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A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…
Minimization of boundary curvature is a classic regularization technique for image segmentation in the presence of noisy image data. Techniques for minimizing curvature have historically been derived from descent methods which could be…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required smoothing properties can be different or even contradictive among different tasks. Nevertheless, the inherent smoothing nature of…
Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging…
In the optimization of convex domains under a PDE constraint numerical difficulties arise in the approximation of convex domains in $\mathbb{R}^3$. Previous research used a restriction to rotationally symmetric domains to reduce shape…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…
This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals. The method relies on sums of squares of…
Approximation theory plays an important role in image processing, especially image deconvolution and decomposition. For piecewise smooth images, there are many methods that have been developed over the past thirty years. The goal of this…
The joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…
The elliptical shape prior information plays a vital role in improving the accuracy of image segmentation for specific tasks in medical and natural images. Existing deep learning-based segmentation methods, including the Segment Anything…
Model binarization can significantly compress model size, reduce energy consumption, and accelerate inference through efficient bit-wise operations. Although binarizing convolutional neural networks have been extensively studied, there is…
This paper presents a novel approach for segmenting moving objects in unconstrained environments using guided convolutional neural networks. This guiding process relies on foreground masks from independent algorithms (i.e. state-of-the-art…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
Selective segmentation is an important application of image processing. In contrast to global segmentation in which all objects are segmented, selective segmentation is used to isolate specific objects in an image and is of particular…
Convolutional neural networks (CNNs) show outstanding performance in many image processing problems, such as image recognition, object detection and image segmentation. Semantic segmentation is a very challenging task that requires…