Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).

基于参数化求和不变量与特征重整的形状匹配

从特征提取和特征匹配两方面考虑,提出了一种鲁棒的形状匹配方法。首先,基于求和不变量,设计了基于面积的形状参数化和归一化方法,提出了参数化求和不变量,该不变量基于形状局部描述且采用积分算子计算,具有较好的鲁棒性和仿射不变性。然后,为进一步提高形状匹配的鲁棒性,在特征匹配上,分析了参数化求和不变量的先验信息,设计了基于特征重整的匹配距离函数,并通过动态规划进行实现。仿真实验表明了所提方法的有效性。

基于仿射不变特征的图像匹配

图像匹配是计算机视觉中的一个重要研究领域，无论在民用还是军用上都有着重要的应用价值。本文以研究室国防重点预研究项目自动目标识别为背景，采用图像匹配方法，实现飞行器定位导航。具体工作流程是：事先利用侦察手段获取飞行器途经下方的地物景象(基准图)并存于飞行器载计算机中，然后当携带相应传感器的飞行器飞过预定的位置范围时，拍摄当地的地物景象(实时图)，将实时图和基准图在飞行器载计算机中进行匹配比较，可确定当前飞行器的准确位置，完成定位导航功能。 由于对同一场景使用相同或不同的传感器(成像设备)，以及在不同条件下(天候、照度、摄像位置和角度等)成像的复杂性和多样性等困难的存在，传统的相关匹配方法对上述困难的克服在方法原理上存在先天不足，所以无法胜任。故本文采用的方法是基于局部不变量特征的图像匹配。局部不变量特征因为能更灵活地描述图像，有效地处理图像复杂和遮挡问题，所以基于局部不变量特征的图像匹配方法对于视点的大变化，图像背景变化，以及目标场景识别等都有较好的效果。 基于局部不变量特征的图像匹配方法的步骤通常分为三部分：(1)用图像区域检测算子提取图像相关区域，(2)构造合适的特征描述区域，(3)选择特征相似度度量准则实现图像区域特征的匹配。本文详细研究了最大稳定极值区域 (MSER)方法，在此基础上进行了改进，具体工作如下：(1)利用高斯核函数对图像平滑采样，建立图像的高斯尺度空间，(2)在图像的高斯尺度空间中，利用MSER检测算子检测出图像在不同尺度下的所有仿射相关区域，(3)由于区域不规则，再用仿射不变的椭圆拟合并归一化，这时所有的区域仅存在旋转的不同，(4)用SIFT特征描述图像区域，得到所有区域的128维特征向量集。(5)采用欧式距离度量特征间的相似度，以最近邻和次近邻的比值作为特征匹配准则进行匹配。 本论文的主要研究工作在于把图像的高斯尺度空间引入到MSER算法中，进而大大改善了MSER算法对于图像的尺度变换、仿射变换以及图像模糊的性能。由于建立了高斯尺度空间，增加了MSER检测算子检测的范围，所以使得改进算法的性能得到了改善。论文第四章给出四组实验，分别为尺度变换，仿射变换，图像模糊和大视点变换。最后通过对匹配结果正确数量和错误数量的统计，论证了改进方法的性能要好于MSER算法。通过对算法复杂度的分析，得出虽然在改进算法引入了图像的高斯尺度空间，但是算法复杂度却并未增加，与MSER算法相同，为O(nloglogn)。

Classification and characterization of places for mapping of environment using hierarchical neural network and omnivision

Mobile robots need autonomy to fulfill their tasks. Such autonomy is related whith their capacity to explorer and to recognize their navigation environments. In this context, the present work considers techniques for the classification and extraction of features from images, using artificial neural networks. This images are used in the mapping and localization system of LACE (Automation and Evolutive Computing Laboratory) mobile robot. In this direction, the robot uses a sensorial system composed by ultrasound sensors and a catadioptric vision system equipped with a camera and a conical mirror. The mapping system is composed of three modules; two of them will be presented in this paper: the classifier and the characterizer modules. Results of these modules simulations are presented in this paper.

