Showing papers on "Affine involution published in 1997"
Proceedings Article•
23 Aug 1997TL;DR: A new technique for affine reconstruction from two affine images is developed, which consists in first estimating the affine epipolar geometry and then performing a triangulation for each point match with respect to an implicit common affine basis.
Abstract: This paper addresses the recovery of structure and motion from two uncalibrated images of a scene under full perspective or under affine projection. Epipolar geometry, projective reconstruction, and affine reconstruction are elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A general expression of the fundamental matrix is derived which is valid for any projection model without lens distortion (including full perspective and affine camera). A new technique for affine reconstruction from two affine images is developed, which consists in first estimating the affine epipolar geometry and then performing a triangulation for each point match with respect to an implicit common affine basis. This technique is very efficient.
28 citations
TL;DR: This paper proposes new “hypergeometric” filters for the problem of image matching under the translational and affine model that can be applied to a broad class of matching problems as long as the transformation between the two image patches can be mathematically represented in the frequency domain.
Abstract: This paper proposes new “hypergeometric” filters for the problem of image matching under the translational and affine model. This new set of filters has the following advantages: (1) High-precision registration of two images under the translational and affine model. Because the window effects are eliminated, we are able to achieve superb performance in both translational and affine matching. (2) Affine matching without exhaustive search or image warping. Due to the recursiveness of the filters in the spatial domain, We are able to analytically express the relation between filter outputs and the six affine parameters. This analytical relation enables us to directly compute these affine parameters. (3) Generality. The approach we demonstrate here can be applied to a broad class of matching problems as long as the transformation between the two image patches can be mathematically represented in the frequency domain.
14 citations
TL;DR: In this paper, the infimum and supremum measurements of affine operators and Littlewood-Paley energy functions with matrix dilations are derived and a matrix-dilation oversampling theorem on preservation of frame-bound ratios is established.
Abstract: Affine operators and Littlewood--Paley energy functions with matrix dilations are considered in this paper. Estimates and comparisons of the infimum and supremum measurements of these two operations are derived. These results are applied to the study of affine frames and wavelets. In particular, multivariate matrix-dilated wavelet families are characterized and a matrix-dilation oversampling theorem on preservation of frame-bound ratios is established.
11 citations
TL;DR: In this paper, it was shown that affine complete algebras are congruence distributive, i.e., all polynomial operations over the universe are compatible with all its congruences.
Abstract: An algebra is affine complete iff its polynomial operations are the same as all the operations over its universe that are compatible with all its congruences. A variety is affine complete iff all its algebras are. We prove that every affine complete variety is congruence distributive, and give a useful characterization of all arithmetical, affine complete varieties of countable type. We show that affine complete varieties with finite residual bound have enough injectives. We also construct an example of an affine complete variety without finite residual bound.¶ We prove several results concerning residually finite varieties whose finite algebras are congruence distributive, while leaving open the question whether every such variety must be congruence distributive.
10 citations
9 citations
1 Nov 1997
TL;DR: In this paper, it was shown that the operator T with constant coefficients is semi-Fredholm with dim Ker T* < ∞, and it is Fredholm with ind T = 0 in the case λ i ≠ λ j.
Abstract: Solvability conditions for the equation in classes of continuous or smooth functions ϕ(x) in ℝyn are investigated. We establish that this equation is normally solvable in some class of smooth functions. Moreover, we prove that the operator T with constant coefficients is semi-Fredholm with dim Ker T* < ∞, and it is Fredholm with ind T = 0 in the case λ i ≠ λ j .
2 citations
Journal Article•
1 citations
TL;DR: In this article, a proof of Auslander's conjecture for affine spaces of dimension at most 6 is given for real affine space A of finite dimension, where Γ is a subgroup of the group of all affine transformations of A. Theorem 6.1.
Abstract: Let Γ be a subgroup of the group of all affine transformations of a real affine space A of finite dimension. Suppose that Γ acts properly discontinuously on A. We determine which orthogonal groups can occur as Zariski closures of the linear part of Γ. Our methods yield a proof of Auslander's conjecture for affine spaces of dimension at most 6.