Related papers: Relaxed Total Generalized Variation Regularized Pi…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…
Recently, patch deformation-based methods have demonstrated significant strength in multi-view stereo by adaptively expanding the reception field of patches to help reconstruct textureless areas. However, such methods mainly concentrate on…
We introduce a model-based iterative method to obtain shear modulus images of tissue using magnetic resonance elastography. The method jointly finds the displacement field that best fits multifrequency tissue displacement data and the…
We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…
In this paper, we propose a meshfree method based on the Gaussian radial basis function (RBF) to solve both classical and fractional PDEs. The proposed method takes advantage of the analytical Laplacian of Gaussian functions so as to…
Minimization of regularized losses is a principled approach to weak supervision well-established in deep learning, in general. However, it is largely overlooked in semantic segmentation currently dominated by methods mimicking full…
Automatic multiple sclerosis (MS) lesion segmentation using multi-contrast magnetic resonance (MR) images provides improved efficiency and reproducibility compared to manual delineation. Current state-of-the-art automatic MS lesion…
Image segmentation is a crucial but challenging task that has many applications. In medical imaging for instance, intensity inhomogeneity and noise are common. In thigh muscle images, different muscles are closed packed together and there…
We consider X-ray coherent scatter imaging, where the goal is to reconstruct momentum transfer profiles (spectral distributions) at each spatial location from multiplexed measurements of scatter. Each material is characterized by a unique…
A ruled surface is a shape swept out by moving a line in 3D space. Due to their simple geometric forms, ruled surfaces have applications in various domains such as architecture and engineering. In the past, various approaches have been…
We introduce discretizations of infinite-dimensional optimization problems with total variation regularization and integrality constraints on the optimization variables. We advance the discretization of the dual formulation of the total…
We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic…
Recent advancements in 3D Gaussian Splatting (3DGS), which lead to high-quality novel view synthesis and accelerated rendering, have remarkably improved the quality of radiance field reconstruction. However, the extraction of mesh from a…
We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…
Microvascular networks are challenging to model because these structures are currently near the diffraction limit for most advanced three-dimensional imaging modalities, including confocal and light sheet microscopy. This makes semantic…
A robust estimator, namely M-smoother, for piecewise-constant smoothing is revisited in this paper. Starting from its generalized formulation, we propose a numerical scheme/framework for solving it via a series of weighted-average filtering…
Image segmentation is an important task in the domain of computer vision and medical imaging. In natural and medical images, intensity inhomogeneity, i.e. the varying image intensity, occurs often and it poses considerable challenges for…
The need for an efficient method of integration of a dense normal field is inspired by several computer vision tasks, such as shape-from-shading, photometric stereo, deflectometry, etc. Inspired by edge-preserving methods from image…