From Gestalt Theory to Image Analysis: A Probabilistic Approach

This book introduces the reader to a recent theory in Computer Vision yielding elementary techniques to analyse digital images. These techniques are inspired from and are a mathematical formalization of the Gestalt theory. Gestalt theory, which had never been formalized is a rigorous realm of vision psychology developped between 1923 and 1975. From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability and statistics, in the context of image analysis. The authors maintain a public software, MegaWave, containing implementations of most of the image analysis techniques developped in the book. The book is intended for researchers and engineers. It is mathematically self-contained and requires only the basic notions in probability and calculus.

[1]  Xiaoming Huo,et al.  Near-optimal detection of geometric objects by fast multiscale methods , 2005, IEEE Transactions on Information Theory.

[2]  Yann Gousseau,et al.  An A Contrario Decision Method for Shape Element Recognition , 2006, International Journal of Computer Vision.

[3]  H. C. Longuet-Higgins,et al.  A computer algorithm for reconstructing a scene from two projections , 1981, Nature.

[4]  L. Moisan,et al.  Maximal meaningful events and applications to image analysis , 2003 .

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

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

[7]  Frédéric Sur,et al.  Extracting Meaningful Curves from Images , 2005, Journal of Mathematical Imaging and Vision.

[8]  Pablo Musé.  Sur la définition et la reconnaissance des formes planes dans les images numériques , 2004 .

[9]  Patrick Bouthemy,et al.  A general criterion for image similarity detection , 2005 .

[10]  Olivier D. Faugeras,et al.  The fundamental matrix: Theory, algorithms, and stability analysis , 2004, International Journal of Computer Vision.

[11]  Joseph E. Yukich.  Asymptotics for weighted minimal spanning trees on random points , 2000 .

[12]  J. Littlewood.  On the probability in the tail of a binomial distribution , 1969, Advances in Applied Probability.

[13]  Jean-Michel Morel,et al.  Automatic image analysis : a challenge for Computer Vision , 2001 .

[14]  Lionel Moisan,et al.  Edge Detection by Helmholtz Principle , 2001, Journal of Mathematical Imaging and Vision.

[15]  A. Witkin,et al.  On the Role of Structure in Vision , 1983 .

[16]  Stephen C. Jensen,et al.  Measure: an interactive tool for accurate forensic photo/videogrammetry , 1995, Optics & Photonics.

[17]  Donald Geman,et al.  Coarse-to-Fine Face Detection , 2004, International Journal of Computer Vision.

[18]  Craig A. Tovey,et al.  Connect the dots: how many random points can a regular curve pass through? , 2005, Advances in Applied Probability.

[19]  Jorma Rissanen,et al.  Stochastic Complexity in Statistical Inquiry , 1989, World Scientific Series in Computer Science.

[20]  Yann Gousseau,et al.  Unsupervised thresholds for shape matching , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

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

[22]  Julie Delon,et al.  A Unified Framework for Detecting Groups and Application to Shape Recognition , 2007, Journal of Mathematical Imaging and Vision.

[23]  S AbutablebAhmed.  Automatic thresholding of gray-level pictures using two-dimensional entropy , 1989 .

[24]  H. Keselman,et al.  Multiple Comparison Procedures , 2005 .

[25]  Y. J. Tejwani,et al.  Robot vision , 1989, IEEE International Symposium on Circuits and Systems,.

[26]  Jean-Michel Morel,et al.  A Kanizsa programme , 1996 .

[27]  Shimon Ullman,et al.  Structural Saliency: The Detection Of Globally Salient Structures using A Locally Connected Network , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[28]  F. Attneave.  Some informational aspects of visual perception. , 1954, Psychological review.

[29]  Alberto Martelli,et al.  Edge detection using heuristic search methods , 1972, Comput. Graph. Image Process..

[30]  Yann Gousseau,et al.  Shape Recognition Based on an a Contrario Methodology , 2006, Statistics and Analysis of Shapes.

[31]  Du-Ming Tsai,et al.  A fast histogram-clustering approach for multi-level thresholding , 1992, Pattern Recognit. Lett..

[32]  A. Rosenfeld,et al.  Edge and Curve Detection for Visual Scene Analysis , 1971, IEEE Transactions on Computers.

[33]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[34]  Andrew K. C. Wong,et al.  A new method for gray-level picture thresholding using the entropy of the histogram , 1985, Comput. Vis. Graph. Image Process..

[35]  P. J. Diggle.  INTRODUCTION TO THE THEORY OF COVERAGE PROCESSES: (Wiley Series in Probability and Mathematical Statistics) , 1990 .

[36]  David Mumford,et al.  Filtering, Segmentation and Depth , 1993, Lecture Notes in Computer Science.

[37]  WU Xian-yuan.  Seif-containning Property of Euclidean Minimal Spanning Trees on Infinite Random Points , 2000 .

[38]  Ewald Hering,et al.  Grundzüge der Lehre vom Lichtsinn. , 1920 .

[39]  K. Alexander.  Finite clusters in high-density continuous percolation: Compression and sphericality , 1993 .

