3D discrete rotations using hinge angles

In this paper, we study 3D rotations on grid points computed by using only integers. For that purpose, we investigate the intersection between the 3D half-grid and the rotation plane. From this intersection, we define 3D hinge angles which determine a transit of a grid point from a voxel to its adjacent voxel during the rotation. Then, we give a method to sort all 3D hinge angles with integer computations. The study of 3D hinge angles allows us to design a 3D discrete rotation and to estimate the rotation between a pair of digital images in correspondence.     

Exact, scaled image rotations in finite Radon transform space

The Finite Radon Transform (FRT) is a discrete analogue of classical tomography. The FRT permits exact reconstruction of a discrete object from its discrete projections. The set of projection angles for the FRT is intrinsic to each image array size. It is shown here that the set of FRT angles is closed under a rotation by any of its members. A periodic re-ordering of the elements of the 1D FRT projections is then equivalent to an exact 2D image rotation. FRT-based rotations require minimal interpolation and preserve all of the original image pixel intensities. This approach has applications in image feature matching, multi-scale data representation and data encryption.     

结合块旋转和马赛克拼图的生成式伪装方法

目的 搜索式无载体信息隐藏容量低,涉及大量载体密集传输;纹理合成无载体隐藏只能生成简单质地的纹理图像;马赛克拼图信息隐藏尽管能产生有意义图像,但需修改嵌入参数。针对以上问题,提出一种结合块旋转和马赛克拼图的生成式伪装方法。方法 将灰度图像进行圆形化并添加随机转角构建马赛克,通过随机坐标决定秘密信息的隐藏位置;在隐藏位置,根据密钥和放置位置来放置代表秘密比特串的圆形图像和施加认证转角,对于非隐藏位置则放置最接近圆形图像来掩盖秘密信息;将放置过程产生的偏差通过误差扩散分散给周围未处理像素。在提取时,结合质心旋转匹配提取秘密比特并进行转角认证。结果 采用圆形图像表达秘密信息而不涉及修改式嵌入,通过马赛克拼图产生有意义含密掩体,可通过质心旋转匹配提取秘密比特并进行转角认证。对密钥严格依赖,在遭受质量因子为50~80的JPEG压缩和随机转角攻击时,秘密信息可完整恢复,在遭受强度为8%~20%的椒盐噪声攻击时,提取信息的误码率低于5%,且对秘密信息的认证成功率均在80%以上。结论 所提方法具有较好的抗攻击能力,可抵御信道攻击且具备较高的安全性。     

Matrix bounds of the discrete ARE solution

This paper provides new lower and upper matrix bounds of the solution to the discrete algebraic Riccati equation. The lower bound always works if the solution exists. The upper bounds are presented in terms of the solution of the discrete Lyapunov equation and its upper matrix bound. The upper bounds are always calculated if the solution of the Lyapunov equation exists. A numerical example shows that the new bounds are tighter than previous results in many cases.     

Euler angles: conversion of arbitrary rotation sequences to specific rotation sequence

Euler angles have been used to describe the orientation of objects in two‐dimensional and three‐dimensional spaces since its formulation by Leonhard Euler. Many applications intended to represent the rotation of a body have been developed on the basis of Euler angles. Two‐dimensional rotations are combined in sequence to represent three‐dimensional rotations. Because there are three axes in a three‐dimensional Euclidean space (X, Y and Z), 12 rotation sequences in three dimensions are possible: XYZ, XZY, YXZ, YZX, ZXY, ZYX, XYX, ZYZ, ZXZ, YXY, XZX and YZY. Each rotation sequence yields different results, and different applications implement a different rotation sequence. Thus, conversion between different rotation sequences becomes essential to make applications developed in different rotation sequences compatible with each other. In this paper, a new method is introduced to convert arbitrary rotation sequences to a specific rotation sequence of choice. A sample program is also developed in a MATLAB‐Simulink environment to demonstrate the use of the new method in converting an arbitrary Euler rotation sequence to the specific Euler rotation sequence of XYZ. A six‐degrees‐of‐freedom animation block is used in the program to aid users to graphically see the rotation of a body in three‐dimensional space. Copyright © 2013 John Wiley & Sons, Ltd.     

Angle counts for isothetic polygons and polyhedra

In the case of isothetic simple polyhedra there are only six different types of 3D angles. This article states and proofs a formula about counts of these angles. This complements formulas in combinatorial topology such as Euler’s polyhedron formula, or the previously known formula on angle counts for isothetic polygons. The latter formula and the shown equality for angle counts of isothetic simple polyhedra are useful formulas for analyzing isothetic boundaries in 2D digital images (e.g. classification into inner (boundary of a hole) or outer boundaries, see Voss [Discrete Images, Objects, and Functions in Zⁿ, Springer, Berlin, 1993]) and isothetic surfaces in 3D digital images (e.g. necessary condition for a complete surface scan).     

