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...appear in a purely random environment is very low. It seems that human perception follows this rule to some extent, and this framework has been applied notably to gestalts detection with some success =-=[3, 5]-=-. The absence of parameters mainly comes from the fact that no generative probability model of events has to be defined, but only a rarity measure in a well-defined random environment. In addition, so...

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...ting casual matches, that is matches that can be produced by chance. Specifically, we make use of an a contrario methodology, first introduced in [6] and then applied, among other things, to grouping =-=[7]-=- and shape matching [16]. The principle of such approaches is to detect or match features when a certain null hypothesis is rejected. The plan of the paper is as follows. In Section 2, we detail the k...

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... [7] for curves that are graphs of Hölder functions and in [15] for chirps (highly oscillating functions), chaining chirplets in good continuation. Good-continuation principles are also considered in =-=[18, 19]-=- inspired by the Gestalt theory of vision, with applications to the detection of (parametric) geometric object in images. 21.2 Networks of polynomial pieces We define a network of polynomial pieces t...

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...rithm can disclose the directions of the hypercone. We propose here a very different paradigm, inspired by works in computer vision proposing a partial gestalt system based on the Helmholtz principle =-=[7]-=-. This principle groups a set of observed objects into one class if it is very unlikely that randomness could have generated such configuration. This is also known in statistics as a contrario detecti...

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...is quite general and the matching methodology is not restricted to the specific shape elements introduced in Sect. 2. The decision rule relies on a framework introduced by Desolneux, Moisan and Morel =-=[12, 14]-=-, based on a statistical principle, the Helmholtz principle. The adaptation of this principle to the shape matching problem leads to an automatic decision rule. In Sect. 4, we present some experiments...

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... Theory [4], underlining the importance of perceptual grouping for human visual perception. Desolneux et al. proposed to apply their statistical framework to detect alignments in images [3], clusters =-=[5]-=-, and edges [6]. Since then, the a contrario framework have been used in various purposes, such as motion detection [7], shape recognition [8], object matching [9], and local features matching [10]. T...

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... k-means [29], graph-based methods have been proposed for point clustering [36, 40]. Geometrical grouplets [30] consider contour grouping in the framework of harmonic analysis. The a contrario school =-=[10, 8, 7, 9]-=- applies probabilistic approaches to address the perceptual grouping such as point clustering and contour detection. Variational formulations [34, 33, 1], Markov Random Fields [14] and graph cuts [40]...

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...tistical test T, and on 6sthe significance level of the test. In order to avoid the usual problems linked with significance levels, we used a multiple statistical test, introduced by Desolneux et al. =-=[12]-=- and that we further developed in the case of histograms in [10]. This multiple test presents the advantage of having a significance level with a clear physical meaning and easy to fix. However, other...

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...les. Next, a number of possible grouping hypotheses is created. The hypotheses differ one from another by image features. Then, these groups are analyzed based on the theory of Gestalt, formalized in =-=[3]-=-, and only the most meaningful ones are kept. To construct the groups the following features are used: geometrical features, intensity and color means of the region, intensity and color means of the o...