From FNS to HEIV: A Link between Two Vision Parameter Estimation Methods

Authors:
Wojciech Chojnacki;Michael J. Brooks;Anton van den Hengel;Darren Gawley
Affiliations:
-;-;-;-
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
2004

Citing 9
Cited 12

Three-dimensional computer vision: a geometric viewpoint

Three-dimensional computer vision: a geometric viewpoint
The symmetric eigenvalue problem

The symmetric eigenvalue problem
Direct Least Square Fitting of Ellipses

IEEE Transactions on Pattern Analysis and Machine Intelligence
Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint

International Journal of Computer Vision - Special issue on a special section on visual surveillance
On the Fitting of Surfaces to Data with Covariances

IEEE Transactions on Pattern Analysis and Machine Intelligence
Rationalising the Renormalisation Method of Kanatani

Journal of Mathematical Imaging and Vision
Statistical Optimization for Geometric Computation: Theory and Practice

Statistical Optimization for Geometric Computation: Theory and Practice
Heteroscedastic errors-in-variables models in computer vision

Heteroscedastic errors-in-variables models in computer vision
Revisiting Hartley's Normalized Eight-Point Algorithm

IEEE Transactions on Pattern Analysis and Machine Intelligence

Point Matching under Large Image Deformations and Illumination Changes

IEEE Transactions on Pattern Analysis and Machine Intelligence
FNS, CFNS and HEIV: A Unifying Approach

Journal of Mathematical Imaging and Vision
When are Simple LS Estimators Enough? An Empirical Study of LS, TLS, and GTLS

International Journal of Computer Vision
Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications

IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Convergence of Fitting Algorithms in Computer Vision

Journal of Mathematical Imaging and Vision
A Bilinear Approach to the Parameter Estimation of a General Heteroscedastic Linear System, with Application to Conic Fitting

Journal of Mathematical Imaging and Vision
Statistical Optimization for Geometric Fitting: Theoretical Accuracy Bound and High Order Error Analysis

International Journal of Computer Vision
Error Analysis in Homography Estimation by First Order Approximation Tools: A General Technique

Journal of Mathematical Imaging and Vision
Robust fitting of ellipses and spheroids

Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Robust ellipse and spheroid fitting

Pattern Recognition Letters
Optimal estimation of homogeneous vectors

SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Geometric property based ellipse detection method

Journal of Visual Communication and Image Representation

Quantified Score

Hi-index	0.14

Visualization

Abstract

Abstract--Problems requiring accurate determination of parameters from image-based quantities arise often in computer vision. Two recent, independently developed frameworks for estimating such parameters are the FNS and HEIV schemes. Here, it is shown that FNS and a core version of HEIV are essentially equivalent, solving a common underlying equation via different means. The analysis is driven by the search for a nondegenerate form of a certain generalized eigenvalue problem and effectively leads to a new derivation of the relevant case of the HEIV algorithm. This work may be seen as an extension of previous efforts to rationalize and interrelate a spectrum of estimators, including the renormalization method of Kanatani and the normalized eight-point method of Hartley.