Constrained connectivity for hierarchical image partitioning and simplification

This paper introduces an image partitioning and simplification method based on the constrained connectivity paradigm. According to this paradigm, two pixels are said to be connected if they satisfy a series of constraints defined in terms of simple measures such as the maximum gray-level differences over well-defined pixel paths and regions. The resulting connectivity relation generates a unique partition of the image definition domain. The simplification of the image is then achieved by setting each segment of the partition to the mean value of the pixels falling within this segment. Fine to coarse partition hierarchies (and, therefore, images of increasing degree of simplification) are produced by varying the threshold value associated with each connectivity constraint. The paper also includes a generalization to multichannel images, application examples, a review of related image segmentation techniques, and pseudocode for an implementation based on queue and stack data structures.

[1]  YANG WANG,et al.  On parameter-dependent connected components of gray images , 1996, Pattern Recognit..

[2]  Shigeo Abe DrEng.  Pattern Classification , 2001, Springer London.

[3]  Xin He,et al.  Parallel Algorithms for Gray-Scale Digitized Picture Component Labeling on a Mesh-Connected Computer , 1994, J. Parallel Distributed Comput..

[4]  Yll Haxhimusa,et al.  Grouping and segmentation in a hierarchy of graphs , 2004, IS&T/SPIE Electronic Imaging.

[5]  Azriel Rosenfeld,et al.  Fuzzy Digital Topology , 1979, Inf. Control..

[6]  José Crespo,et al.  The flat zone approach: A general low-level region merging segmentation method , 1997, Signal Process..

[7]  Charles T. Zahn,et al.  Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters , 1971, IEEE Transactions on Computers.

[8]  Azriel Rosenfeld,et al.  The fuzzy geometry of image subsets , 1984, Pattern Recognit. Lett..

[9]  Philippe Salembier,et al.  Connected operators and pyramids , 1993, Optics & Photonics.

[10]  Pierre Soille,et al.  Morphological image compositing , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Ulisses Braga-Neto,et al.  Grayscale level connectivity: theory and applications , 2004, IEEE Transactions on Image Processing.

[12]  Luc Vincent,et al.  Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  G. Coray,et al.  Order independence in local clustering algorithms , 1975 .

[14]  Yee Leung,et al.  Clustering by Scale-Space Filtering , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[16]  Makoto Nagao,et al.  Region extraction and shape analysis in aerial photographs , 1979 .

[17]  Andrew Mehnert,et al.  An improved seeded region growing algorithm , 1997, Pattern Recognit. Lett..

[18]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Richard M. Leahy,et al.  An Optimal Graph Theoretic Approach to Data Clustering: Theory and Its Application to Image Segmentation , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Morris Goldberg,et al.  Hierarchy in Picture Segmentation: A Stepwise Optimization Approach , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Hervé Le Men,et al.  The hierarchy of the cocoons of a graph and its application to image segmentation , 2003, Pattern Recognit. Lett..

[22]  Azriel Rosenfeld,et al.  On connectivity properties of grayscale pictures , 1981, Pattern Recognit..

[23]  Petros Maragos,et al.  Nonlinear Scale-Space Representation with Morphological Levelings , 2000, J. Vis. Commun. Image Represent..

[24]  J. Gower,et al.  Minimum Spanning Trees and Single Linkage Cluster Analysis , 1969 .

[25]  R.P.H.M. Schoenmakers.  Integrated methodology for segmentation of large optical satellite images in land applications of remote sensing , 1995 .

[26]  Narendra Ahuja.  On detection and representation of multiscale low-level image structure , 1995, CSUR.

[27]  Ramesh C. Jain,et al.  Segmentation through Variable-Order Surface Fitting , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Theodosios Pavlidis,et al.  Segmentation of pictures and maps through functional approximation , 1972, Comput. Graph. Image Process..

[29]  Claude L. Fennema,et al.  Scene Analysis Using Regions , 1970, Artif. Intell..

[30]  Rangaraj M. Rangayyan,et al.  Adaptive-neighborhood histogram equalization for image enhancement , 1992, CVGIP Graph. Model. Image Process..

[31]  Petros Maragos,et al.  Morphological Scale-Space Representation with Levelings , 1999, Scale-Space.

[32]  Daniel P. Huttenlocher,et al.  Efficient Graph-Based Image Segmentation , 2004, International Journal of Computer Vision.

[33]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[34]  Tony Lindeberg,et al.  Effective Scale: A Natural Unit for Measuring Scale-Space Lifetime , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[35]  Pierre Soille,et al.  Morphological partitioning of multispectral images , 1996, J. Electronic Imaging.

[36]  Azriel Rosenfeld,et al.  A critical view of pyramid segmentation algorithms , 1990, Pattern Recognit. Lett..

[37]  Makoto Nagao,et al.  A Structural Analysis of Complex Aerial Photographs , 1980, Advanced Applications in Pattern Recognition.

[38]  Ulisses Braga-Neto,et al.  Alternating Sequential Filters by Adaptive-Neighborhood Structuring Functions , 1996, ISMM.

[39]  Ulisses De Mendonça Braga Neto,et al.  Alternating Sequential Filters by Adaptive-Neighborhood Structuring Functions , 1996 .

[40]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[41]  Silvana G. Dellepiane,et al.  Nonlinear image labeling for multivalued segmentation , 1996, IEEE Trans. Image Process..

[42]  J. P. Sutcliffe,et al.  On the logical necessity and priority of a monothetic conception of class, and on the consequent inadequacy of polythetic accounts of category and categorization , 1994 .

[43]  R. M. Cormack,et al.  A Review of Classification , 1971 .

[44]  Andrea Baraldi,et al.  Single linkage region growing algorithms based on the vector degree of match , 1996, IEEE Trans. Geosci. Remote. Sens..

[45]  Steven W. Zucker,et al.  Region growing: Childhood and adolescence* , 1976 .

[46]  Daniel P. Huttenlocher,et al.  Image segmentation using local variation , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[47]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[48]  Isabelle Bloch.  Fuzzy connectivity and mathematical morphology , 1993, Pattern Recognit. Lett..

[49]  Philippe Salembier,et al.  Flat zones filtering, connected operators, and filters by reconstruction , 1995, IEEE Trans. Image Process..

[50]  Peter Meer,et al.  Image Segmentation from Consensus Information , 1997, Comput. Vis. Image Underst..

[51]  G. Estabrook.  A mathematical model in graph theory for biological classification. , 1966, Journal of theoretical biology.

[52]  Pierre Soille,et al.  Iterative area filtering of multichannel images , 2007, Image Vis. Comput..

[53]  S. Tanimoto.  Pictorial feature distortion in a pyramid , 1976 .

[54]  Ming Li,et al.  Normalized quadtrees with respect to translations , 1982, Comput. Graph. Image Process..

[55]  Xin He,et al.  Parallel algorithms for gray-scale image component labeling on a mesh-connected computer , 1992, SPAA '92.

[56]  Theodosios Pavlidis,et al.  Picture Segmentation by a Tree Traversal Algorithm , 1976, JACM.

[57]  Francisco Sandoval Hernández,et al.  Pyramid segmentation algorithms revisited , 2006, Pattern Recognit..

[58]  Frank Nielsen,et al.  Statistical region merging , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[59]  Ulisses Braga-Neto,et al.  Object-based image analysis using multiscale connectivity , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[60]  Azriel Rosenfeld,et al.  Hierarchical Image Analysis Using Irregular Tessellations , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[61]  Silvana G. Dellepiane,et al.  Extraction of intensity connectedness for image processing , 1995, Pattern Recognit. Lett..