Recovering Epipolar Geometry from Images of Smooth Surfaces

TL;DR

This paper introduces four novel methods for recovering epipolar geometry from images of smooth surfaces, overcoming the challenge of lacking feature points, with two methods providing exact results and two offering approximate solutions.

Contribution

The paper presents four new methods for epipolar geometry recovery from smooth surfaces, including two exact and two approximate techniques based on illumination and curvature features.

Findings

Exact methods (ICPM and OTPM) produce correct results for real images.

Approximate methods (CCPM and CTPM) yield finite solution sets.

Outline and illumination points are unaffected by brightness inconsistencies.

Abstract

We present four methods for recovering the epipolar geometry from images of smooth surfaces. In the existing methods for recovering epipolar geometry corresponding feature points are used that cannot be found in such images. The first method is based on finding corresponding characteristic points created by illumination (ICPM - illumination characteristic points' method (PM)). The second method is based on correspondent tangency points created by tangents from epipoles to outline of smooth bodies (OTPM - outline tangent PM). These two methods are exact and give correct results for real images, because positions of the corresponding illumination characteristic points and corresponding outline are known with small errors. But the second method is limited either to special type of scenes or to restricted camera motion. We also consider two more methods which are termed CCPM (curve characteristic PM) and CTPM (curve tangent PM), for searching epipolar geometry for images of smooth bodies based on a set of level curves with constant illumination intensity. The CCPM method is based on searching correspondent points on isophoto curves with the help of correlation of curvatures between these lines. The CTPM method is based on property of the tangential to isophoto curve epipolar line to map into the tangential to correspondent isophoto curves epipolar line. The standard method (SM) based on knowledge of pairs of the almost exact correspondent points. The methods have been implemented and tested by SM on pairs of real images. Unfortunately, the last two methods give us only a finite subset of solutions including "good" solution. Exception is "epipoles in infinity". The main reason is inaccuracy of assumption of constant brightness for smooth bodies. But outline and illumination characteristic points are not influenced by this inaccuracy. So, the first pair of methods gives exact results.