On the Perceptual Organization of Texture and Shading Flows: From a Geometrical Model to Coherence Computation

Locally parallel dense patterns sometimes called texture flows define a perceptually coherent structure which is important to image segmentation, edge classification, shading analysis, and shape interpretation. This paper develops the notion of texture flow from a geometrical point of view to argue that local measurements of such structures must incorporate two curvatures. We show how basic theoretical considerations lead to a unique model for the local behavior of the flow and allow for the specification of consistency constraints between nearby measurements. The computation of globally coherent structure via neighborhood relationships is demonstrated on synthetic and natural images, and is compared to orientation diffusion. 1. What is texture flow A bear’s fur, a zebra’s stripes, and the wheat on a field all define a visual structure, sometimes called texture flow, whose organization to coherent parts is fundamental to many aspects of computer vision (Fig. 1). Informally, texture flows are defined by their orientation content a dense visual percept characterized by local parallelism and slowly varying dominant local orientation (a.e.). The tendency of the human visual system to organize parallel structure has been observed psychologically [8, 2, 22], and its importance to computer vision has been discussed through the non accidentalness argument [26, 12]. For centuries this class of patterns has been used by artists as a tool to convey both the shape and shading of smoothly varying (continuous) surfaces and their discontinuities. Indeed, since the shading of smooth objects is a texture flow (e.g., when represented by its isoluminance contours), its analysis and segmentation in terms of coherent parts may prove vital for shape from shading (Fig. 2) and for edge classification [5]. Unfortunately, existing computational approaches to the analysis of texture flow, such as fitting [19] or diffuSupported by AFOSR. We deeply thank A. Tannenbaum for stimulating and inspiring discussions. sion [17, 21], ignore certain aspects of its structure. As a result, the processed flow may be distorted, especially around discontinuities (Fig. 2). Furthermore, the fact that coherent flow may contain a wide range of orientations within a small area takes its toll on segmentation methods (e.g., [11, 18]), leading to results that may disagree with perception (Fig. 3). We submit that the analysis of texture flow should be geometrical and should provide answers to two fundamental questions: (i) what should be measured locally, and (ii) how spurious measurements should be refined into globally coherent structures while preserving discontinuities and singularities. Since texture flows are perceptually dense even when the raw measurements are sparse, an adequate analy-