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Viewpoint-Invariant Representation of Generalized Cylinders Using the Symmetry Set
1994
Procedings of the British Machine Vision Conference 1994
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We demonstrate that viewpoint-invariant representations can be obtained from images for a useful class of 3D smooth object. ...
Examples are given of the representations obtained from real perspective images, and their use in a model-based recognition system for canal surfaces. ...
Financial support was provided by the EPSRC, ESPRIT Project 6448 'VIVA', and the University of Oxford. ...
doi:10.5244/c.8.53
dblp:conf/bmvc/PillowUZ94
fatcat:v5uclwnbdbd7hh3e6xgtynpwqy
3D object recognition using invariance
1995
Artificial Intelligence
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A significant part of the paper is a summary of recent results on the construction of invariants for 3D objects from a single perspective view. ...
Invariance overcomes one of the fundamental difficulties in recognising objects from images: that the appearance of an object depends on viewpoint. ...
Ellen Walker of RPI ...
doi:10.1016/0004-3702(95)00023-2
fatcat:k7fmj3bfdjhttf4uwjp5d6p3hy
Geometric invariants and object recognition
1993
International Journal of Computer Vision
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I In this paper we discuss the role of the general invariance concept in object recognition, and review the classical and recent literature on projective invariance. ...
Deformations of objects are another important class of changes for which invariance is useful. ...
A general projectivity involves combinations of perspectivities and affinities. ...
doi:10.1007/bf01539536
fatcat:tve6uhevdndmlg72zo3tweajje
Page 131 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 28, Issue
[page]
1922
American Mathematical Society. Bulletin of the American Mathematical Society
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The second chapter, which deals with parallel-projection upon a single plane, includes sections on cavalier-perspective, shadows under parallel light-rays, affinity and its applications, on the foundations ...
Chapter IV, on central projection, treats of fundamental concepts, so-called restricted perspective, construction of shadows in per- spective, invariance of cross ratio, involutory perspective, applications ...
Isoperimetric normalization of planar curves
1994
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Our invariant descriptor is the first example, to our knowledge, of practical discrimination, up to projectivity, of convex, closed curves. ...
The transformation that takes the contour to its canonical form is a member of the projective group PGL(2), chosen because PGL(2) contains all possible transformations of a plane curve under central projection ...
It operates by obtaining four invariant points on a plane contour which can be used directly to define a transformation to a canonical frame [IO] . ...
doi:10.1109/34.308471
fatcat:nnt4hfi6kzggfe6gl27oskf57m
On differential invariants of planar curves and recognizing partially occluded planar shapes
1995
Annals of Mathematics and Artificial Intelligence
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The derivation of signature functions, generalizing the intrinsic curvature versus arc-length representation in the case of rigid motions in the plane, is based on differential invariants associated to ...
Viewing transformations like similarity, affine and projective maps may distort planar shapes considerably. ...
Acknowledgements We thank Nir Katzir, Isaac Weiss and Haim Wolfson for many useful discussions and references on this subject. ...
doi:10.1007/bf01530829
fatcat:bnu2sje6cvdyrg3srjnku4q5qu
Page 4756 of Mathematical Reviews Vol. , Issue 95h
[page]
1995
Mathematical Reviews
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of conjugate nets and congruences, La- place sequences, conjugate normal congruences and connection with theory of surfaces in Euclidean space); and (6) Perspectives (tangency invariants for curves, projective ...
Let [ c H® be a Jordan curve which has, for any p € B, a one-to-one p-projection on a p-convex curve in S®. ...
Shape from periodic texture using the eigenvectors of local affine distortion
2001
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces ...
The required affine distortion matrices are computed using the correspondences between spectral peaks, established on the basis of their energy ordering. ...
The intuitive justification for this result is that under perspective projection the only direction which remains invariant at all locations on the image plane is the tilt direction. ...
doi:10.1109/34.977570
fatcat:nikrtvw2xbckloss4hqldbitpm
Shape from Texture: Homogeneity Revisited
2000
Procedings of the British Machine Vision Conference 2000
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But once the plane vanishing line has been obtained, then texels locations can be determined, and the geometry of the scene plane computed up to an affine transformation. ...
