On affine registration of planar point sets using complex numbers

Authors:
Jeffrey Ho;Ming-Hsuan Yang
Affiliations:
Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32607, United States;Electrical Engineering and Computer Science, University of California, Merced, CA 95344, United States
Venue:
Computer Vision and Image Understanding
Year:
2011

Citing 31
Cited 2

Model-based image matching using location

Model-based image matching using location
Three-dimensional object recognition

ACM Computing Surveys (CSUR) - Annals of discrete mathematics, 24
Principal Warps: Thin-Plate Splines and the Decomposition of Deformations

IEEE Transactions on Pattern Analysis and Machine Intelligence
Object recognition by computer: the role of geometric constraints

Object recognition by computer: the role of geometric constraints
Least-Squares Estimation of Transformation Parameters Between Two Point Patterns

IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing solid objects by alignment with an image

International Journal of Computer Vision
The revised Fundamental Theorem of Moment Invariants

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Method for Registration of 3-D Shapes

IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
Feature-based correspondence: an eigenvector approach

Image and Vision Computing - Special issue: BMVC 1991
Iterative point matching for registration of free-form curves and surfaces

International Journal of Computer Vision
Active shape models—their training and application

Computer Vision and Image Understanding
Rigid, affine and locally affine registration of free-form surfaces

International Journal of Computer Vision
Matching 3-D anatomical surfaces with non-rigid deformations using octree-splines

International Journal of Computer Vision
Multi-Level Shape Representation Using Global Deformations andLocally Adaptive Finite Elements

International Journal of Computer Vision
Graph Matching With a Dual-Step EM Algorithm

IEEE Transactions on Pattern Analysis and Machine Intelligence
Cross-Weighted Moments and Affine Invariants for Image Registration and Matching

IEEE Transactions on Pattern Analysis and Machine Intelligence
Active Appearance Models

IEEE Transactions on Pattern Analysis and Machine Intelligence
Reliable and Efficient Pattern Matching Using an Affine Invariant Metric

International Journal of Computer Vision
Geometric Hashing: An Overview

IEEE Computational Science & Engineering
Comparing Images Using the Hausdorff Distance

IEEE Transactions on Pattern Analysis and Machine Intelligence
Modal Matching for Correspondence and Recognition

IEEE Transactions on Pattern Analysis and Machine Intelligence
Pairwise Data Clustering by Deterministic Annealing

IEEE Transactions on Pattern Analysis and Machine Intelligence
Affine Point Pattern Matching

Proceedings of the 23rd DAGM-Symposium on Pattern Recognition
Multiple View Geometry in Computer Vision

Multiple View Geometry in Computer Vision
A new point matching algorithm for non-rigid registration

Computer Vision and Image Understanding - Special issue on nonrigid image registration
Pattern Classification (2nd Edition)

Pattern Classification (2nd Edition)
A unified framework for alignment and correspondence

Computer Vision and Image Understanding
Using Spatial Sorting and Ranking in Model-Based Object Recognition

ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
A Robust Algorithm for Point Set Registration Using Mixture of Gaussians

ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Affine invariant comparison of point-sets using convex hulls and hausdorff distances

Pattern Recognition
Image registration and object recognition using affine invariants and convex hulls

IEEE Transactions on Image Processing

Smooth point-set registration using neighboring constraints

Pattern Recognition Letters
3D affine registration using teaching-learning based optimization

3D Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a novel algorithm for affine registration of 2D point sets. The main idea is to treat the 2D points as complex numbers and from each point set, a polynomial with complex coefficients can be computed whose roots are the points in the given point set. The two-step algorithm first reduces the affine registration problem to a rigid registration problem, and the unknown rotation is then computed using the coefficients of these polynomials. The algorithm is entirely algebraic with clear underlying geometric motivation. The implementation is straightforward and it takes less than a second to compute the affine transformation for point sets containing hundreds of points. We validate the algorithm on a variety of synthetic 2D point sets as well as point sets extracted from real-world images.