Point-based medialness for 2D shape description and identification

Abstract

We propose a perception-based medial point description of a natural form (2D: static or in articulated movement) as a framework for a shape representation which can then be efficiently used in biological species identification and matching tasks. Medialness is defined by adapting and refining a definition first proposed in the cognitive science literature when studying the visual attention of human subjects presented with articulated biological 2D forms in movement, such as horses, dogs and humans (walking, running). In particular, special loci of high medialness for the interior of a form in movement, referred to as "hot spots", prove most attractive to the human perceptual system. We propose an algorithmic process to identify such hot spots. In this article we distinguish exterior from interior shape representation. We further augment hot spots with extremities of medialness ridges identifying significant concavities (from outside) and convexities (from inside). Our representation is strongly footed in results from cognitive psychology, but also inspired by know-how in art and animation, and the algorithmic part is influenced by techniques from more traditional computer vision. A robust shape matching algorithm is designed that finds the most relevant targets from a database of templates by comparing feature points in a scale, rotation and translation invariant way. The performance of our method has been tested on several databases. The robustness of the algorithm is further tested by perturbing the data-set at different levels.

Medialness and the Perception of Visual Art

“…Our combination of these two apparently different representations (one of regions, the other of contours) can be unified-a concept we refer to as p-medialness (for perception-based medialness)-as shown in our recent work (Aparajeya and Leymarie, 2016;Leymarie et al, 2014b), by relating medialness to contour features by identifying end of medial ridges to so-called 'curvature extrema'. As indicated by recent studies in perception and cognition models, such extrema are better thought of as combining significant curvature peaks with regional support (De Winter and Wagemans, 2008), rather than referring to the traditional mathematical definition biased towards a purely local concept and analysis.…”

“…We then walk along ridge regions (typically thick traces around ridge lines of the medialness landscape) to locate its peaks: these are then kept as interior medial dominant points or hot spots. Some of the technical details are provided in Appendix 1; a more complete view on the algorithmic implementation is available in other recent publications (Aparajeya and Leymarie, 2016;Leymarie et al, 2014b).…”

“…In the proposed visualization we do not allow for crossings over junctions (i.e., where more than two ridges used to find peaks Figure 11. Illustration of the successive steps in isolating internal dominant points as hot spots: (a) medialness representation of (the interior of) a standing dog; (b) corresponding extracted significant ridges using a morphological top-hat transform (Aparajeya and Leymarie, 2016;Serra, 1988;Vincent, 1993); (c) internal dominant points illustrated as dark gray dots together with the original object's boundary; and (d) possible visualization of shape primitives as 'sausages' obtained by connecting adjacent and sufficiently overlapping interior medial annuli.…”

“…If the external dominant point is reasonably far from the object's boundary, then it proves difficult to retrieve a (shape-based) match with the modified form. We instead use the intersection of the main ridge orientation with the boundary (i.e., extrapolating the ridge orientation until it crosses the nearby object's boundary) to identify a more robust (under deformations) representative locus for the concavity; details in (Aparajeya and Leymarie, 2016). Pairs of dark arrows along the contour illustrate the local support for concavity while the arrow along the medial ridge (dark with white pointy head) indicates the direction of flow of medialness (away from the concavity).…”

“…How to set the tolerance ε in order to have desirable scaling properties thus needs to be addressed. We have argued elsewhere in setting ε as a logarithmic function of R(p) with a logarithmic base of value x = 1.5 (Aparajeya and Leymarie, 2016): ε p = log x ( R ( p ) + 1 ) (8.3) To select points of internal dominance, a 'black' top-hat transform (Serra, 1988;Vincent, 1993) is applied, resulting in a series of dark areas which typically correspond to peaks, ridges and passes of the medialness map when considered as a height field. Figure 11b shows the result obtained after applying the black top hat transform on a medialness image.…”