Invariant fitting of two view geometry.

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.
• 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.