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We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…

The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Such techniques reorder the nodes in the grid…

This paper introduces a new reconfiguration problem of matchings in a triangular grid graph. In this problem, we are given a nearly perfect matching in which each matching edge is labeled, and aim to transform it to a target matching by…

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the…

A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to…

rdering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an $\ell_1$ norm…

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor…

Image matting and image harmonization are two important tasks in image composition. Image matting, aiming to achieve foreground boundary details, and image harmonization, aiming to make the background compatible with the foreground, are…

The latent code of the recent popular model StyleGAN has learned disentangled representations thanks to the multi-layer style-based generator. Embedding a given image back to the latent space of StyleGAN enables wide interesting semantic…

We present a deep learning framework based on a generative adversarial network (GAN) to perform super-resolution in coherent imaging systems. We demonstrate that this framework can enhance the resolution of both pixel size-limited and…

The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…

Limited by the computational efficiency and accuracy, generating complex 3D scenes remains a challenging problem for existing generation networks. In this work, we propose DepthGAN, a novel method of generating depth maps with only semantic…

It is a difficult task to classify images with multiple class labels using only a small number of labeled examples, especially when the label (class) distribution is imbalanced. Emotion classification is such an example of imbalanced label…

We propose an unsupervised, mid-level representation for a generative model of scenes. The representation is mid-level in that it is neither per-pixel nor per-image; rather, scenes are modeled as a collection of spatial, depth-ordered…

Texture models based on Generative Adversarial Networks (GANs) use zero-padding to implicitly encode positional information of the image features. However, when extending the spatial input to generate images at large sizes, zero-padding can…

In 2022, Olivier Longuet, a French mathematics teacher, created a game called the \textit{calissons puzzle}. Given a triangular grid in a hexagon and some given edges of the grid, the problem is to find a calisson tiling such that no input…

Non-uniform blur, mainly caused by camera shake and motions of multiple objects, is one of the most common causes of image quality degradation. However, the traditional blind deblurring methods based on blur kernel estimation do not perform…

GAN-based techniques that generate and synthesize realistic faces have caused severe social concerns and security problems. Existing methods for detecting GAN-generated faces can perform well on limited public datasets. However, images from…

It is common but challenging to address high-resolution image blending in the automatic photo editing application. In this paper, we would like to focus on solving the problem of high-resolution image blending, where the composite images…