Abstract-This paper introduces a new edge-grouping method to detect perceptually salient structures in noisy images. Specifically, we define a new grouping cost function in a ratio form, where the numerator measures the boundary proximity of the resulting structure and the denominator measures the area of the resulting structure. This area term introduces a preference towards detecting larger-size structures and, therefore, makes the resulting edge grouping more robust to image noise. To find the optimal edge grouping with the minimum grouping cost, we develop a special graph model with two different kinds of edges and then reduce the grouping problem to finding a special kind of cycle in this graph with a minimum cost in ratio form. This optimal cycle-finding problem can be solved in polynomial time by a previously developed graph algorithm. We implement this edge-grouping method, test it on both synthetic data and real images, and compare its performance against several available edge-grouping and edge-linking methods. Furthermore, we discuss several extensions of the proposed method, including the incorporation of the well-known grouping cues of continuity and intensity homogeneity, introducing a factor to balance the contributions from the boundary and region information, and the prevention of detecting self-intersecting boundaries.

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.

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Convexity is an important geometric property of many natu-

As an important geometric property of many structures or structural components, convexity plays an important role in computer vision and image understanding. In this paper, we describe a general approach that can force various edge-grouping algorithms to detect only convex structures from a set of boundary fragments. The basic idea is to remove some fragments and fragment connections so that, on the remaining ones, a prototype edge-grouping algorithm that detects closed boundaries without the convexity constraint can only produce convex closed boundaries. We show that this approach takes polynomial time and preserves the grouping optimality by not excluding any valid convex boundary from the search space. Choosing the recently developed ratio-contour algorithm as the prototype grouping algorithm, we develop a new convex-grouping algorithm, which can detect convex salient boundaries with good continuity and proximity in a globally optimal fashion. To facilitate the application of this convex-grouping algorithm, we develop a new fragment-connection method based on four-point Bezier curves. We demonstrate the performance of this convex-grouping algorithm by conducting experiments on both synthetic and real images. In addition, we provide a comparison with some prior edge-grouping algorithms. Finally, we show that the proposed convex-grouping algorithm can be further extended to detect convex open boundaries, derive region-based image hierarchies, and incorporate some simple human-computer interactions.