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Perceptual grouping: Curvature enhanced closure of elongated structures

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. Content. Introduction. Orientation score.

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Perceptual grouping: Curvature enhanced closure of elongated structures

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  1. Perceptual grouping: Curvature enhanced closure of elongated structures By Gijs Huisman Committee: prof. dr. ir. B.M. ter Haar Romenyprof. dr. ir. P. Hilbersdr. L.M.J. Florackdr. ir. R. Duitsir. E.M. Franken

  2. Content

  3. Introduction

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

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

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

  7. G-convolution Normal convolution G-convolution

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

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

  10. G-convolution Adaptive 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

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

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

  13. Non-Linear Operations • DC-Extraction • MIN-Extraction • Erosion

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

  15. Non-Linear Operations Results Erosion Advection No preprocessing MIN-extraction DC-extraction Straight Curved Intensity

  16. Curvature estimation • Inner product stochastic completion kernel • Inner product Gaussian based kernel • Region estimation • Hessian based method

  17. Curvature estimation Results Stochastic Gaussian Region Hessian

  18. Curvature estimation Results Curvature measurement on a cross section of the circle line Stochastic Gaussian Region Hessian

  19. Curvature estimation Results Stochastic Gaussian Region Hessian

  20. Experiments Mode line extraction

  21. Experiments Mode line extraction

  22. Experiments Mode line extraction Mode line extraction on artificial image

  23. Plane DC Min Plane DC Min Experiments Increased gap filling

  24. Experiments • Improved smoothness Straight Curved

  25. Experiments Adaptive shooting Straight shooting result Original image Orientation score Curvature estimate Enhanced image

  26. Mean Filling Min Filling 1.5 1 0.5 0 3 2 1 Method Method 0 3 1 2 1 2 3 Experiments Adaptive shooting Original Straight shooting (1) Curved Shooting (2) Curved Shooting (3)

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

  28. Experiments • Examples Medical images Adaptive shooting Straight shooting

  29. Conclusion Conclusions • Curvature enhanced shooting does improve the gap filling • Successful method of curve extraction • Good method to estimate the curvature Recommendations • 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

  30. Questions?

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