Optimal Contour Closure by Superpixel Grouping

Abstract

Abstract. Detecting contour closure, i.e., finding a cycle of disconnected contour fragments that separates an object from its background, is an important problem in perceptual grouping. Searching the entire space of possible groupings is intractable, and previous approaches have adopted powerful perceptual grouping heuristics, such as proximity and co-curvilinearity, to manage the search. We introduce a new formulation of the problem, by transforming the problem of finding cycles of contour fragments to finding subsets of superpixels whose collective boundary has strong edge support in the image. Our cost function, a ratio of a novel learned boundary gap measure to area, promotes spatially coherent sets of superpixels. Moreover, its properties support a global optimization procedure using parametric maxflow. We evaluate our framework by comparing it to two leading contour closure approaches, and find that it yields improved performance.

Superpixel Cut for Figure-Ground Image Segmentation

“…The previous work most related to ours is Levinshtein et al (Levinshtein et al, 2010), which transformed the problem of finding contour closure to finding subsets of superpixels. They defined the cost function as a ratio of a boundary gap measure to area, which promotes spatially coherent sets of superpixels.…”

“…Inspired by their approach, we define our similarity measure as boundary gap. However, as we will argue in Section 3., our proposed cost function, which minimizes the inter-class similarity and maximizing the intra-class similarity, is a more reasonable cost function than the closure cost proposed in (Levinshtein et al, 2010, Levinshtein et al, 2012.…”

“…Previously, Malik, 2000, Stahl andWang, 2007) show that normalization of the cut by a measure that is proportional to the size of the selection yields better results. (Levinshtein et al, 2010, Levinshtein et al, 2012 also adopt this measure and try to minimize a cost that is a ratio of a cut to a selection size. However, foreground may not be chosen optimally in complex scenes due to the background clutter or similarity of foreground and background.…”

“…(2) has a trivial solution by setting x to be vector 1 (all foreground). This issue can be resolved by penalizing some superpixels, as proposed in (Levinshtein et al, 2010). Specific details on this penalty will be given in Section 3.3.…”

“…In recent years an increasingly popular way to solve various image labeling problems like object segmentation, stereo and single view reconstruction is to formulate them using superpixels obtained from unsupervised segmentation algorithms (Li et al, 2004, Levinshtein et al, 2010, Brendel and Todorovic, 2010. For instance, they may belong to the same object or may have the same surface orientation.…”