Two-View Orthographic Epipolar Geometry: Minimal and Optimal Solvers

Abstract

We will in this paper present methods and algorithms for estimating two-view geometry based on an orthographic camera model. We use a previously neglected nonlinear criterion on rigidity to estimate the calibrated essential matrix. We give efficient algorithms for estimating it minimally (using only three point correspondences), in a least squares sense (using four or more point correspondences), and optimally with respect to the number of inliers. The inlier-optimal algorithm is based on a three-point solver and gives a fourth-order polynomial time algorithm. These methods can be used as building blocks to robustly find inlier correspondences in the presence of high degrees of outliers. We show experimentally that our methods can be used in many instances, where the orthographic camera model isn't generally used. A case of special interest is situations with repetitive structures, which give high amounts of outliers in the initial feature point matching.

A Structure From Motion Pipeline for Orthographic Multi-View Images

“…Blonquist and Pack [16] propose a bundle adjustment variant specially optimized for orthographic images. In addition, Oskarsson [17] , Larsson et al [18] and Julià et al [4] Fig. 1: Proposed SfM Pipeline Architecture.…”

An Efficient Point-Matching Method Based on Multiple Geometrical Hypotheses

“…The fundamental matrix F is a conventional way to demonstrate the relationship between r and m [18,27]. F contains the intrinsic geometry of the two views, named the epipolar geometry.…”

“…In two views, the main purpose of the minimization process is to correctly determine a single epipolar line with the aim of finding an optimum epipole [18,39]. Proposed methods have been developed for situations in which there is an important number of wrong correspondences.…”

“…Over the last 20 years, different methods for addressing the point-matching problem have been proposed. Methods and techniques based on the analysis and optimization of the invariant descriptors [12][13][14], estimation of affine transformations/homographies/perspective transformations [15][16][17], epipolar geometry analysis [18][19][20], optical flow-based methods [21,22], and methods based on geometric and photometric constraints [4,23] are some of the approaches already explored.…”