Anisotropic diffusion of multivalued images with applications to color filtering

A general framework for anisotropic diffusion of multivalued images is presented. We propose an evolution equation where, at each point in time, the directions and magnitudes of the maximal and minimal rate of change in the vector-image are first evaluated. These are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric. Then, the image diffuses via a system of coupled differential equations in the direction of minimal change. The diffusion "strength" is controlled by a function that measures the degree of dissimilarity between the eigenvalues. We apply the proposed framework to the filtering of color images represented in CIE-L*a*b* space.

[1]  David A. Huffman,et al.  A method for the construction of minimum-redundancy codes , 1952, Proceedings of the IRE.

[2]  W D Wright,et al.  Color Science, Concepts and Methods. Quantitative Data and Formulas , 1967 .

[3]  R. Nevatia.  A Color Edge Detector and Its Use in Scene Segmentation , 1977 .

[4]  Silvano Di Zenzo,et al.  A note on the gradient of a multi-image , 1986, Comput. Vis. Graph. Image Process..

[5]  Allen Gersho,et al.  Image Compression Based On Vector Quantization With Finite Memory , 1987 .

[6]  Ian H. Witten,et al.  Arithmetic coding for data compression , 1987, CACM.

[7]  Nasser M. Nasrabadi,et al.  Image coding using vector quantization: a review , 1988, IEEE Trans. Commun..

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

[9]  Nasser M. Nasrabadi,et al.  Image compression using address-vector quantization , 1990, IEEE Trans. Commun..

[10]  Y. Feng,et al.  A dynamic finite-state vector quantization scheme , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[11]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[12]  Aldo Cumani,et al.  Edge detection in multispectral images , 1991, CVGIP Graph. Model. Image Process..

[13]  Mark Nitzberg,et al.  Nonlinear Image Filtering with Edge and Corner Enhancement , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Kou-Hu Tzou.  High-order entropy coding for images , 1992, IEEE Trans. Circuits Syst. Video Technol..

[15]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[16]  Joan L. Mitchell,et al.  JPEG: Still Image Data Compression Standard , 1992 .

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

[18]  Chaur-Heh Hsieh,et al.  Image compression using finite-state vector quantization with derailment compensation , 1993, IEEE Trans. Circuits Syst. Video Technol..

[19]  Chaur-Heh Hsieh,et al.  New Fuzzy Clustering Algorithms For Vector Quantization Of Images , 1993, IEEE 1993 International Conference on Consumer Electronics Digest of Technical Papers.

[20]  Guido Gerig,et al.  Vector-Valued Diffusion , 1994, Geometry-Driven Diffusion in Computer Vision.

[21]  Antonin Chambolle,et al.  Partial differential equations and image processing , 1994, Proceedings of 1st International Conference on Image Processing.

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

[23]  Guillermo Sapiro,et al.  Color Snakes , 1997, Comput. Vis. Image Underst..