Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity by measuring the lack of isometry, deal with similarity by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations by resorting to the special affine arc-length definition in classical affine geometry. Here, we propose a computa...

High quality key-dependent S-boxes can break the preconditions of many cryptanalysis technologies, but it is difficult to construct them efficiently. Here, we proposed a method for fast constructing good key-dependent S-boxes, which are generated by means of a key-dependent affine transformation on a good base S-box. We proved their security by classifying the evaluative criteria of S-boxes int...

This paper addresses the recovery of structure and motion from two uncalibrated images of a scene under ful l 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 matr ix...

The Affine partitioning framework, which unifies many useful program transforms such as unimodular transformations, loop fusion, fission, scaling, reindexing, and statement reordering, has been proved to be successful in automatic discovery of the loop-level parallelization in programs. The affine partition algorithm was improved from the aspects of compile-time and runtime efficiency in this p...

Extracting features is one of the core issues in pattern recognition, in which affine invariant is important method to recognize object under complex environment. To solve the issues of the error increasing and the low efficiency for affine invariant extraction algorithms, a improved feature extraction algorithm based on region partition is proposed. First, the algorithm gets the centroid and o...

In this paper we present the basic theory of the Monge-Ampère equation together with a selection of geometric applications, mainly to affine geometry. First we introduce the Monge-Ampère measure and the resultant notion of generalized solution of Aleksandrov. Then we discuss a priori estimates and regularity, followed by the existence and uniqueness of solutions to various boundary value proble...

We define a new family F̃w(X) of generating functions for w ∈ S̃n which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions such as their symmetry and conjecture certain positivity properties. As an application, we relate these functions to the k-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. ...

We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by FominGreene-Reiner-Shimozono, and we extend this notion to affine permutations. The balanced labellings give a natural encoding of the reduced decompositions of affine permutations. We show that the sum of weight monomials of the column...

Techniques based on Interval and Affine Arithmetic and their modifications are shown to provide reliable function range evaluation for the purposes of surface interrogation. In this paper we present a technique for the reliable interrogation of implicit surfaces using a modification of Affine Arithmetic called Revised Affine Arithmetic. We extend the range of functions presented in Revised Affi...