Improving the stability of algebraic curves for applications

An algebraic curve is defined as the zero set of a polynomial in two variables. Algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics. The main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data. Usually, arguments against using algebraic curves involve references to mathematicians Wilkinson (and Runge). The first goal of this article is to understand the stability issue of algebraic curve fitting. Then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed, and its properties are investigated. The fitting algorithm is of sufficient stability for very fast position-invariant shape recognition, position estimation, and shape tracking, based on invariants and new representations. Among appropriate applications are shape-based indexing into image databases.     

Affine-invariant B-spline moments for curve matching

The article deals with the problem of matching and recognizing planar curves that are modeled by B-splines, independently of possible affine transformations to which the original curve has been subjected (for example, rotation, translation, scaling, orthographic, and semiperspective projections), and possible occlusion. It presents a fast algorithm for estimating the B-spline control points that is robust to nonuniform sampling, noise, and local deformations. Curve matching is achieved by using a similarity measure based on the B-spline knot points introduced by Cohen et al. (1991). This method, however, can neither handle the affine transformation between the curves nor the occlusion. Solutions to these two problems are presented through the use of a new class of weighted B-spline curve moments that are well defined for both open and closed curves. The method has been applied to classifying affine-transformed aircraft silhouettes, and appears to perform well.     

Automatic matching of homologous histological sections

The role of neuroanatomical atlases is undergoing a significant redefinition as digital atlases become available. These have the potential to serve as more than passive guides and to hold the role of directing segmentation and multimodal fusion of experimental data. Key elements needed to support these new tasks are registration algorithms. For images derived from histological procedures, the need is for techniques to map the two-dimensional (2-D) images of the sectional material into the reference atlas which may be a full three-dimensional (3-D) data set or one consisting of a series of 2-D images. A variety of 2-D-2-D registration methods are available to align experimental images with the atlas once the corresponding plane of section through the atlas has been identified. Methods to automate the identification of the homologous plane, however, have not been previously reported. Here, the authors use the external section contour to drive the identification and registration procedure. For this purpose, the authors model the contours by B-splines because of their attractive properties the most important of which are: (1) smoothness and continuity; (2) local controllability which implies that local changes in shape are confined to the B-spline parameters local to that change; (3) shape invariance under affine transformation, which means that the affine transformed curve is still a B-spline whose control points are related to the object control points through the transformation. The authors present a fast algorithm for estimating the control points of the B-spline which is robust to nonuniform sampling, noise, and local deformations. Curve matching is achieved by using a similarity measure that depends directly on the parameters of the B-spline. Performance tests are reported using histological material from rat brains     

一种新的仿射不变特征及其在平面曲线匹配中的应用

构造了一种新的仿射变换不变特征,提出了一种适合于仿射变换的曲线匹配算法。首先将整个轮廓区域进行仿射区域划分,得到一系列子区域质心点;然后将质心和子区域的质心点按规则构成三角形,计算三角形的面积比序列,并将其规范化,构造新的仿射不变特征。在该不变特征的基础上设计新的识别向量和差异度度量函数,通过计算待识别目标与模型曲线之...     

基于注意度的线激光视觉测量的三维形状检测

针对工件在产线上的摆置方位识别困难识别率低等问题,提出了一种基于注意度的线激光视觉测量的曲线形状识别方法。采用激光视觉三维测量技术提取工件表面的光迹信息,将工件的方位识别转换为曲线形状识别的问题。在匹配算法方面,定义了两种距离测度,分别作为粗匹配和精确匹配的误差评价函数;在识别准确性方面,定义了一种基于注意度的模板相似性测度的分类方法。实验结果表明,本文提出的方法识别率高,耗时短,对工件的平移和偏移不敏感;能满足工业生产实时检测要求,应用范围广。     

Image registration by "Super-curves"

We solve the 2-D affine image registration problem by curve matching and alignment. Our approach starts with a super-curve, which is formed by superimposing two affine related curves in one coordinate system. We use B-spline fusion technique to find a single B-spline approximation of the super-curve and a registration between the two curves simultaneously. This approach achieves superior accuracy and efficiency in curve matching and alignment. We then address the occlusion problem by finding partial match between the curves segmented using inflections and cusps, which are affine invariant. The combination of edge detection and curve alignment lead to accurate image registration.     

