Abstract
The correspondence function (CF) is a concept recently introduced to reject the mismatches from given putative correspondences. The fundamental idea of the CF is that the relationship of some corresponding points between two images to be registered can be described by a pair of vector-valued functions, estimated by a nonparametric regression method with more flexibility than the normal parametric model, for example, homography matrix, similarity transformation, and projective transformations. Mismatches are rejected by checking their consistency with the CF. This paper proposes a visual scheme to investigate the fundamental principles of the CF and studies its characteristics by experimentally comparing it with the widely used parametric model epipolar geometry (EG). It is shown that the CF describes the mapping from the points in one image to their corresponding points in another image, which enables a direct estimation of the positions of the corresponding points. In contrast, the EG acts by reducing the search space for corresponding points from a two-dimensional space to a line, which is a problem in one-dimensional space. As a result, the undetected mismatches of the CF are usually near the correct corresponding points, but many of the undetected mismatches of the EG are far from the correct point.
Highlights
Finding point correspondences between two images is a fundamental problem in computer vision [1, 2]
This paper proposes a visual scheme to investigate the fundamental principles of the correspondence function (CF) and studies its characteristics by experimentally comparing it with the widely used parametric model epipolar geometry (EG)
The fundamental idea of CF is that, for two given images I and I of a scene, the relationships between their corresponding points (CPs) can be described by a pair of vector-valued functions, which are estimated by a nonparametric regression method
Summary
Finding point correspondences between two images is a fundamental problem in computer vision [1, 2]. Compared with the representations based on a large spatial area, local feature descriptors are usually more robust to brightness variation, deformation, and occlusion but have less distinctiveness. This typically results in a high percentage of mismatches/outliers among the computed putative correspondences, which are very likely to ruin traditional estimation methods [8,9,10]. The fundamental idea of CF is that, for two given images I and I of a scene, the relationships between their CPs can be described by a pair of vector-valued functions, which are estimated by a nonparametric regression method. The result of the difference between EG and CF is that the undetected mismatches by CF are usually near the correct CPs, but many of the undetected mismatches of EG are far from the correct correspondence
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