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Invariant fitting of two view geometry.

P H S Torr¹, A W Fitzgibbon

¹School of Mathematics and Computing, Oxford Brookes University, Wheatley, Oxford OX33 1HX, UK. philiptorr@brookes.ac.uk

IEEE Transactions on Pattern Analysis and Machine Intelligence

|October 6, 2004

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This study extends conic fitting methods to determine epipolar geometry, finding a unique normalization for invariant estimation of the Essential matrix (E) or Fundamental matrix (F). The novel approach enhances stability and equiform invariance in computer vision tasks.

Area of Science:

Computer Vision
Geometric Deep Learning
Image Analysis

Background:

Epipolar geometry is crucial for 3D reconstruction and scene understanding.
Existing methods for estimating Essential (E) and Fundamental (F) matrices have limitations in stability and invariance.
Conic fitting methods offer a robust foundation for geometric estimation.

Purpose of the Study:

To extend conic fitting methods for robust epipolar geometry determination.
To develop an invariant method for estimating the Essential matrix (E) in calibrated cases and the Fundamental matrix (F) in uncalibrated cases.
To introduce a novel normalization technique for improved stability and equiform invariance.

Main Methods:

Extension of Bookstein's and Sampson's conic fitting algorithms.

Related Experiment Videos

Development of a unique normalization for image transformation invariance.

Application of eigenvector methods to a derived quadratic form for matrix estimation.

Comparison with existing methods like Hartley's preconditioning.

Main Results:

A novel method for determining epipolar geometry (E or F) invariant to Euclidean transformations.
Identification of a single, suitable normalization for coefficient fitting.
Demonstration of improved stability compared to previous techniques.
Invariance to equiform transformations achieved.

Conclusions:

The proposed method provides a stable and invariant approach to epipolar geometry estimation.
This technique enhances the accuracy of 3D reconstruction and related computer vision applications.
The method is applicable to both calibrated and uncalibrated vision systems.