An Empirical Study of Non-Rigid Surface Feature Matching of Human from 3D Video

This paper presents an empirical study of affine invariant feature detectors to perform matching on video sequences of people with non-rigid surface deformation. Recent advances in feature detection and wide baseline matching have focused on static scenes. Video frames of human movement capture highly non-rigid deformation such as loose hair, cloth creases, skin stretching and free flowing clothing. This study evaluates the performance of six widely used feature detectors for sparse temporal correspondence on single view and multiple view video sequences. Quantitative evaluation is performed of both the number of features detected and their temporal matching against and without ground truth correspondence. Recall-accuracy analysis of feature matching is reported for temporal correspondence on single view and multiple view sequences of people with variation in clothing and movement. This analysis identifies that existing feature detection and matching algorithms are unreliable for fast movement with common clothing.

Casamento de modelos baseado em projeções radiais e circulares invariante a pontos de vista.

Este trabalho aborda o problema de casamento entre duas imagens. Casamento de imagens pode ser do tipo casamento de modelos (template matching) ou casamento de pontos-chaves (keypoint matching). Estes algoritmos localizam uma região da primeira imagem numa segunda imagem. Nosso grupo desenvolveu dois algoritmos de casamento de modelos invariante por rotação, escala e translação denominados Ciratefi (Circula, radial and template matchings filter) e Forapro (Fourier coefficients of radial and circular projection). As características positivas destes algoritmos são a invariância a mudanças de brilho/contraste e robustez a padrões repetitivos. Na primeira parte desta tese, tornamos Ciratefi invariante a transformações afins, obtendo Aciratefi (Affine-ciratefi). Construímos um banco de imagens para comparar este algoritmo com Asift (Affine-scale invariant feature transform) e Aforapro (Affine-forapro). Asift é considerado atualmente o melhor algoritmo de casamento de imagens invariante afim, e Aforapro foi proposto em nossa dissertação de mestrado. Nossos resultados sugerem que Aciratefi supera Asift na presença combinada de padrões repetitivos, mudanças de brilho/contraste e mudanças de pontos de vista. Na segunda parte desta tese, construímos um algoritmo para filtrar casamentos de pontos-chaves, baseado num conceito que denominamos de coerência geométrica. Aplicamos esta filtragem no bem-conhecido algoritmo Sift (scale invariant feature transform), base do Asift. Avaliamos a nossa proposta no banco de imagens de Mikolajczyk. As taxas de erro obtidas são significativamente menores que as do Sift original.

Geometric Distortion Insensitive Image Watermarking in Affine Covariant Regions

Feature-based image watermarking schemes, which aim to survive various geometric distortions, have attracted great attention in recent years. Existing schemes have shown robustness against rotation, scaling, and translation, but few are resistant to cropping, nonisotropic scaling, random bending attacks (RBAs), and affine transformations. Seo and Yoo present a geometrically invariant image watermarking based on affine covariant regions (ACRs) that provide a certain degree of robustness. To further enhance the robustness, we propose a new image watermarking scheme on the basis of Seo's work, which is insensitive to geometric distortions as well as common image processing operations. Our scheme is mainly composed of three components: 1) feature selection procedure based on graph theoretical clustering algorithm is applied to obtain a set of stable and nonoverlapped ACRs; 2) for each chosen ACR, local normalization, and orientation alignment are performed to generate a geometrically invariant region, which can obviously improve the robustness of the proposed watermarking scheme; and 3) in order to prevent the degradation in image quality caused by the normalization and inverse normalization, indirect inverse normalization is adopted to achieve a good compromise between the imperceptibility and robustness. Experiments are carried out on an image set of 100 images collected from Internet, and the preliminary results demonstrate that the developed method improves the performance over some representative image watermarking approaches in terms of robustness.

Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

Brief review of invariant texture analysis methods

This paper considers invariant texture analysis. Texture analysis approaches whose performances are not affected by translation, rotation, affine, and perspective transform are addressed. Existing invariant texture analysis algorithms are carefully studied and classified into three categories: statistical methods, model based methods, and structural methods. The importance of invariant texture analysis is presented first. Each approach is reviewed according to its classification, and its merits and drawbacks are outlined. The focus of possible future work is also suggested.

An existence theorem for G-structure preserving affine immersions

We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of isometric immersions into products of space forms.