Non-linear Diffusion for Interactive Multi-scale Watershed Segmentation

Multi-scale watersheds have proven useful for interactive segmentation of 3D medical images. For simpler segmentation tasks, the speed up compared to manual segmentation is more than one order of magnitude. Even where the image evidence does not very strongly support the task, the interactive watershed segmentation provides a speed up of a factor two. In this paper we evaluate a broad class of non-linear diffusion schemes for the purpose of interactively segmenting gray and white matter of the brain in T1-weighted MR images. Through a new scheme GAN, we show that diffusion similar to the nonlinear Perona-Malik scheme is superior to the other evaluated diffusion schemes. This provides a speed up factor of two compared to the linear diffusion scheme.

[1]  Alan C. Evans,et al.  An Extensible MRI Simulator for Post-Processing Evaluation , 1996, VBC.

[2]  Peter Johansen,et al.  Gaussian Scale-Space Theory , 1997, Computational Imaging and Vision.

[3]  Bart M. ter Haar Romeny,et al.  Geometry-Driven Diffusion in Computer Vision , 1994, Computational Imaging and Vision.

[4]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[5]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[7]  Niklas Nordström,et al.  Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection , 1990, Image Vis. Comput..

[8]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[9]  John M. Gauch,et al.  Image segmentation and analysis via multiscale gradient watershed hierarchies , 1999, IEEE Trans. Image Process..

[10]  D. Louis Collins,et al.  Design and construction of a realistic digital brain phantom , 1998, IEEE Transactions on Medical Imaging.

[11]  John M. Gauch,et al.  Multiresolution Analysis of Ridges and Valleys in Grey-Scale Images , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Mads Nielsen,et al.  Generic Events for the Gradient Squared with Application to Multi-Scale Segmentation , 1997, Scale-Space.

[13]  Alan C. F. Colchester,et al.  Superficial and deep structure in linear diffusion scale space: isophotes, critical points and separatrices , 1995, Image Vis. Comput..

[14]  James Damon,et al.  Generic Properties of Solutions to Partial Differential Equations , 1997 .

[15]  S. Webb.  The Physics of Medical Imaging , 1990 .

[16]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[17]  Max A. Viergever,et al.  Nonlinear Multiscale Representations for Image Segmentation , 1997, Comput. Vis. Image Underst..

[18]  M. Gage,et al.  An isoperimetric inequality with applications to curve shortening , 1983 .

[19]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.

[20]  O. Witte,et al.  Functional Mapping of the Human Brain , 2000 .

[21]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[22]  Jean-Michel Morel,et al.  Morphological Approach to Multiscale Analysis: From Principles to Equations , 1994, Geometry-Driven Diffusion in Computer Vision.

[23]  Stephen M. Pizer,et al.  A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Joachim Weickert,et al.  Anisotropic diffusion in image processing , 1996 .

[25]  Tony Lindeberg,et al.  Scale-Space Theory in Computer Vision , 1993, Lecture Notes in Computer Science.