An Analysis of IrisCode

IrisCode is an iris recognition algorithm developed in 1993 and continuously improved by Daugman. It has been extensively applied in commercial iris recognition systems. IrisCode representing an iris based on coarse phase has a number of properties including rapid matching, binomial impostor distribution and a predictable false acceptance rate. Because of its successful applications and these properties, many similar coding methods have been developed for iris and palmprint identification. However, we lack a detailed analysis of IrisCode. The aim of this paper is to provide such an analysis as a way of better understanding IrisCode, extending the coarse phase representation to a precise phase representation, and uncovering the relationship between IrisCode and other coding methods. Our analysis demonstrates that IrisCode is a clustering algorithm with four prototypes; the locus of a Gabor function is a 2-D ellipse with respect to a phase parameter and can be approximated by a circle in many cases; Gabor function can be considered as a phase-steerable filter and the bitwise hamming distance can be regarded as a bitwise phase distance. We also discuss the theoretical foundation of the impostor binomial distribution. We use this analysis to develop a precise phase representation which can enhance accuracy. Finally, we relate IrisCode and other coding methods.      

Plane curve matching under affine transformations

It is common to use an affine transformation to approximate the plane curve matching problem under a projective transformation. The plane curve itself can be used as an identity to solve the parameters of an affine transformation. The objective of the paper is to obtain a closed form solution to the transformation parameters using lower order derivatives of a plane curve. A unique solution to the parameters of an affine transformation with up to second order derivatives is presented using differential invariants as well as the available global information. In discrete space, derivatives are obtained by numerical means. Achieving accurate numerical derivatives is always a crucial application issue. Different differentiation filters were experimented with in calculating derivatives of discrete plane curves. The ICP (iterative closest point) method was employed to improve the results obtained by the proposed invariant scheme, which was believed to be an important step towards the practical use of differential invariant schemes.     

An algorithm for successive identification of reflections

A new algorithm for successive identification of seismic reflections is proposed. Generally, the algorithm can be viewed as a curve matching method for images with specific structure. However, in the paper, the algorithm works on seismic signals assembled to constitute an image in which the investigated reflections produce curves. In numerical examples, the authors work on signals assembled in CMP gathers. The key idea of the algorithm is to estimate the reflection curve parameters and the reflection coefficients along these curves by combining the multipulse technique and the generalized Radon transform. The multipulse technique is used for wavelet identification in each trace, and the generalized Radon transform is used to coordinate the wavelet identification between the individual traces. Furthermore, a stop criterion and a reflection validation procedure are presented. The stop criterion stops the reflection estimation when the actual estimated reflection is insignificant. The reflection validation procedure ensures that the estimated reflections follow the shape of the investigated reflection curves. The algorithm is successfully used in two numerical examples. One is based on a synthetic CMP gather, whereas the other is based on a real recorded CMP gather. Initially, the algorithm requires an estimate of the wavelet that can be performed by any wavelet estimation method.     

Detection and segmentation of generic shapes based on affinemodeling of energy in eigenspace

This paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images. The set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles, circles etc. The shape set is represented by its vectorial edge map transformed over a wide range of affine parameters. We use vectorial boundary instead of regular boundary to improve the robustness to noise, background clutter and partial occlusion. Our approach consists of a detection stage and a verification stage. In the detection stage, we first derive the energy from the principal eigenvectors of the set. Next, an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen-space. Local peaks of the posterior probability map are located and indicate candidate detections. We use energy/probability based detection since we find that the underlying distribution is not Gaussian and resembles a hypertoroid. In the verification stage, each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained. The angular representation used in the verification stage yields better results than a Euclidean distance representation. Experiments are performed in various interfering distortions, and robust detection and segmentation are achieved.     