H ∞ observer design for uncertain nonlinear discrete‐time systems with time‐delay: LMI optimization approach

We present a robust H _∞ observer for a class of nonlinear discrete‐time systems. The class under study includes an unknown time‐varying delay limited by upper and lower bounds, as well as time‐varying parametric uncertainties. We design a nonlinear H _∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time‐varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi‐objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples. Copyright © 2014 John Wiley & Sons, Ltd.     

基于FPGA的高速高质量图像旋转

为了进行高质量、高速的图像旋转变换 ,通过对传统图像旋转矩阵的分解 ,将图像在二维空间中的旋转运算分解成为三次一维空间内的平移运算 ,从而将用于图像旋转运算的二维插值运算简化为在一维空间中进行的一维插值运算。为了保证图像旋转后的质量 ,采用 3阶 B-样条对每次平移后像素点的灰度值进行插值运算 ,并提出了一种基于 IIR和 FIR数字滤波器的 3阶 B-样条插值法的高速实现方案 ;最后针对 2 5 6灰度级 ,2 5 6× 2 5 6像素的图像设计出一种基于 FPGA的高速、高质量的硬件图像旋转及显示系统     

基于FPGA的二维码图像旋转系统

阐述了在图像预处理阶段将二维码图像旋转至端正的必要性。设计了一种求取QR二维码图像旋转角度的算法以及一种可将二维码图像旋转任意角度的算法。求取旋转角度算法简捷有效,能以较低的硬件代价实现。图像旋转算法利用了CORDIC算法以及双线性插值算法,采用高速流水线架构在FPGA上实现。整个设计在Altera公司的DE2平台下进行了验证。实验结果表明,这两种算法结合使用可以快速有效地将带有一定歪斜角度的二维码图像旋转端正,速度可以达到90.9 MHz,旋转后的图像细节清晰,能有效提高二维码的识别率。     

Mutual information, variation, and Fano’s inequality

Some upper and lower bounds are obtained for the maximum of the absolute value of the difference between the mutual information |I(X; Y) ? I(X′; Y′)| of two pairs of discrete random variables (X, Y) and (X′, Y′) via the variational distance between the probability distributions of these pairs. In particular, the upper bound obtained here substantially generalizes and improves the upper bound of [1]. In some special cases, our upper and lower bounds coincide or are rather close. It is also proved that the lower bound is asymptotically tight in the case where the variational distance between (X, Y) and (X′ Y′) tends to zero.     

Constraints on length and angle

Given a perspective projection of line segments on the image plane, the constraints on their 3D positions and orientations are derived on the assumption that their true lengths or the true angles they make are known. The approach here is first to transform images of line segments to the center of the image plane as if the camera were rotated to aim at them. The 3D information extracted in this canonical position is then transformed back to the original configuration. Examples are given, by using real images, for analytical 3D recovery of a rectangular corner and a corner with two right angles.     

Measure of circularity for parts of digital boundaries and its fast computation

This paper focuses on the design of an effective method that computes the measure of circularity of a part of a digital boundary. An existing circularity measure of a set of discrete points, which is used in computational metrology, is extended to the case of parts of digital boundaries. From a single digital boundary, two sets of points are extracted so that the circularity measure computed from these sets is representative of the circularity of the digital boundary. Therefore, the computation consists of two steps. First, the inner and outer sets of points are extracted from the input part of a digital boundary using digital geometry tools. Next, the circularity measure of these sets is computed using classical tools of computational geometry. It is proved that the algorithm is linear in time in the case of convex parts thanks to the specificity of digital data, and is in O(nlogn) otherwise. Experiments done on synthetic and real images illustrate the interest of the properties of the circularity measure.     

基于边缘几何特征的图像精确匹配方法

提出一组快速高精度计算切线斜率的五点公式,用以估计图像边缘曲线的角度特征,并利用角度直方图估计图像几何变换的旋转参数,实现具有大旋转差异图像间的粗匹配．在进行角度补偿后,利用灰度互相关判据搜索匹配点对,计算出几何变换参数,实现较高精度的旋转和平移校正,最后用松弛迭代法完成图像的精确匹配．与基于小波方向角特征的匹配方法相比,文中方法利用图像中主要的边缘信息实施匹配,具有较好的鲁捧性,可成功实现对各类具有较大相关程度图像间的精确匹配,对图形匹配也具有重要意义．     

从单幅灰度图像中求解三维物体姿态的方法

诸如车辆之类的三维物体的运动常常被约束于一个平面上.这种平面约束显著减少二维图像到三维目标的匹配自由度,从而使得这类三维目标的识别问题得到极大简化.基于此,本文提出一种从单幅定标的灰度图像中求解约束于一已知平面的三维目标的方法.该方法首先计算出给定模型所有可能的旋转角度,再通过聚类获得一些可能的旋转角度类.在每个角度类中,我们对目标所有可能的位置进行计算,并通过聚类获得在此旋转角度下的位置类.之后将候选的角度和位置进行过滤并进行优化以获得最终结果.该算法对于三维目标的部分遮挡具有较好的适应性,其有效性得到实验验证.     

