Invariant computations for analytic projective geometry

Finite Projective Geometry based Fast, Conflict-free Parallel Matrix Computations

Matrix computations, especially iterative PDE solving (and the sparse matrix vector multiplication subproblem within) using conjugate gradient algorithm, and LU/Cholesky decomposition for solving system of linear equations, form the kernel of many applications, such as circuit simulators, computational fluid dynamics or structural analysis etc. The problem of designing approaches for paralleliz...

Projective Geometry, Duality and Plücker Coordinates for Geometric Computations with Determinants on GPUs

Many algorithms used are based on geometrical computation. There are several criteria in selecting appropriate algorithm from already known. Recently, the fastest algorithms have been preferred. Nowadays, algorithms with a high stability are preferred. Also today’s technology and computer architecture, like GPU etc., plays a significant role for large data processing. However, some algorithms a...

Projective Geometry for Image Analysis

Exploiting projective geometry for view-invariant monocular human motion analysis in man-made environments

Example-based approaches have been very successful for human motion analysis but their accuracy strongly depends on the similarity of the viewpoint in testing and training images. In practice, roof-top cameras are widely used for video surveillance and are usually placed at a significant angle from the floor, which is different from typical training viewpoints. We present a methodology for view...

Projective Geometry Considered Harmful

Methods based on projective geometry have become popular in machine vision because they lead to elegant mathematics, and easy-to-solve linear equations [Longuett-Higgins 81, Hartley 97a, Quan & Lan 99]. It is often not realized that one pays a heavy price for this. Such method do not correctly model the physics of image formation and as a result require more correspondences and are considerably...