Meaningful Alignments

We propose a method for detecting geometric structures in an image, without any a priori information. Roughly speaking, we say that an observed geometric event is “meaningful” if the expectation of its occurences would be very small in a random image. We discuss the apories of this definition, solve several of them by introducing “maximal meaningful events” and analyzing their structure. This methodology is applied to the detection of alignments in images.

[1]  M. Wertheimer.  Untersuchungen zur Lehre von der Gestalt. II , 1923 .

[2]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[3]  T. MacRobert.  Higher Transcendental Functions , 1955, Nature.

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

[5]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

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

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

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

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

[10]  J. Stoyanov,et al.  Exercise Manual in Probability Theory , 1988 .

[11]  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.

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

[13]  Karl J. Friston,et al.  Comparing Functional (PET) Images: The Assessment of Significant Change , 1991, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

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

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

[16]  Jean-Michel Morel,et al.  Variational methods in image segmentation , 1995 .

[17]  Jonathan D. Cohen,et al.  Improved Assessment of Significant Activation in Functional Magnetic Resonance Imaging (fMRI): Use of a Cluster‐Size Threshold , 1995, Magnetic resonance in medicine.

[18]  Gérard G. Medioni,et al.  Inferring global pereeptual contours from local features , 1996, International Journal of Computer Vision.