基于差分进化算法和遗传算法的混合优化 算法及其在阵列天线方向图综合中的应用

阵列天线方向图综合作为智能天线的一项重要技术对于复杂系统的优化问题提出了更高的要求.本文结合差分进化的基本思想和遗传算法的基因交叉和变异方法构建了一种新的混合优化方法.该算法使用差分进化算子作为主要优化手段,结合遗传算法优胜劣汰的基本思想以及其中的交叉和变异方法,通过融合两种优化方法各自的优点,可以显著改善多参数、高度非线性问题的优化结果、提高计算效率.计算机仿真结果表明,与现有算法相比,该算法用于天线方向图综合具有收敛速度快、优化能力强、算法可靠等优势.     

基于空间变换迭代的SIFT特征图像匹配算法

SIFT（Scale Invariant Feature Transform）特征由于具有旋转、平移和尺度不变性在图像匹配中得到了广泛的应用。但直接运用SIFT特征进行匹配,存在两个问题:易受匹配参数的影响,出现较多的错漏匹配现象;只适用于相似变换情况下的图像匹配,对于高维的仿射变换情况则难以奏效,而在实际图像匹配中这种情况更为常见。针对以上问题,提出了一种空间变换迭代的SIFT特征图像匹配方法。把SIFT特征点集匹配转化为SIFT特征向量与点集的几何分布信息相关的函数最优化求解问题,通过在确定性退火框架下,迭代求解空间仿射变换与点集匹配对应关系,最终得到最优的SIFT特征点匹配关系。仿真实验表明:在较大仿射变换情况下该方法仍能实现图像SIFT特征点集的正确匹配。     

Parametric shape representation by a deformable NURBS model for cardiac functional measurements

This paper proposes a method of parametric representation and functional measurement of 3-D cardiac shapes in a deformable nonuniform rational B-splines (NURBS) model. This representation makes it very easy to automatically evaluate the functional parameters and myocardial kinetics of the heart, since quantitative analysis can be followed in a simple way. In the model, local deformation and motion on the cardiac shape are expressed in adjustable parameters. Especially, an effective integral algorithm is used for volumetric measurement of a NURBS shape since the volume is the most basic parameter in cardiac functional analysis. This method promises the numerical computation to be very convenient, efficient, and accurate, in comparison with traditional methods. Practical experiments are carried out, and results show that the algorithm can get satisfactory measurement accuracy and efficiency. The parametric NURBS model in cylindrical coordinates is not only very suitable to fit the anatomical surfaces of a cardiac shape, but also easy for geometric transformation and nonrigid registration, and able to represent local dynamics and kinetics, and thus, can easily be applied for quantitative and functional analysis of the heart.     

基于透视不变量的平面曲线的识别

提出一种快速有效的平面曲线的识别方法,在这种方法中,我们从单幅图象中提取表征曲线形状的描述子,该描述子由曲线上透视不变点之间的射影距离不变量构成,且不受物体和摄象机之间的位置、方向以及摄象机物理参数的影响。因此这种识别算法不受透视畸变的限制,本文用一组起初的平面物体进行了识别实验,结果表明这些形状描述 平面 曲线的识别有很好的性能。     

Automatic 3-D grayscale volume matching and shape analysis.

Recently, shape matching in three dimensions (3-D) has been gaining importance in a wide variety of fields such as computer graphics, computer vision, medicine, and biology, with applications such as object recognition, medical diagnosis, and quantitative morphological analysis of biological operations. Automatic shape matching techniques developed in the field of computer graphics handle object surfaces, but ignore intensities of inner voxels. In biology and medical imaging, voxel intensities obtained by computed tomography (CT), magnetic resonance imagery (MRI), and confocal microscopes are important to determine point correspondences. Nevertheless, most biomedical volume matching techniques require human interactions, and automatic methods assume matched objects to have very similar shapes so as to avoid combinatorial explosions of point. This article is aimed at decreasing the gap between the two fields. The proposed method automatically finds dense point correspondences between two grayscale volumes; i.e., finds a correspondent in the second volume for every voxel in the first volume, based on the voxel intensities. Mutiresolutional pyramids are introduced to reduce computational load and handle highly plastic objects. We calculate the average shape of a set of similar objects and give a measure of plasticity to compare them. Matching results can also be used to generate intermediate volumes for morphing. We use various data to validate the effectiveness of our method: we calculate the average shape and plasticity of a set of fly brain cells, and we also match a human skull and an orangutan skull.