Perceptual grouping: Curvature enhanced closure of elongated structures By Gijs Huisman Committee: prof. dr. ir. B.M. ter Haar Romeny prof. dr. ir. P. Hilbers dr. L.M.J. Florack dr. ir. R. Duits ir. E.M. Franken

2/30 Content 1.Introduction 2.Orientation scores Cake kernels 3.G-convolution Stochastic completion kernel Adaptive G-Convolution 4.Mode line extraction Theory 5.Non-linear operations Advection based enhancement 3 non-linear operations 6.Curvature estimation 4 methods Test results 7.Experiments Mode line extraction Increased gap filling Improved smoothness Adaptive shooting Examples medical images 8.Conclusion Conclusions Recommendations

3/30 Introduction

4/30 Orientation score An orientation score has 2 spatial dimensions and 1 orientation dimension

5/30 Orientation Score An orientation score is obtained by wavelet transformation of an image Where and Reconstruction of an image is possible by an inverse wavelet transform

6/30 Orientation score Cake Kernels The waveletis defined by: The function is defined by B- splines: Main advantage is easily adaptive kernels with good reconstruction properties is defined by a 2D gauss

7/30 G-convolution Normal convolution G-convolution

8/30 Stochastic Completion Kernel G-convolution The used kernel depicts a probability density function for the continuation of a line kernel in an orientation score.

9/30 G-convolution Stochastic Completion Kernel Gap closing operation with the stochastic completion kernel

10/30 G-convolution Making the G-convolution adaptive means that the kernel properties change with the position in the orientation score. Kernels are adapted to fit the local curvature Adaptive

11/30 Mode line extraction Very often the lines itself are demanded instead of an enhanced image. Any point is part of a local mode line if and at the point Lines in the spatial plane are 3D ridges in an orientation score.

12/30 Non-Linear Operations Enhancement can be done before and after an G-convolution Non ideal cake kernel response: DC-extraction MIN-Extraction Erosion Advection

13/30 Non-Linear Operations DC-Extraction MIN-Extraction Erosion

14/30 Non-Linear Operations Advectio n A force field directed towards the local mode lines: By means of advection the score can now be sharpened

15/30 Non-Linear Operations Results Erosion DC-extractionMIN-extraction Straight Curved Advection Intensity No preprocessing

16/30 Curvature estimation 1.Inner product stochastic completion kernel 2.Inner product Gaussian based kernel 3.Region estimation 4.Hessian based method

17/30 Curvature estimation Results Stochastic Gaussian Region Hessian

18/30 Curvature estimation Results Curvature measurement on a cross section of the circle line Stochastic Gaussian Regio n Hessian

19/30 Curvature estimation Results Stochastic Gaussian Region Hessian

20/30 Experiments Mode line extraction

21/30 Experiments Mode line extraction

22/30 Experiments Mode line extraction Mode line extraction on artificial image

23/30 Experiments Increased gap filling Plane DCMin Plane DCMin

24/30 Experiments Improved smoothness Straight Curved

25/30 Experiments Adaptive shooting Original imageOrientation score Straight shooting result Curvature estimate Enhanced image

26/30 Experiments Adaptive shooting OriginalStraight shooting (1)Curved Shooting (2)Curved Shooting (3) Mean Filling Method Min Filling Method

27/30 Experiments Examples Medical images Blood vessel extraction on images of the human retina Original Threshold Straight shooting Blood vessels

28/30 Experiments Examples Medical images Straight shooting Adaptive shooting

29/30 Conclusion Curvature enhanced shooting does improve the gap filling Successful method of curve extraction Good method to estimate the curvature Improve the accuracy of the curve extraction method Better numerical implementation advection enhancement Devise a method to extract the correct curves (e.g. fast marching) Better tuning of the cake kernel parameters Conclusions Recommendations

30/30 Questions?