Related papers: Geometric Median Shapes
High-dimensional data poses unique challenges in outlier detection process. Most of the existing algorithms fail to properly address the issues stemming from a large number of features. In particular, outlier detection algorithms perform…
Element Method. The Finite Volume Method guarantees local and global mass conservation. A property not satisfied by the Finite Volume Method. On the down side, the Finite Volume Method requires non trivial modifications to attain high order…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
The connected $k$-median problem is a constrained clustering problem that combines distance-based $k$-clustering with connectivity information. The problem allows to input a metric space and an unweighted undirected connectivity graph that…
We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm…
Median filtering is a non-linear smoothing technique widely used in digital image processing to remove noise while retaining sharp edges. It is particularly well suited to removing outliers (impulse noise) or granular artifacts (speckle…
Mesh-based learning is one of the popular approaches nowadays to learn shapes. The most established backbone in this field is MeshCNN. In this paper, we propose infusing MeshCNN with geometric reasoning to achieve higher quality learning.…
Deep learning models have achieved significant success in various image related tasks. However, they often encounter challenges related to computational complexity and overfitting. In this paper, we propose an efficient approach that…
Artificial data synthesis is currently a well studied topic with useful applications in data science, computer vision, graphics and many other fields. Generating realistic data is especially challenging since human perception is highly…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…
Computing the diameter, and more generally, all eccentricities of an undirected graph is an important problem in algorithmic graph theory and the challenge is to identify graph classes for which their computation can be achieved in…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
We will propose a new algorithm for finding critical points of cost functions defined on a differential manifold. We will lift the initial cost function to a manifold that can be embedded in a Riemannian manifold (Euclidean space) and will…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
The proliferation of floating anthropogenic debris in rivers has emerged as a pressing environmental concern, exerting a detrimental influence on biodiversity, water quality, and human activities such as navigation and recreation. The…
We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable…