By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, ηsubdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued v...

In this paper, we suggest and consider a class of new three-step approximation schemes for generalized general set-valued mixed quasi variational inequalities. We also consider and analyze a new class of extragradienttype methods for solving generalized set-valued variational inequalities. The proposed methods include several new and known methods as special cases. Our results present a signifi...

We propose a novel variational approach based on a level set formulation of the Mumford-Shah functional and shape priors. We extend the functional by a labeling function which indicates image regions in which the shape prior is enforced. By minimizing the proposed functional with respect to both the level set function and the labeling function, the algorithm selects image regions where it is fa...

In this paper, we consider saliency detection problems from a unique perspective. We provide an implicit representation for the saliency map using level set evolution (LSE), and then combine LSE approach with energy functional minimization (EFM). Instead of introducing sophisticated segmentation procedures, we propose a flexible and lightweight LSE-EFM framework for saliency detection. The expe...

We consider variational inequality problems for set-valued vector fields on general Riemannian manifolds. The existence results of the solution, convexity of the solution set, and the convergence property of the proximal point algorithm for the variational inequality problems for set-valued mappings on Riemannian manifolds are established. Applications to convex optimization problems on Riemann...

A general abstract duality result is proposed for equations which are governed by the sum of two operators (possibly multivalued). It allows to unify a large number of variational duality principles, including the Clarke-Ekeland least dual action principle and the Singer-Toland duality. Moreover, it offers a new duality approach to some central questions in the theory of variational inequalitie...

Variational frameworks based on level set methods are popular for the general problem of image segmentation. They combine different feature channels in an energy minimization approach. In contrast to other popular segmentation frameworks, e.g. the graph cut framework, current level set formulations do not allow much user interaction. Except for selecting the initial boundary, the user is barely...

Identifying the Region or Object of Interest in a natural scene is a complex task because the content of natural images consists of the multiple non-uniform sub-regions and the intensity inhomogeneities. In this paper, we present a novel Region of Interest (ROI) detection method to minimize the ROI in the images automatically. We applied the geometric active contours that forces the variational...

In many applications it is necessary to track a moving and deforming boundary on the plane from infrequent, sparse measurements. For instance, each of a set of mobile observers may be able to tell the position of a point on the boundary. Often boundary components split, merge, appear, and disappear over time. Data are typically sparse and noisy and the underlying dynamics is uncertain. To addre...

Traditional texture mapping uses sampled images of limited resolution to represent patterns on surfaces. Sampling inherently assumes that the underlying pattern is band limited, which in plain language means that it must not contain any crisp edges. Unfortunately, most real world patterns violate that constraint, and the result is that texture mapped surfaces appear either artificially pixelate...