[40]  Kim L. Boyer,et al.  Robust Contour Decomposition Using a Constant Curvature Criterion , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[41]  Jaime López-Krahe,et al.  Contribution to the Determination of Vanishing Points Using Hough Transform , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[42]  Terrence J. Sejnowski,et al.  Edges are the Independent Components of Natural Scenes , 1996, NIPS.

[43]  Michael Lindenbaum,et al.  An Integrated Model for Evaluating the Amount of Data Required for Reliable Recognition , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[44]  Patrick Bouthemy,et al.  A maximality principle applied to a contrario motion detection , 2005, IEEE International Conference on Image Processing 2005.

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

[46]  Charles V. Stewart,et al.  MINPRAN: A New Robust Estimator for Computer Vision , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[47]  Pascal Fua,et al.  Model driven edge detection , 1990, Machine Vision and Applications.

[48]  D. Donoho,et al.  Adaptive multiscale detection of filamentary structures embedded in a background of uniform random points , 2003 .

[49]  W. Hoeffding.  Probability inequalities for sum of bounded random variables , 1963 .

[50]  Lionel Moisan,et al.  A Probabilistic Criterion to Detect Rigid Point Matches Between Two Images and Estimate the Fundamental Matrix , 2004, International Journal of Computer Vision.

[51]  Andrew Zisserman,et al.  Motion Clustering using the Trilinear Constraint over Three Views , 1995 .

[52]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[53]  T. A. Azlarov,et al.  Refinements of Yu. V. Prokhorov's theorems on the asymptotic behavior of the binomial distribution , 1987 .

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

[55]  Richard I. Hartley,et al.  Self-Calibration of Stationary Cameras , 1997, International Journal of Computer Vision.

[56]  Agnès Desolneux,et al.  Vanishing Point Detection without Any A Priori Information , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[57]  Philip H. S. Torr,et al.  The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix , 1997, International Journal of Computer Vision.

[58]  J. Rissanen.  A UNIVERSAL PRIOR FOR INTEGERS AND ESTIMATION BY MINIMUM DESCRIPTION LENGTH , 1983 .

[59]  N. Madras,et al.  THE SELF-AVOIDING WALK , 2006 .

[60]  F. Cao.  Application of the Gestalt principles to the detection of good continuations and corners in image level lines , 2004 .

[61]  Carsten Rother,et al.  A New Approach for Vanishing Point Detection in Architectural Environments , 2000, BMVC.

[62]  Gilbert Saporta,et al.  Probabilités, Analyse des données et statistique , 1991 .

[63]  Rikard Berthilsson,et al.  A Statistical Theory of Shape , 1998, SSPR/SPR.

[64]  Julie Delon,et al.  Automatic color palette , 2005, IEEE International Conference on Image Processing 2005.

[65]  Françoise Dibos,et al.  Real-time segmentation of moving objects in a video sequence by a contrario detection , 2005, IEEE International Conference on Image Processing 2005.

[66]  Charles T. Loop,et al.  Estimating the Fundamental Matrix by Transforming Image Points in Projective Space , 2001, Comput. Vis. Image Underst..

[67]  Ian D. Reid,et al.  Single View Metrology , 2000, International Journal of Computer Vision.

[68]  Zhengyou Zhang,et al.  Determining the Epipolar Geometry and its Uncertainty: A Review , 1998, International Journal of Computer Vision.

[69]  E. Brunswik,et al.  Ecological cue-validity of proximity and of other Gestalt factors. , 1953, The American journal of psychology.

[70]  J. G. Jenkins.  Gesetze des Sehens. , 1937 .

[71]  Lionel Moisan,et al.  Variational Snake Theory , 2003 .

[72]  Andrew Zisserman,et al.  Planar grouping for automatic detection of vanishing lines and points , 2000, Image Vis. Comput..

[73]  David Mumford,et al.  Statistics of natural images and models , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[74]  Frédéric Sur.  Décision à contrario pour la reconnaissance de formes , 2004 .

[75]  Lionel Moisan,et al.  A Grouping Principle and Four Applications , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[76]  O. Faugeras,et al.  The Geometry of Multiple Images , 1999 .

[77]  Richard I. Hartley,et al.  Kruppa's Equations Derived from the Fundamental Matrix , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[78]  Xavier Armangué,et al.  A survey addressing the fundamental matrix estimation problem , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[79]  Jean-Michel Morel,et al.  Geometry and Color in Natural Images , 2002, Journal of Mathematical Imaging and Vision.

[80]  Yann Gousseau,et al.  Accurate estimates of false alarm number in shape recognition , 2004 .

[81]  L. Santaló.  Integral geometry and geometric probability , 1976 .

[82]  Joachim M. Buhmann,et al.  Histogram clustering for unsupervised image segmentation , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[83]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[84]  Song-Chun Zhu,et al.  Embedding Gestalt Laws in Markov Random Fields , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[85]  Denis G. Pelli,et al.  The remarkable inefficiency of word recognition , 2003, Nature.

[86]  Antonio Criminisi,et al.  Creating Architectural Models from Images , 1999, Comput. Graph. Forum.

