Convexity Shape Prior for Segmentation

Abstract

Abstract. Convexity is known as an important cue in human vision. We propose shape convexity as a new high-order regularization constraint for binary image segmentation. In the context of discrete optimization, object convexity is represented as a sum of 3-clique potentials penalizing any 1-0-1 configuration on all straight lines. We show that these non-submodular interactions can be efficiently optimized using a trust region approach. While the cubic number of all 3-cliques is prohibitively high, we designed a dynamic programming technique for evaluating and approximating these cliques in linear time. Our experiments demonstrate general usefulness of the proposed convexity constraint on synthetic and real image segmentation examples. Unlike standard secondorder length regularization, our convexity prior is scale invariant, does not have shrinking bias, and is virtually parameter-free.

Convexity Shape Constraints for Image Segmentation

“…For each exemplary image, in addition to the result of our method, we also show the respective result obtained without convexity constraints. Finally, we provide a comparison to state of the art [6] on two exemplary images. We employ a four-connected grid graph in all experiments.…”

“…In contrast, our method is able to obtain the globally optimal solution. On a second, biological image (Figure 7 bottom), we ran [6] (a) Table 1: For each experiment, we list the image resolution in pixels (Res), the energy of the solution obtained without convexity constraints (E), the energy of the solution obtained with convexity constraints (ConvexE), the number of times that convexity constraints are iteratively added to the ILP (# Iter), the run-time of the algorithm with convexity constraints (Time), and the gap achieved in the final iteration (Gap). with two different initializations, namely the standard Graph Cut solution, as well as a box that we manually placed around the sought structure.…”

“…Image segmentation is a challenging task for which often times the use of suitable prior knowledge about the shape of the sought objects plays an important role. One interesting shape prior is convexity [9,10,7,6]. In natural images, it often occurs that there are multiple convex structures of the same or different classes present in one image, such as wheels or various fruit, as well as composite structures constructed from convex parts, such as bricks and floor tiles.…”

Data-driven scene parsing method for recognizing construction site objects in the whole image

“…This extra region represents inaccurate features of an object, thereby leading to a poor recognition rate. To minimize this problem, segmentation methods, such as graph cut [72,73] or GrabCut [70,74] can assist users in extracting an exact region of interest using user inputs as prior information for segmentation. Above all, for some applications, a target object of interest in an image should account for a detectable and labelable size.…”

The Improvement of the Processes of a Class of Graph-Cut-Based Image Segmentation Algorithms

“…These algorithms realize many improvements in many different ways. Some make progress by modifying the energy function, such as adding shape priors [2]- [5] or texture priors [6]- [8] to the energy function to render segmentation more accurate. Some help decrease the runtime of the algorithm.…”