operations

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Filling gaps in line structures

Non-linear operations

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Probability density function (PDF)

Stochastic completion kernel should be applied to an orientation score containing the probability density of lines in the image.

• Probability is obtained by creating 2D-histogram of 2 features: gray values of the image and orientation score values. Only for line structures.

• The Bayesian theorem is used to calculate the desired probability.

• PDF is estimated by kernel density estimation of the histogram.

Non-linear operations

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

1 Orientation score thinning

Thinning with a certain number of pixels of the orientation score in both the spatial dimensions and the orientation dimension.

2 Angular thinning

The two orientations that give maximum orientation score responses get values, all other orientations are put to zero.

Non-linear operations

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

3 Pyramid thinning

Non-linear operations

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

4 Normal power enhancement

5 Power enhancement

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Measures for gap filling:

• mean fillingRatio of mean gap filling and mean of line structure.

• min fillingRatio of minimal gap filling

and mean line structure.

• background ratioRatio of mean background

and mean of line structure and gap.

• fill backRatio of mean gap filling and mean background.

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Evaluation of non-linear operations

1 Orientation score thinning

4 Normal power enhancement

5 Power enhancement

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Noise robustnessNSR = 0.5 NSR = 2.5 NSR = 5.0

N = 0.5

N = 1.5

N = 2.5

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Noise robustness

NSR is noise to signal

ratio

N is scale of Gaussian

correlation of noise

Filling measure

Corr

ela

tion o

f nois

e

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Obtained PDFUsed ground truth

Probability density function

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Examples of artificial images

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Examples of artificial images

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

– Examples of medical images

Original After preprocessing Result

[1]

[2]

Experiments

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

– Examples of medical images

Original After preprocessing Result

[3]

Conclusion

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Conclusions

• New method is successfully generated.

• Method performs reasonable on lower noise levels.

• PDF detects line structures but filling of gap is weak due to enlargement of the gap.

• Larger gaps or high curvature result in weaker filling.

• Some undesired filling might be caused by line structures that are close together and are not part of the same line.

• Medical images need a lot of preprocessing to prevent background artifacts.

Overall the method gives reasonable results for filling gaps and enhancing line structures.

Conclusion

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Recommendations

• Deblurring afterwards is necessary!

• Include curvature in stochastic completion kernel to fill gaps in lines with high curvature.

• Adjust width of cake kernels to detect lines at different scales.

• Optimize parameters of stochastic completion kernel.

• Find a better non-linear enhancement operation.

• Improve PDF results by creating extra PDF for line endings.

• Preprocess (medical) images!

Acknowledgment

Introduction

Orientation scores

Linear operations

Non-linear operations

Experiments

Conclusion

Thanks to:

Committee, especially Erik, Remco and Markus.

Family, friends and housemates.

Questions?

[1] http://www.vistaradiology.com/NewFiles/Ultrasound.html

[2] J.J. Staal, M.D. Abramoff, M. Niemeijer, M.A. Viergever, and B. van Ginneken. Ridge based vessel segmentation in color images of the retina. IEEE Transactions on Medical Imaging, 23(4): 501–509, 2004.

[3] Philips StentBoost