Multi-view Geometry: Correspondences Refinement Based on Algebraic Properties
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.
Code (0)
등록된 구현이 없습니다.
Tasks
3D ReconstructionSimilar Papers 제목 키워드 기반
Algebraic Relations and Triangulation of Unlabeled Image Points
In multiview geometry when correspondences among multiple views are unknown the image points can be understood as being unlabeled. This is a common problem in computer vision. We give a novel approach to handle such a si…
Snapshot of Algebraic Vision
In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry …
3D Scene ReconstructionSurveyMoRe: Monocular Geometry Refinement via Graph Optimization for Cross-View Consistency
Monocular 3D foundation models offer an extensible solution for perception tasks, making them attractive for broader 3D vision applications. In this paper, we propose MoRe, a training-free Monocular Geometry Refinement m…
Novel View Synthesis3D ReconstructionThe Joint Image Handbook
Given multiple perspective photographs, point correspondences form the "joint image", effectively a replica of three dimensional space distributed across its two-dimensional projections. This set can be characterized by …
Tangent Sampson Error: Fast Approximate Two-view Reprojection Error for Central Camera Models
In this paper we introduce the Tangent Sampson error, which is a generalization of the classical Sampson error in two-view geometry that allows for arbitrary central camera models. It only requires local gradients of…