The objective of this paper is to estimate the orientation of a scene plane from an uncalibrated perspective image under the assumption that the scene is coated with a homogeneous (but unknown) texture ...
This work was supported by the EU Esprit Project IMPROOFS. ...
doi:10.5244/c.14.9
dblp:conf/bmvc/CriminisiZ00
fatcat:klyubshcmve5xjxkmdjynzjwae
Abstracts of Papers: Geometry
1946
Bulletin of the American Mathematical Society
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ABSTRACTS OF PAPERS 435 GEOMETRY 181. Reinhold Baer: Projectivities with fixed points on every line of the plane. ...
But already in the projective plane with coordinates from the field of real quaternions there may be found projectivities which are neither perspectivities nor involutions, and which still belong to our ...
Another example is that the parallel of a plane curve lies on the cylinder with elements orthogonal to the plane of the original curve and whose directorial curve is the evolute. ...
doi:10.1090/s0002-9904-1946-08573-0
fatcat:nu7pqbtdfbg4redcs2vjzwl75u
Characteristic Number: Theory and Its Application to Shape Analysis
2014
Axioms
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In this paper, we present a projective invariant named after the characteristic number of planar algebraic curves. ...
Existing invariants in projective geometry are typically defined on the limited number (e.g., five for the classical cross-ratio) of collinear planar points and also lack the ability to characterize the ...
Author Contributions XF invented the idea of the applications of CN. ZL invented the original idea of the theory of CN. JZ proved the affine invariance of the characteristic ratio. ...
doi:10.3390/axioms3020202
fatcat:nttlxabbzncv7brrypggvmg7nu
Invariants and fixed structures lead the way to change
[chapter]
1996
Lecture Notes in Computer Science
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The use of invariants quickly gained impetus in the computer vision community. ...
Then, however, the paper moves on to corroborate the importance of certain geometrical entities, called "fixed structures". ...
Depending on the degree to which the fixed structures have been identified, one would then have to use 3D projective, affine, or metric invariants for 3D shape recognition. ...
doi:10.1007/3-540-61577-6_23
fatcat:hlizjgie2vduxexl44hemgm3q4
What Makes Viewpoint Invariant Properties Perceptually Salient?: A Computational Perspective
[chapter]
2000
The Kluwer International Series in Engineering and Computer Science
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However, we show that viewpoint invariance is not sufficient to distinguish these Gestalt properties; one can define an infinite number of viewpoint invariant properties that are not perceptually salient ...
We then show that generally, the perceptually salient viewpoint invariant properties are minimal, in the sense that they can be derived using less image information than non-salient properties. ...
to the first four in a way that is invariant under perspective projection. ...
doi:10.1007/978-1-4615-4413-5_8
fatcat:cdcl4vzgmzhxrcuc4lewr3ao3e
Application of affine-invariant Fourier descriptors to recognition of 3-D objects
1990
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions. ...
In this work, the method of Fourier descriptors has been extended to produce a set of normalized coefficients which are invariant under any affine transformation (translation, rotation, scaling, and shearing ...
The projection used was one which optimized the normalized between-cluster distance of the projected data. Specifically, one may define
C. ...
doi:10.1109/34.56206
fatcat:vkxd464zd5cgfo5s6h3rq3afnq
Influence of 3D Centro-Symmetry on a 2D Retinal Image
2020
Symmetry
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In this study, the geometrical properties of 3D centro-symmetry and its 2D orthographic and perspective projections were examined to find out whether 3D centro-symmetry plays any role in the perception ...
180° about an axis that is normal to the plane. ...
Now, consider a 3D centro-symmetrical pair of planar contours Φ and Ψ and their 2D perspective projections ϕ and ψ. Plane Π Φ of Φ and plane Π Ψ of Ψ are parallel to one another. ...
doi:10.3390/sym12111863
fatcat:4gomxke6hrdkbofcjrvagoz43y
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