Multiresolution segmentation of natural images: from linear to nonlinear scale-space representations

In this paper, we introduce a framework that merges classical ideas borrowed from scale-space and multiresolution segmentation with nonlinear partial differential equations. A nonlinear scale-space stack is constructed by means of an appropriate diffusion equation. This stack is analyzed and a tree of coherent segments is constructed based on relationships between different scale layers. Pruning this tree proves to be a very efficient tool for unsupervised segmentation of different classes of images (e.g., natural, medical, etc.). This technique is light on the computational point of view and can be extended to nonscalar data in a straightforward manner.

[1]  Milan Sonka,et al.  Image Processing, Analysis and Machine Vision , 1993, Springer US.

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

[3]  Max A. Viergever,et al.  Probabilistic Multiscale Image Segmentation , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Tony Lindeberg,et al.  Edge Detection and Ridge Detection with Automatic Scale Selection , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[5]  Max A. Viergever,et al.  Comparison of multiscale representations for a linking-based image segmentation model , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[6]  Tony F. Chan,et al.  A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model , 2002, International Journal of Computer Vision.

[7]  N. Na THE SCIENCE OF COLOR , 1952 .

[8]  Max A. Viergever,et al.  Linear scale-space , 1994, Journal of Mathematical Imaging and Vision.

[9]  Stanley Osher,et al.  Total variation based image restoration with free local constraints , 1994, Proceedings of 1st International Conference on Image Processing.

[10]  Rolf D. Henkel,et al.  Segmentation in Scale Space , 1995, CAIP.

[11]  Jan-Olof Eklundh,et al.  Scale detection and region extraction from a scale-space primal sketch , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[12]  Tony Lindeberg Edge Detection and Ridge Detection with Automatic Scale Selection , 2004, International Journal of Computer Vision.

[13]  J. Weickert Scale-Space Properties of Nonlinear Diffusion Filtering with a Diffusion Tensor , 1994 .

[14]  P. Lions,et al.  Axioms and fundamental equations of image processing , 1993 .

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

[16]  Tony Lindeberg,et al.  Scale-space theory : A framework for handling image structures at multiple scales , 1996 .

[17]  Taein Lee,et al.  Active contour models , 2005 .

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

[19]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[20]  Anil K. Jain,et al.  Unsupervised texture segmentation using Gabor filters , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[21]  G. Matheron Random Sets and Integral Geometry , 1976 .

[22]  Ron Kimmel,et al.  A general framework for low level vision , 1998, IEEE Trans. Image Process..

[23]  Max A. Viergever,et al.  Heuristic Linking Models in Multiscale Image Segmentation , 1997, Comput. Vis. Image Underst..

[24]  Milan Sonka,et al.  Image processing analysis and machine vision [2nd ed.] , 1999 .

[25]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[26]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  J. Koenderink The structure of images , 2004, Biological Cybernetics.

[28]  S. Mallat A wavelet tour of signal processing , 1998 .

[29]  B. M. Ter,et al.  Introduction to Scale-Space Theory : Multiscale Geometric Image Analysis , 1997 .

[30]  Max A. Viergever,et al.  Blurring strategies for image segmentation using a multiscale linking model , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[31]  Pierre Vandergheynst,et al.  Segmentation of natural images using Scale-Space representations: A linear and a non-linear approach , 2002, 2002 11th European Signal Processing Conference.

[32]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.

[33]  N. Zheng,et al.  Variation-Based Image Segmentation and its Multiscale Realizations , 2001 .

[34]  Thomas S. Huang,et al.  Image processing , 1971 .

[35]  Tony Lindeberg,et al.  Scale-Space for Discrete Signals , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[36]  F. Ziliani,et al.  Unsupervised segmentation using modified pyramidal linking approach , 1998 .

[37]  Luc Florack,et al.  Hierarchical Pre-Segmentation without Prior Knowledge , 2001, ICCV.

[38]  Tony Lindeberg Kth Scale-space: A framework for handling image structures at multiple scales , 1996 .

[39]  Mohamed A. Deriche,et al.  Scale-Space Properties of the Multiscale Morphological Dilation-Erosion , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

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

[41]  Michael Unser,et al.  Texture classification and segmentation using wavelet frames , 1995, IEEE Trans. Image Process..

[42]  Koen L. Vincken,et al.  Probabilistic multiscale image segmentation by the hyperstack , 1995 .

[43]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[44]  Guillermo Sapiro,et al.  Geodesic Active Contours , 1995, International Journal of Computer Vision.

[45]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[46]  Jean-Michel Morel,et al.  A review of P.D.E. models in image processing and image analysis , 2002 .