Representing images by means of interval-valued fuzzy sets. Application to stereo matching

Stereo matching tries to find correspondences between locations in a pair of displaced images of the same scene in order to extract the underlying depth information. Pixel correspondence estimation suffers from occlusions, noise or bias. In this work, we introduce a novel approach to represent images by means of interval-valued fuzzy sets to overcome the uncertainty due to the above mentioned problems. Our aim is to take advantage of this representation in the stereo matching algorithm. The image interval-valued fuzzification process that we propose is based on image segmentation in a different way to the common use of segmentation in stereo vision. We introduce interval-valued fuzzy similarities to compare windows whose pixels are represented by intervals. In the experimental analysis we show the goodness of this representation in the stereo matching problem. The new representation together with the new similarity measure that we introduce shows a better overall behavior with respect to other very well-known methods.

[1]  R. Mesiar,et al.  Aggregation operators: new trends and applications , 2002 .

[2]  Humberto Bustince,et al.  Restricted equivalence functions , 2006, Fuzzy Sets Syst..

[3]  Li Hong,et al.  Segment-based stereo matching using graph cuts , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[4]  Chris Cornelis,et al.  Advances and challenges in interval-valued fuzzy logic , 2006, Fuzzy Sets Syst..

[5]  Emanuele Trucco,et al.  SSD Disparity Estimation for Dynamic Stereo , 1996, BMVC.

[6]  Ramin Zabih,et al.  Non-parametric Local Transforms for Computing Visual Correspondence , 1994, ECCV.

[7]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[8]  Francisco Herrera,et al.  Fuzzy Sets and Their Extensions: Representation, Aggregation and Models - Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision , 2007, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models.

[9]  Carlos Lopez-Molina,et al.  Interval-Valued Restricted Equivalence Functions Applied on Clustering Techniques , 2009, IFSA/EUSFLAT Conf..

[10]  Humberto Bustince,et al.  On the relevance of some families of fuzzy sets , 2007, Fuzzy Sets Syst..

[11]  Reinhard Männer,et al.  Calculating Dense Disparity Maps from Color Stereo Images, an Efficient Implementation , 2004, International Journal of Computer Vision.

[12]  Humberto Bustince,et al.  Semiautoduality in a restricted family of aggregation operators , 2007, Fuzzy Sets Syst..

[13]  Laurent Moll,et al.  Real time correlation-based stereo: algorithm, implementations and applications , 1993 .

[14]  Humberto Bustince,et al.  Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets , 1996, Fuzzy Sets Syst..

[15]  Gaspar Mayor,et al.  Aggregation Operators , 2002 .

[16]  Francisco Herrera,et al.  Fuzzy Sets and Their Extensions: Representation, Aggregation and Models , 2008 .

[17]  Bohdan S. Butkiewicz,et al.  Features Stereo Matching Based on Fuzzy Logic , 2009, IFSA/EUSFLAT Conf..

[18]  Darius Burschka,et al.  Advances in Computational Stereo , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Vicenç Torra,et al.  Aggregation operators , 2007, Int. J. Approx. Reason..

[20]  Richard Szeliski,et al.  A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms , 2001, International Journal of Computer Vision.

[21]  Humberto Bustince,et al.  Image thresholding using restricted equivalence functions and maximizing the measures of similarity , 2007, Fuzzy Sets Syst..

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

[23]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[24]  Fabrizio Russo,et al.  FIRE operators for image processing , 1999, Fuzzy Sets Syst..

[25]  Chris Cornelis,et al.  On the representation of intuitionistic fuzzy t-norms and t-conorms , 2004, IEEE Transactions on Fuzzy Systems.

[26]  J. Montero,et al.  A Survey of Interval‐Valued Fuzzy Sets , 2008 .

[27]  Federico Tombari,et al.  Segmentation-Based Adaptive Support for Accurate Stereo Correspondence , 2007, PSIVT.

[28]  B. Cyganek.  An Introduction to 3D Computer Vision Techniques and Algorithms , 2009 .

[29]  Ivan Kalaykov,et al.  Measures Based on Fuzzy Similarity for Stereo Matching of Color Images , 2006, Soft Comput..

[30]  Changming Sun,et al.  Fast Stereo Matching Using Rectangular Subregioning and 3D Maximum-Surface Techniques , 2002, International Journal of Computer Vision.

[31]  Humberto Bustince,et al.  Automatic Histogram Threshold Using Fuzzy Measures , 2010, IEEE Transactions on Image Processing.

[32]  Andreas Klaus,et al.  Segment-Based Stereo Matching Using Belief Propagation and a Self-Adapting Dissimilarity Measure , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[33]  H. Bustince,et al.  Generation of interval-valued fuzzy and atanassov's intuitionistic fuzzy connectives from fuzzy connectives and from K α operators: Laws for conjunctions and disjunctions, amplitude , 2008 .