[87]  Jefferey A. Shufelt,et al.  Performance Evaluation and Analysis of Vanishing Point Detection Techniques , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

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

[89]  Luc Van Gool,et al.  The cascaded Hough transform , 1997, Proceedings of International Conference on Image Processing.

[90]  O. Reiser,et al.  Principles Of Gestalt Psychology , 1936 .

[91]  Jean Anastassiadis.  Définition des fonctions eulériennes par des équations fonctionnelles , 1966 .

[92]  Seth J. Teller,et al.  Automatic recovery of relative camera rotations for urban scenes , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[93]  S. Osher,et al.  Geometric Level Set Methods in Imaging, Vision, and Graphics , 2011, Springer New York.

[94]  J. Michael Steele,et al.  Minimal Spanning Trees for Graphs with Random Edge Lengths , 2002 .

[95]  N. Krüger,et al.  Multi-modal estimation of collinearity and parallelism in natural image sequences , 2002, Network.

[96]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[97]  H. Maître.  2 - Un panorama de la transformation de Hough , 1985 .

[98]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[99]  J. Quintanilla,et al.  Clustering in a Continuum Percolation Model , 1997, Advances in Applied Probability.

[100]  Rahul Roy,et al.  Critical intensities of Boolean models with different underlying convex shapes , 2002, Advances in Applied Probability.

[101]  Ugo Montanari,et al.  On the optimal detection of curves in noisy pictures , 1971, CACM.

[102]  A. M. Bruckstein,et al.  ON EDGE DETECTION , EDGE INTEGRATION AND GEOMETRIC ACTIVE CONTOURS , 2002 .

[103]  R. R. Bahadur.  Some Approximations to the Binomial Distribution Function , 1960 .

[104]  Laura Igual,et al.  A Contrast Invariant Approach to Motion Estimation , 2005, Scale-Space.

[105]  Ernst Gombrich,et al.  The Story of Art , 1950 .

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

[107]  Chein-I Chang,et al.  A relative entropy-based approach to image thresholding , 1994, Pattern Recognit..

[108]  David G. Lowe,et al.  Perceptual Organization and Visual Recognition , 2012 .

[109]  Ali Esmaili,et al.  Probability and Random Processes , 2005, Technometrics.

[110]  Isaac Balberg.  Continuum Percolation , 2009, Encyclopedia of Complexity and Systems Science.

[111]  Jean-Michel Morel,et al.  Computational gestalts and perception thresholds , 2003, Journal of Physiology-Paris.

[112]  Alfred M. Bruckstein,et al.  Regularized Laplacian Zero Crossings as Optimal Edge Integrators , 2003, International Journal of Computer Vision.

[113]  Jacques Froment,et al.  La g eom etrie des images naturelles et ses algorithmes , 1998 .

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

[115]  Doron Shaked,et al.  Deriving Stopping Rules for the Probabilistic Hough Transform by Sequential Analysis , 1996, Comput. Vis. Image Underst..

[116]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[117]  Rachid Deriche,et al.  A Robust Technique for Matching two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry , 1995, Artif. Intell..

[118]  Saïd Ladjal,et al.  Dequantizing image orientation , 2002, IEEE Trans. Image Process..

[119]  Larry S. Davis,et al.  A survey of edge detection techniques , 1975 .

[120]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[121]  Rachid Deriche,et al.  Using Canny's criteria to derive a recursively implemented optimal edge detector , 1987, International Journal of Computer Vision.

[122]  Jeffrey S. Perry,et al.  Edge co-occurrence in natural images predicts contour grouping performance , 2001, Vision Research.

[123]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[124]  G. Bennett.  Probability Inequalities for the Sum of Independent Random Variables , 1962 .

[125]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[126]  Roger Mohr,et al.  Epipole and fundamental matrix estimation using virtual parallax , 1995, Proceedings of IEEE International Conference on Computer Vision.

[127]  Pascal Monasse,et al.  Fast computation of a contrast-invariant image representation , 2000, IEEE Trans. Image Process..

[128]  G. Legge,et al.  Contrast discrimination in noise. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[129]  Steven W. Zucker,et al.  Trace Inference, Curvature Consistency, and Curve Detection , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[130]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[131]  Jose Luis Lisani,et al.  Detection of major changes in satellite images , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[132]  J. Yukich,et al.  Weak laws of large numbers in geometric probability , 2003 .

[133]  Thierry Pun,et al.  Entropic thresholding, a new approach , 1981 .

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

[135]  E. Slud.  Distribution Inequalities for the Binomial Law , 1977 .

[136]  Gérard G. Medioni,et al.  Inferring global perceptual contours from local features , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[137]  J. Seaman.  Introduction to the theory of coverage processes , 1990 .

[138]  Patrick Bouthemy,et al.  Probabilistic parameter-free motion detection , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[139]  Mi-Suen Lee,et al.  N-Dimensional Tensor Voting and Application to Epipolar Geometry Estimation , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[140]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[141]  M. Talagrand.  The missing factor in Hoeffding's inequalities , 1995 .

[142]  M. Okamoto.  Some inequalities relating to the partial sum of binomial probabilities , 1959 .

[143]  Hermann von Helmholtz,et al.  Treatise on Physiological Optics , 1962 .