Rotation-discriminating template matching based on Fourier coefficients of radial projections with robustness to scaling and partial occlusion

We consider brightness/contrast-invariant and rotation-discriminating template matching that searches an image to analyze A for a query image Q. We propose to use the complex coefficients of the discrete Fourier transform of the radial projections to compute new rotation-invariant local features. These coefficients can be efficiently obtained via FFT. We classify templates in “stable” and “unstable” ones and argue that any local feature-based template matching may fail to find unstable templates. We extract several stable sub-templates of Q and find them in A by comparing the features. The matchings of the sub-templates are combined using the Hough transform. As the features of A are computed only once, the algorithm can find quickly many different sub-templates in A, and it is suitable for finding many query images in A, multi-scale searching and partial occlusion-robust template matching.     

The twin domination number in generalized de Bruijn digraphs

Let G=(V,A) be a digraph. A set T of vertices of G is a twin dominating set of G if for every vertex v∈V?T, there exist u,w∈T (possibly u=w) such that arcs (u,v),(v,w)∈A. The twin domination numberγ^∗(G) of G is the cardinality of a minimum twin dominating set of G. In this paper we investigate the twin domination number in generalized de Bruijn digraphs GB(n,d). For the digraphs GB(n,d), we first establish sharp bounds on the twin domination number. Secondly, we give the exact values of the twin domination number for several types of GB(n,d) by constructing minimum twin dominating sets in the digraphs. Finally, we present sharp upper bounds for some special generalized de Bruijn digraphs.     

Estimating the distance to uncontrollability: A fast method and a slow one

For a linear control system (A,B), the distance to uncontrollability is characterized by

, where σ_n([A − λI,B]) is the smallest singular value of the augmented matrix [A − λI,B]. Two methods are developed to estimate the distance to uncontrollability, giving both a lower bound and an upper bound. One method is fast, requiring only one spectral decomposition of A and computations of three smallest singular values and being used for well-conditioned A. The other is slow, requiring computations of a large number of the smallest singular values, but it produces bounds as tight as possible and also a region containing global minimizers. Newton's method can be used to compute the global minimizers if one really wants.     

A double color image encryption scheme based on three-dimensional brownian motion

Image encryption is an efficient technique for image protection. This paper presents a double color image encryption (DCIE) scheme based on three-dimensional (3D) Brownian motion. The architecture of diffusion, confusion and diffusion is adopted. The proposed algorithm firstly decomposes two color plain images into R, G, B components and bit planes, then conducts XOR operation between every bit plane and a key bit plane generated from carrier images; next, arranges all the bit planes into a 3D bit matrix, performs block-in 3D Brownian motion confusion and block confusion on it, which can permute the elements across bit planes and across plain images; finally, a subsequent diffusion process is utilized to improve the encryption effect. Simulation results and performance analyses illustrate that the proposed encryption scheme can simultaneously encrypt two color images into noise-like ones that have strong ability of resisting various known attacks.     

基于小波的图像边界配准

将碎片图像拼接成原始图像是一项非常有实用价值的应用,寻找匹配边是关健一环。首先对角点间边界L₀变换为具有旋转不变性的曲线L₁,利用小波包对L₁进行分解和重构,获得不同分辨率下的边界曲线L₂。然后,对L₂进行离散余弦变换,得到一组特征矢量,求特征矢量间的欧氏距离D,D值最小的两个矢量对应的边界为相似边界,再对相似边界进行配准。从而达到拼接图像碎片恢复原始图像的目的。该算法具有识别相似边准确和旋转不变性的特点。     

Asymptotic confidence interval for conditional probability at decision making

Consideration was given to construction of a unilateral asymptotic confidence interval for an unknown conditional probability of the event A under the condition B. Analytical expressions for the boundaries of such interval were obtained for various a priori restrictions on the probabilities of the events A and B such that the probability of the event B is separable from zero by a certain value, as well that there exists an upper a priori restriction on the probability of the event A. The interval estimates obtained were compared in precision.