An automatic method for generating affine moment invariants

Affine moment invariants are important if one wants to recognize the surface of a plane in three dimensions when the orientation of the plane is not known beforehand and only two-dimensional information is available. The notion of generating function is introduced as a simple and straightforward way to derive various affine invariants. By this notion, we can get the explicit construction of much more affine moment invariants. Based on this conclusion, a large set of invariant polynomials can be generated automatically and immediately by the algorithm we have designed. These new affine moment invariants can be applied to recognize the image. Approaches in this paper will improve the practicability of affine invariants in object recognition applications.     

Affine Curvature Scale Space with Affine Length Parametrisation

The maxima of Curvature Scale Space (CSS) image have been used to represent 2D shapes under affine transforms. The CSS image is expected to be in the MPEG-7 package of standards. Since the CSS image employs the arc length parametrisation which is not affine invariant, we expect some deviations in the maxima of the CSS image under general affine transforms. Affine length and affine curvature have already been introduced and used as alternatives to arc length and conventional curvature in affine transformed environments. The utility of using these parameters to enrich the CSS representation is addressed in this paper. We use arc length to parametrise the curve prior to computing its CSS image. The parametrisation has been proven to be invariant under affine transformation and has been used in many affine invariant shape recognition methods. Since the organisation of the CSS image is based on curvature zero crossings of the curve, in this paper, we also investigate the advantages and shortcomings of using affine curvature in computation of the CSS image. The enriched CSS representations are then used to find similar shapes from a very large prototype database, and also a small classified database, both consisting of original as well as affine transformed shapes. An improvement is observed over the conventional CSS image.     

仿射变换在密码学中的应用

为了使信息在传输的过程中更加安全,提出仿射变换的概念.仿射变换可以看作一个简单的加密系统,给出仿射变换的条件,以及仿射变化的优点.     

Coarse-grained loop parallelization: Iteration Space Slicing vs affine transformations

Automatic coarse-grained parallelization of program loops is of great importance for parallel computing systems. This paper presents the theory of Iteration Space Slicing aimed at extracting synchronization-free parallelism available in arbitrarily nested program loops. We demonstrate that Iteration Space Slicing algorithms permits for extracting more coarse-grained parallelism than that extracted by means of the Affine Transformation Framework provided that we are able to calculate the transitive closure of the union of relations describing all dependences in the affine loop. Experimental results show that by means of Iteration Space Slicing algorithms, we are able to extract coarse-grained parallelism for many loops of NAS and UTDSP benchmarks. Problems to be resolved in order to enhance the theory of Iteration Space Slicing are discussed.     

Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic

We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and sub-formulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster.     

A Unified Theory of Uncalibrated Stereo for Both Perspective and Affine Cameras

This paper addresses the recovery of structure and motion from uncalibrated images of a scene under full perspective or under affine projection. Particular emphasis is placed on the configuration of two views, while the extension to $N$ views is given in Appendix. A unified expression of the fundamental matrix is derived which is valid for any projection model without lens distortion (including full perspective and affine camera). Affine reconstruction is considered as a special projective reconstruction. The theory is elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A new technique for affine reconstruction 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.     

基于仿射变换的图象定位方法

本文主要针对复杂地物背景下的一般图象目标,在应用本征空间方法进行鲁棒跟踪等方面做了大量研究工作.放弃了基于平移运动模型的传统相关算法,改用仿射变换运动模型,借助快速解法,在保持跟踪定位鲁棒性的基础上,实现了以实时的速度处理目标发生的旋转、平移、放缩等仿射变化.通过理论分析以及大量实验验证,配合以适当的模板更新策略,该方法可以构成一种替代传统互相关跟踪的新方法.     

Ray casting implicit fractal surfaces with reduced affine arithmetic

A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store.     

Differential Evolution as a viable tool for satellite image registration

A software system grounded on Differential Evolution to automatically register multiview and multitemporal images is designed, implemented and tested through a set of 2D satellite images on two problems, i.e. mosaicking and changes in time. Registration is effected by looking for the best affine transformation in terms of maximization of the mutual information between the first image and the transformation of the second one, and no control points are needed in this approach. This method is compared against five widely available tools, and its effectiveness is shown.     

3D object recognition using invariants of 2D projection curves

This paper presents a new method for recognizing 3D objects based on the comparison of invariants of their 2D projection curves. We show that Euclidean equivalent 3D surfaces imply affine equivalent 2D projection curves that are obtained from the projection of cross-section curves of the surfaces onto the coordinate planes. Planes used to extract cross-section curves are chosen to be orthogonal to the principal axes of the defining surfaces. Projection curves are represented using implicit polynomial equations. Affine algebraic and geometric invariants of projection curves are constructed and compared under a variety of distance measures. Results are verified by several experiments with objects from different classes and within the same class.