Affine involution

Abstract: (1.2) N(T, V)= {m V(Z): Ilmll T} where we denote by V(A), for any ring A, the set of A-points of V. Hence I1\" is some Euclidean norm on R\". The only general method available for such problems is the Hardy-Littlewood circle method, which however has certain limitations, requiring roughly that the codimension of V in the ambient space A\", as well as the degree of the equations (1.1), be small relative to n. Furthermore, there are restrictions on the size of the singular sets of the related varieties:

Abstract: An almost affine code is a code C for which the size of all codes obtained by multiple puncturing of C is a power of the alphabet size. Essentially, almost affine codes are the same as ideal perfect secret haring schemes or partial affine geometries. The present paper explores these interrelations, gives short proofs of known and new results, and derives some properties of the distance distribution of almost affine codes.

Abstract: In this paper, we are concentrating on the problem of nonrigid matching of two surfaces described by points. We deform the first surface by attaching to each point a local affine transformation. We ensure that the variation of these affine transformations along the surface is smooth, that the curvature of the deformed surface tends to be preserved and that the corresponding points on the two surfaces tend to be brought nearer. We call this deformation a locally affine deformation. Our framework does not require either a prior parametrization or the knowledge of the topology of the surfaces. It is illustrated with experiments on real biomedical surfaces: faces, brains and hearts. >

Abstract: This paper presents a new affine invariant image transform called multiscale autoconvolution (MSA). The proposed transform is based on a probabilistic interpretation of the image function. The method is directly applicable to isolated objects and does not require extraction of boundaries or interest points, and the computational load is significantly reduced using the fast Fourier transform. The transform values can be used as descriptors for affine invariant pattern classification and, in this article, we illustrate their performance in various object classification tasks. As shown by a comparison with other affine invariant techniques, the new method appears to be suitable for problems where image distortions can be approximated with affine transformations.