Topic

# Similarity (geometry)

About: Similarity (geometry) is a research topic. Over the lifetime, 4427 publications have been published within this topic receiving 109720 citations.

##### Papers published on a yearly basis

##### Papers

More filters

••

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.

6,693 citations

••

05 Sep 2010TL;DR: This work proposes to use binary strings as an efficient feature point descriptor, which is called BRIEF, and shows that it is highly discriminative even when using relatively few bits and can be computed using simple intensity difference tests.

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.

3,558 citations

••

Bell Labs

^{1}TL;DR: The results of two kinds of test applications of a computer program for multidimensional scaling on the basis of essentially nonmetric data are reported to measures of interstimulus similarity and confusability obtained from some actual psychological experiments.

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.

2,461 citations

••

TL;DR: The proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted.

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. >

2,123 citations

••

26 Feb 2002TL;DR: This work formalizes non-metric similarity functions based on the longest common subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to similar portions of the sequences.

Abstract: We investigate techniques for analysis and retrieval of object trajectories in two or three dimensional space. Such data usually contain a large amount of noise, that has made previously used metrics fail. Therefore, we formalize non-metric similarity functions based on the longest common subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translation of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and time warping distance functions (for real and synthetic data) and show the superiority of our approach, especially in the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach.

1,504 citations