Topic
Correspondence problem
About: Correspondence problem is a research topic. Over the lifetime, 1272 publications have been published within this topic receiving 47187 citations.
Papers published on a yearly basis
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Papers
TL;DR: This paper presents work on computing shape models that are computationally fast and invariant basic transformations like translation, scaling and rotation, and proposes shape detection using a feature called shape context, which is descriptive of the shape of the object.
Abstract: We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by: (1) solving for correspondences between points on the two shapes; (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits, and the COIL data set.
7,367 citations
TL;DR: A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the two projections is unknown.
Abstract: A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the two projections is unknown. This problem is relevant not only to photographic surveying1 but also to binocular vision2, where the non-visual information available to the observer about the orientation and focal length of each eye is much less accurate than the optical information supplied by the retinal images themselves. The problem also arises in monocular perception of motion3, where the two projections represent views which are separated in time as well as space. As Marr and Poggio4 have noted, the fusing of two images to produce a three-dimensional percept involves two distinct processes: the establishment of a 1:1 correspondence between image points in the two views—the ‘correspondence problem’—and the use of the associated disparities for determining the distances of visible elements in the scene. I shall assume that the correspondence problem has been solved; the problem of reconstructing the scene then reduces to that of finding the relative orientation of the two viewpoints.
2,828 citations
7 May 1994
TL;DR: A new approach to the correspondence problem that makes use of non-parametric local transforms as the basis for correlation, which can result in improved performance near object boundaries when compared with conventional methods such as normalized correlation.
Abstract: We propose a new approach to the correspondence problem that makes use of non-parametric local transforms as the basis for correlation. Non-parametric local transforms rely on the relative ordering of local intensity values, and not on the intensity values themselves. Correlation using such transforms can tolerate a significant number of outliers. This can result in improved performance near object boundaries when compared with conventional methods such as normalized correlation. We introduce two non-parametric local transforms: the rank transform, which measures local intensity, and the census transform, which summarizes local image structure. We describe some properties of these transforms, and demonstrate their utility on both synthetic and real data.
2,151 citations
TL;DR: The authors describe a camera for performing single lens stereo analysis, which incorporates a single main lens along with a lenticular array placed at the sensor plane and extracts information about both horizontal and vertical parallax, which improves the reliability of the depth estimates.
Abstract: Ordinary cameras gather light across the area of their lens aperture, and the light striking a given subregion of the aperture is structured somewhat differently than the light striking an adjacent subregion. By analyzing this optical structure, one can infer the depths of the objects in the scene, i.e. one can achieve single lens stereo. The authors describe a camera for performing this analysis. It incorporates a single main lens along with a lenticular array placed at the sensor plane. The resulting plenoptic camera provides information about how the scene would look when viewed from a continuum of possible viewpoints bounded by the main lens aperture. Deriving depth information is simpler than in a binocular stereo system because the correspondence problem is minimized. The camera extracts information about both horizontal and vertical parallax, which improves the reliability of the depth estimates. >
1,349 citations
TL;DR: This survey is motivated in part by recent developments in space–time registration, where one seeks a correspondence between non‐rigid and time‐varying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline.
Abstract: We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours or point sets. This survey is motivated in part by recent developments in space–time registration, where one seeks a correspondence between non-rigid and time-varying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult because it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function and solution approach. We conclude the survey by discussing open problems and future perspectives.
760 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 2 |
| 2023 | 13 |
| 2022 | 8 |
| 2021 | 13 |
| 2020 | 17 |
| 2019 | 15 |