A symbolic-numeric silhouette algorithm (original) (raw)

Silhouette-based 2D-3D Pose Estimation Using Algebraic Surfaces

masters thesis, 2009

In this contribution we present a formulation of the 2D-3D pose estimation problem using implicit algebraic surfaces. To model the projective mapping, we apply novel Dixon resultant heuristics to deal with the rapidly increasing polynomial degrees of projected image outlines. The advantages as well as disadvantages of using linearised twist coordinates for pose representation are also discussed. We also show that for pose estimation purposes, using simple algebraic distance is more practical than using a first-order approximation of the exact Euclidean distance between a point and an implicitly defined entity. While not as effective as current explicit approaches, our implicit formulation offers potential improvements in silhouette-based pose estimation.

Silhouette-Based 2D-3D Pose Estimation using implicit algebraic surfaces

2007

I would like to thank my supervisor Dr. Bodo Rosenhahn for all his help, guidance and patience and for proofreading the text. I also thank Prof. Dr. Joachim Weickert for insightful discussions and proofreading. I cannot but acknowledge the wonderful and bureaucracy-free environment of the MPII and the assistance provided by the Graphics group secretaries Sabine Budde and Conny Liegl. I would also like to thank Dr. Robert H. Lewis for considerable help in computing resultants using his computer algebra system Fermat. I thank Prof. Dr. Wolfram Decker for introducing me to SINGULAR and elimination theory, Arno Eigenwillig for his help with resultants and Ioannis Emiris and George Tzoumas for tips on computing matrix determinants by interpolation. I wish to thank my roommates Sarmad and Nassim for helping me stay sane and for tolerating my alarm clock that always seemd to wake them up. Special thanks also to Dominique Beaulieu and Robert Herzog at the Graphics group for making my stay worthwile and helping out with T E Xnical stuff now and then. Last but not least, I wish to thank my family for all their support and I dedicate this thesis to my parents for always being there.

Robust Silhouette Shadow Volumes on Contemporary Hardware

2014

The paper describes an algorithm, which produces shadow volumes for an arbitrary triangle model without visual artifacts. The algorithm has been implemented, optimized, and evaluated for a number of contemporary hardware platforms. The main contribution of the paper is removal of visual artifacts caused by limited precision of floating point arithmetics. The paper also presents an overview of the implementation and result of the optimizations on individual platforms. Finally, the conclusions are drawn and the future work is outlined. CR Categories: I.3.3 [Computer Graphics]: Three-Dimensional Graphics and Realism—Display Algorithms I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Radiosity;

Marching intersections: An efficient approach to shape-from-silhouette

Proceedings of VMV …, 2002

A new shape-from-silhouette algorithm for the creation of 3D digital models is presented. The algorithm is based on the use of the Marching Intersection (MI) data structure, a volumetric scheme which allows efficient representation of 3D polyhedra and reduces the boolean operations between them to simple boolean operations on linear intervals. MI supports the definition of a direct shapefrom-silhouette approach: the 3D conoids built from the silhouettes extracted from the images of the object are directly intersected to form the resulting 3D digital model. Compared to existing methods, our approach allows high quality models to be obtained in an efficient way. Examples on synthetic objects together with quantitative and qualitative evaluations are given.

Fast and Robust Tessellation-Based Silhouette Shadows

2014

Figure 1: The image shows the transformation of a quad into three overlapping shadow volume sides. The transition from part a) to part b) is tessellation of quad with Multiplicity = 3. Only green and blue triangles will be drawn. Yellow and gray triangles will be degenerated. The transition from part b) over part c) to part d) shows degeneration process. Red and purple vertices 3, 4 and 7, 8 from part a) form only one vertex in part d). The transition from part d) to part e) shows rotation around red and purple vertices. This transformation creates three overlapping sides of shadow volume. Positions of vertices A, B, C, D that form initial quad, can be computed according to equations 2. ABSTRACT

A complete modular resultant algorithm targeted for realization on graphics hardware

International Symposium on Parallel Symbolic Computation, 2010

This paper presents a complete modular approach to computing bivariate polynomial resultants on Graphics Processing Units (GPU). Given two polynomials, the algorithm first maps them to a prime field for sufficiently many primes, and then processes each modular image individually. We evaluate each polynomial at several points and compute a set of univariate resultants for each prime in parallel on

Foreword to the Special Focus on Advances in Symbolic and Numeric Computation IV

Mathematics in Computer Science, 2022

The conference counted with the sponsorship of Wolfram Research which distinguished two Young Researchers for their relevant works, as in previous editions of this event. The conference proceedings book (ISBN-978-989-99410-6-9) is published online on the ECCOMAS website. Most of the papers in this special focus are extended or new versions of communications presented at the 5th International Conference on Numerical and Symbolic Computation, being their topics example of the multidisciplinary character of this event. Numerical and symbolic computation methods and techniques are undoubtedly fundamental tools in a wide range of science and technology fields, as illustrated by the following six papers selected for this Special Focus.

Tangential Distance Fields for Mesh Silhouette Problems

Computer Graphics Forum, 2009

We consider a tangent-space representation of surfaces which maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, we introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We call the resulting scalar field a tangential distance field or TDF. When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a specific application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques, such as greedy local search, thus leading to efficient algorithms. In this paper, we use four applications to illustrate the benefit of using TDFs: multi-origin silhouette extraction in Hough space, silhouette-based view point selection, camera path planning, and light source placement.