Robust and unsupervised perceptual grouping of curves of dots

Abstract

The Gestalt school of psychology proposed the existence of a short list of grouping laws governing visual perception. Among them, the law of good continuation can be stated as All else being equal, elements that can be seen as smooth continuations of each other tend to be grouped together [6] (Fig. 2). In the computational domain, attention to the Gestalt laws has been given since the early days of computer vision. D. Lowe was among the first to state the importance of incorporating the Gestalt principles of co-linearity, co-curvilinearity and simplicity for perceptual grouping algorithms [5]. Various computational formalizations of the good continuation principle have been proposed ever since, most notably the tensor voting approach [2, 3]. In this work1, we propose a new model and algorithm for the perceptual grouping by good continuation using a simple model that favors local symmetries, and with a detection control based on the non-accidentalness principle. This allows the method to be general in the sense that it can capture smooth curves of any shape and scale, and is robust to outliers and noise. It is also unsupervised because detections are given by their statistical significance, which requires only a single parameter, namely the number of false detections that would be allowed in an image of random noise. The proposed algorithm consists of two main steps: building candidate chains of points, and validating them. Candidate chains of points are built by considering triplets of points formed by joining nearest neighbors. Once valid triplets have been obtained, a graph representation is produced where each node corresponds to a triplet. A classic path finding algorithm is run on this graph to obtain paths between all pairs of triplets. Finally, the paths found are validated as non-accidental or rejected using thresholds obtained with the a contrario approach [1].