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Similarity (geometry)

About: Similarity (geometry) is a(n) research topic. Over the lifetime, 4427 publication(s) have been published within this topic receiving 109720 citation(s).

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Journal ArticleDOI: 10.1109/34.993558
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.

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Topics: Shape analysis (digital geometry) (64%), Heat kernel signature (58%), Shape context (58%) ...read more

6,426 Citations


Open accessBook ChapterDOI: 10.1007/978-3-642-15561-1_56
05 Sep 2010-
Abstract: We propose to use binary strings as an efficient feature point descriptor, which we call BRIEF. We show that it is highly discriminative even when using relatively few bits and can be computed using simple intensity difference tests. Furthermore, the descriptor similarity can be evaluated using the Hamming distance, which is very efficient to compute, instead of the L2 norm as is usually done. As a result, BRIEF is very fast both to build and to match. We compare it against SURF and U-SURF on standard benchmarks and show that it yields a similar or better recognition performance, while running in a fraction of the time required by either.

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  • Fig. 9. Left: Using CenSurE keypoints instead of SURF keypoints. BRIEF works slightly better with CenSurE than with SURF keypoints. Right: Recognition rate when matching the first image of the Wall dataset against a rotated version of itself, as a function of the rotation angle.
    Fig. 9. Left: Using CenSurE keypoints instead of SURF keypoints. BRIEF works slightly better with CenSurE than with SURF keypoints. Right: Recognition rate when matching the first image of the Wall dataset against a rotated version of itself, as a function of the rotation angle.
  • Fig. 3. Recognition rate for the five different test geometries introduced in section 3.2.
    Fig. 3. Recognition rate for the five different test geometries introduced in section 3.2.
  • Fig. 6. Recognition rates on (a) Wall (b) Fountain. (c) Graffiti (d) Trees (e) Jpg (f) Light. The trailing 16, 32, or 64 in the descriptor’s name is its length in bytes. It is much shorter than those of SURF and U-SURF, which both are 256. For completeness, we also compare to a recent approach called Compact Signatures [7] which has been shown to be very efficient. We obtained the code from OpenCV’s SVN repository.
    Fig. 6. Recognition rates on (a) Wall (b) Fountain. (c) Graffiti (d) Trees (e) Jpg (f) Light. The trailing 16, 32, or 64 in the descriptor’s name is its length in bytes. It is much shorter than those of SURF and U-SURF, which both are 256. For completeness, we also compare to a recent approach called Compact Signatures [7] which has been shown to be very efficient. We obtained the code from OpenCV’s SVN repository.
  • Fig. 4. Distributions of Hamming distances for matching pairs of points (thin blue lines) and for non-matching pairs (thick red lines) in each of the five image pairs of the Wall dataset. They are most separated for the first image pairs, whose baseline is smaller, ultimately resulting in higher recognition rates.
    Fig. 4. Distributions of Hamming distances for matching pairs of points (thin blue lines) and for non-matching pairs (thick red lines) in each of the five image pairs of the Wall dataset. They are most separated for the first image pairs, whose baseline is smaller, ultimately resulting in higher recognition rates.
  • Fig. 5. Data sets used for comparison purposes. Each one contains 6 images and we consider 5 image pairs by matching the first one against all others.
    Fig. 5. Data sets used for comparison purposes. Each one contains 6 images and we consider 5 image pairs by matching the first one against all others.
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Topics: Hamming distance (56%), Feature (machine learning) (52%), Binary number (50%) ...read more

3,092 Citations


Journal ArticleDOI: 10.1007/BF02289630
Roger N. Shepard1Institutions (1)
01 Jun 1962-Psychometrika
Abstract: A computer program is described that is designed to reconstruct the metric configuration of a set of points in Euclidean space on the basis of essentially nonmetric information about that configuration. A minimum set of Cartesian coordinates for the points is determined when the only available information specifies for each pair of those points—not the distance between them—but some unknown, fixed monotonic function of that distance. The program is proposed as a tool for reductively analyzing several types of psychological data, particularly measures of interstimulus similarity or confusability, by making explicit the multidimensional structure underlying such data.

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Topics: Euclidean distance (60%), Set function (59%), Metric (mathematics) (58%) ...read more

2,369 Citations


Journal ArticleDOI: 10.1109/34.88573
Abstract: In many applications of computer vision, the following problem is encountered. Two point patterns (sets of points) (x/sub i/) and (x/sub i/); i=1, 2, . . ., n are given in m-dimensional space, and the similarity transformation parameters (rotation, translation, and scaling) that give the least mean squared error between these point patterns are needed. Recently, K.S. Arun et al. (1987) and B.K.P. Horn et al. (1987) presented a solution of this problem. Their solution, however, sometimes fails to give a correct rotation matrix and gives a reflection instead when the data is severely corrupted. The proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted. >

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Topics: Rotation (mathematics) (54%), Transformation (function) (53%), Similarity (geometry) (53%) ...read more

1,783 Citations


Proceedings ArticleDOI: 10.1109/ICPR.1994.576361
M.-P. Dubuisson1, Anil K. JainInstitutions (1)
09 Oct 1994-
Abstract: The purpose of object matching is to decide the similarity between two objects. This paper introduces 24 possible distance measures based on the Hausdorff distance between two point sets. These measures can be used to match two sets of edge points extracted from any two objects. Based on experiments on synthetic images containing various levels of noise, the authors determined that one of these distance measures, called the modified Hausdorff distance (MHD) has the best performance for object matching. The advantages of MHD ever other distances are also demonstrated on several edge snaps of objects extracted from real images.

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Topics: Hausdorff distance (67%), Similarity (geometry) (58%), Distance measures (57%) ...read more

1,389 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20224
2021209
2020217
2019240
2018204
2017217

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Topic's top 5 most impactful authors

Longin Jan Latecki

10 papers, 618 citations

Xiang Bai

8 papers, 289 citations

Paolo Ciaccia

7 papers, 292 citations

Edwin R. Hancock

6 papers, 88 citations

Benjamin B. Kimia

5 papers, 574 citations

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