A minimum entropy approach to adaptive image polygonization

This paper introduces a novel adaptive image segmentation algorithm which represents images by polygonal segments. The algorithm is based on an intuitive generative model for pixel intensities and its associated cost function which can be effectively optimized by a hierarchical triangulation algorithm. A triangular mesh is iteratively refined and reorganized to extract a compact description of the essential image structure. After analyzing fundamental convexity properties of our cost function, we adapt an information-theoretic bound to assess the statistical significance of a given triangulation step. The bound effectively defines a stopping criterion to limit the number of triangles in the mesh, thereby avoiding undesirable overfitting phenomena. It also facilitates the development of a multiscale variant of the triangulation algorithm, which substantially improves its computational demands. The algorithm has various applications in contextual classification, remote sensing, and visual object recognition. It is particularly suitable for the segmentation of noisy imagery.

[1]  J. Wade Davis,et al.  Statistical Pattern Recognition , 2003, Technometrics.

[2]  Harry Shum,et al.  Image segmentation by data driven Markov chain Monte Carlo , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[3]  Robert D. Nowak,et al.  Unsupervised progressive parsing of Poisson fields using minimum description length criteria , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).

[4]  Stephen V. Stehman,et al.  Selecting and interpreting measures of thematic classification accuracy , 1997 .

[5]  Joachim M. Buhmann,et al.  Stochastic Algorithms for Exploratory Data Analysis: Data Clustering and Data Visualization , 1998, Learning in Graphical Models.

[6]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[7]  Robert D. Nowak,et al.  Coding theoretic approach to image segmentation , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[8]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[9]  Joachim M. Buhmann,et al.  Contextual classification by entropy-based polygonization , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[10]  S. Quegan,et al.  Understanding Synthetic Aperture Radar Images , 1998 .

[11]  Joachim M. Buhmann,et al.  A New Contour-Based Approach to Object Recognition for Assembly Line Robots , 2001, DAGM-Symposium.

[12]  Ole Fogh Olsen,et al.  Multi-Scale Watershed Segmentation , 1997, Gaussian Scale-Space Theory.

[13]  Yvan G. Leclerc,et al.  Constructing simple stable descriptions for image partitioning , 1989, International Journal of Computer Vision.

[14]  David H. Douglas,et al.  ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE , 1973 .

[15]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[16]  D. Donoho.  On Minimum Entropy Segmentation , 1994 .

[17]  Alan L. Yuille,et al.  Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Linda G. Shapiro,et al.  Computer and Robot Vision , 1991 .

[19]  Arnold W. M. Smeulders,et al.  Combining region splitting and edge detection through guided Delaunay image subdivision , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[20]  Urs Ramer,et al.  An iterative procedure for the polygonal approximation of plane curves , 1972, Comput. Graph. Image Process..

[21]  Jianhua Lin,et al.  Divergence measures based on the Shannon entropy , 1991, IEEE Trans. Inf. Theory.

[22]  Jitendra Malik,et al.  Contour and Texture Analysis for Image Segmentation , 2001, International Journal of Computer Vision.

[23]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[24]  Joachim M. Buhmann,et al.  Histogram clustering for unsupervised segmentation and image retrieval , 1999, Pattern Recognit. Lett..

[25]  N. Pérez de la Blanca,et al.  Improving classical contextual classifications , 1998 .

[26]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[27]  Joachim M. Buhmann,et al.  On spatial quantization of color images , 2000, IEEE Trans. Image Process..

[28]  Miguel Ángel García,et al.  Approximation and Processing of Intensity Images with Dicontinuity-Preserving Adaptive Triangular Meshes , 2000, ECCV.

[29]  Joachim M. Buhmann,et al.  Unsupervised Texture Segmentation in a Deterministic Annealing Framework , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

[31]  Rachid Deriche,et al.  Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation , 2002, International Journal of Computer Vision.

[32]  Paul S. Heckbert,et al.  Survey of Polygonal Surface Simplification Algorithms , 1997 .

[33]  Emanuele Trucco,et al.  Computer and Robot Vision , 1995 .

[34]  Emanuele Trucco,et al.  Robust motion and correspondence of noisy 3-D point sets with missing data , 1999, Pattern Recognit. Lett..

[35]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[36]  Joachim M. Buhmann,et al.  A New Adaptive Algorithm for the Polygonization of Noisy Imagery , 2001 .