Globally Optimal Grouping for Symmetric Closed Boundaries by Combining Boundary and Region Information

Abstract

Abstract-Many natural and man-made structures have a boundary that shows a certain level of bilateral symmetry, a property that plays an important role in both human and computer vision. In this paper, we present a new grouping method for detecting closed boundaries with symmetry. We first construct a new type of grouping token in the form of symmetric trapezoids by pairing line segments detected from the image. A closed boundary can then be achieved by connecting some trapezoids with a sequence of gap-filling quadrilaterals. For such a closed boundary, we define a unified grouping cost function in a ratio form: the numerator reflects the boundary information of proximity and symmetry, and the denominator reflects the region information of the enclosed area. The introduction of the region-area information in the denominator is able to avoid a bias toward shorter boundaries. We then develop a new graph model to represent the grouping tokens. In this new graph model, the grouping cost function can be encoded by carefully designed edge weights, and the desired optimal boundary corresponds to a special cycle with a minimum ratio-form cost. We finally show that such a cycle can be found in polynomial time using a previous graph algorithm. We implement this symmetry-grouping method and test it on a set of synthetic data and real images. The performance is compared to two previous grouping methods that do not consider symmetry in their grouping cost functions.

An Applied Study to Image-G Transmission in Chinese Literary on Gestalt Perception Laws

“…Despite they are actually incomplete fragments of real circular tracks, the separated variables in accommodated resembling of distinction segments can be recognized as a dynamic circuit presented at each dot in perceptual model. The conceptualization of law of closure which would take account of more than solely psychological studies within the exclusively psychological frame (Stahl & Wang, 2008). The concept is explored further in Restle's concept of "motion configuration".…”

Multiscale Symmetric Part Detection and Grouping

“…Many computational models exist for symmetry-based grouping, including Brady and Asada [5], Cham and Cipolla [6], SaintMarc et al [15], Ylä-Jääski and Ade [21] and, more recently, Stahl and Wang [20], among others. Such systems face one or more important limitations: 1) the complexity of pairwise contour grouping to detect symmetry-related contour pairs; 2) the requirements of contour smoothness and precise pointwise correspondence dictated by the geometric emphasis of many such approaches; and 3) that such approaches typically stop short of grouping the detected symmetries (parts) into objects.…”

Optimal Contour Closure by Superpixel Grouping

“…Lowe's [10] early work on perceptual grouping was one of the first to develop a computational model for parallelism, collinearity, and proximity. Many computational models exist for symmetry-based grouping, including Brady and Asada [11], Cham and Cipolla [12], Saint-Marc et al [13], Ylä-Jääski and Ade [14], and more recently, Stahl and Wang [15]. One significant challenge faced by these systems is the complexity of pairwise contour grouping to detect symmetry-related contour pairs.…”