Multi-view Geometry: Correspondences Refinement Based on Algebraic Properties

TL;DR

This paper introduces algebraic properties for multi-view correspondences in 3D reconstruction, enabling a refinement algorithm that improves accuracy by reducing estimation errors significantly.

Contribution

It presents the first theoretical algebraic properties for multi-view correspondences and develops a refinement algorithm combining outlier detection and key-point recovery.

Findings

Reduces average correspondence error from 77 to 55 pixels

Validates the algebraic properties through real 3D reconstruction experiments

Enhances accuracy of feature matching in multi-view 3D reconstruction

Abstract

Correspondences estimation or feature matching is a key step in the image-based 3D reconstruction problem. In this paper, we propose two algebraic properties for correspondences. The first is a rank deficient matrix construct from the correspondences of at least nine key-points on two images (two-view correspondences) and the second is also another rank deficient matrix built from the other correspondences of six key-points on at least five images (multi-view correspondences). To our knowledge, there are no theoretical results for multi-view correspondences prior to this paper. To obtain accurate correspondences, multi-view correspondences seem to be more useful than two-view correspondences. From these two algebraic properties, we propose an refinement algorithm for correspondences. This algorithm is a combination of correspondences refinement, outliers recognition and missing key-points recovery. Real experiments from the project of reconstructing Buddha statue show that the proposed refinement algorithm can reduce the average error from 77 pixels to 55 pixels on the correspondences estimation. This drop is substantial and it validates our results.