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The rapid progress in GPU computing has revolutionized many fields, yet its potential in mathematical programming, such as linear programming (LP), has only recently begun to be realized. This survey aims to provide a comprehensive overview…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
The availability of low cost sensors has led to an unprecedented growth in the volume of spatial data. However, the time required to evaluate even simple spatial queries over large data sets greatly hampers our ability to interactively…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
Spatial perception aims to estimate camera motion and scene structure from visual observations, a problem traditionally addressed through geometric modeling and physical consistency constraints. Recent learning-based methods have…
With the growth of machine learning algorithms with geometry primitives, a high-efficiency library with differentiable geometric operators are desired. We present an optimized Differentiable Geometry Algorithm Library (DGAL) loaded with…
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
We show that if PGA is understood as a subalgebra of CGA in mathematically correct sense, then the flat objects share the same representation in PGA and CGA. Particularly, we treat duality in PGA. This leads to unification of PGA and CGA…
With the advent of specialized hardware such as Graphics Processing Units (GPUs), large scale image localization, classification and retrieval have seen increased prevalence. Designing scalable software architecture that co-evolves with…
The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be…
Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We…
Proper representation of data in graphical visualizations becomes challenging when high accuracy in data types is required, especially in those situations where the difference between double-precision floating-point and single-precision…
We provide a preliminary study on utilizing GPU (Graphics Processing Unit) to accelerate computation for three simulation optimization tasks with either first-order or second-order algorithms. Compared to the implementation using only CPU…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…
${\cal U}$ntil now the representation (i.e. plotting) of curve in Parallel Coordinates is constructed from the point $\leftrightarrow$ line duality. The result is a ``line-curve'' which is seen as the envelope of it's tangents. Usually this…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
The Convex Hull algorithm is one of the most important algorithms in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is…
Quadratic cone programs are rapidly becoming the standard canonical form for convex optimization problems. In this paper we address the question of differentiating the solution map for such problems, generalizing previous work for linear…