Related papers: Relaxed Total Generalized Variation Regularized Pi…

Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…

In this paper we present approaches that address two issues that can occur when the level-set method is used to simulate two-fluid flows in engineering practice. The first issue concerns regularizing the Heaviside function on arbitrary…

Automating Multiple Sclerosis (MS) lesion segmentation would be of great benefit in initial diagnosis as well as monitoring disease progression. Deep learning based segmentation models perform well in many domains, but the state-of-the-art…

We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…

We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional…

In the rapidly evolving field of 3D reconstruction, 3D Gaussian Splatting (3DGS) and 2D Gaussian Splatting (2DGS) represent significant advancements. Although 2DGS compresses 3D Gaussian primitives into 2D Gaussian surfels to effectively…

In this work, we study the dynamics of piecewise smooth systems on a codimension-2 transverse intersection of two codimension-1 discontinuity sets. The Filippov convention can be extended to such intersections, but this approach does not…

We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…

Text-based image segmentation aims to delineate object boundaries within an image from text prompts, offering higher flexibility and broader application scope compared to traditional fixed-category segmentation tasks. Recent studies have…

In this paper, we introduce a novel approach for active contours with free endpoints. A scheme is presented for image segmentation and restoration based on a discrete version of the Mumford-Shah functional where the contours can be both…

We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…

We propose Region-wise (RW) loss for biomedical image segmentation. Region-wise loss is versatile, can simultaneously account for class imbalance and pixel importance, and it can be easily implemented as the pixel-wise multiplication…

In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual error in fourier space domain and variable total variation…

Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation…

This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

In the field of 3D perception using 3D LiDAR sensors, ground segmentation is an essential task for various purposes, such as traversable area detection and object recognition. Under these circumstances, several ground segmentation methods…

The RGB-Depth (RGB-D) Video Object Segmentation (VOS) aims to integrate the fine-grained texture information of RGB with the spatial geometric clues of depth modality, boosting the performance of segmentation. However, off-the-shelf RGB-D…

We propose a machine learning based approach for automatic regularization and polygonization of building segmentation masks. Taking an image as input, we first predict building segmentation maps exploiting generic fully convolutional…

Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…