Perceptual Organization and the Curve Partitioning Problem

I INTRODUCTION A basic attribute of the human visual system is its ability to group elements of a perceived scene or visual field into meaningful or coherent clusters; in addition to clustering or partitioning, the visual system generally imparts structure and often a semantic interpretation to the data. In spite of the apparent existence proof provided by human vision, the general problem of scene partitioning remains unsolved for computer vision. Part of the difficulty resides In the fact that it is not clear to what extent semantic knowledge (e.g., recognizing the appearance of a straight line or some letter of the English alphabet), as opposed to generic criteria (e.g., grouping scene elements on the basis of geometric proximity), is employed in examples of human performance. Since, at present, we cannot hope to duplicate human competence in semantic interpretation, it would be desirable to find a task domain in which the Influence of semantic knowledge is limited. In such a domain it might be possible to discover the generic criteria employed by the human visual system. One of the main goals of the research effort described in this paper is to find a set of generic rules and models that will permit a machine to duplicate human performance in partitioning planar curves. II THE PARTITIONING PROBLEM Even If we are given a problem domain in which explicit semantic cues are missing, to what extent Is partitioning dependent on the purpose, vocabulary, data representation, and past experience of the "partitioning instrument," as opposed to being a search for context Independent "intrinsic structure" in the data? We argue that rather than having a unique formulation, the partitioning problem must be paramaterized along a number of basic dimensions. In the remainder of this section we enumerate some of these dimensions and discuss their relevance. A. Intent (Purpose) of the Partitioning Task In the experiment described in Figure 1, human subjects were presented with the task of partitioning a set of two-dimensional curves with respect to three different objectives: (1) choose a set of contour points that best mark those locations at which curve segments produced by different processes were "glued" together; (2) choose a set of contour points that best allow one to reconstruct the complete curve; (3) choose a set of contour points that would best allow one to distinguish the given curve from others. Each person was given only one of the …