Efficient robust digital hyperplane fitting with bounded error

Authors:
Dror Aiger;Yukiko Kenmochi;Hugues Talbot;Lilian Buzer
Affiliations:
Université Paris-Est, Laboratoire d'Informatique Gaspard-Monge, France;Université Paris-Est, Laboratoire d'Informatique Gaspard-Monge, France;Université Paris-Est, Laboratoire d'Informatique Gaspard-Monge, France;Université Paris-Est, Laboratoire d'Informatique Gaspard-Monge, France
Venue:
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Year:
2011

Citing 14
Cited 2

On a class of O(n2) problems in computational geometry

Computational Geometry: Theory and Applications
MIR: An Approach to Robust Clustering-Application to Range Image Segmentation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography

Communications of the ACM
Use of the Hough transformation to detect lines and curves in pictures

Communications of the ACM
Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling

IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple View Geometry in Computer Vision

Multiple View Geometry in Computer Vision
Convex Optimization

Convex Optimization
Decomposition of a Three-Dimensional Discrete Object Surface into Discrete Plane Pieces

Algorithmica
Numerical Recipes 3rd Edition: The Art of Scientific Computing

Numerical Recipes 3rd Edition: The Art of Scientific Computing
On Approximating the Depth and Related Problems

SIAM Journal on Computing
On Approximate Range Counting and Depth

Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
Approximate range searching: The absolute model

Computational Geometry: Theory and Applications
Efficiently Computing Optimal Consensus of Digital Line Fitting

ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
Fast Polygonal Approximation of Digital Curves Using Relaxed Straightness Properties

IEEE Transactions on Pattern Analysis and Machine Intelligence

O(n 3logn) time complexity for the optimal consensus set computation for 4-Connected Digital Circles

DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Efficient robust digital annulus fitting with bounded error

DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the following fitting problem: given an arbitrary set of N points in a bounded grid in dimension d, find a digital hyperplane that contains the largest possible number of points. We first observe that the problem is 3SUM-hard in the plane, so that it probably cannot be solved exactly with computational complexity better than O(N2), and it is conjectured that optimal computational complexity in dimension d is in fact O(Nd). We therefore propose two approximation methods featuring linear time complexity. As the latter one is easily implemented, we present experimental results that show the runtime in practice.