Homography and Fundamental Matrix Estimation from Region Matches Using an Affine Error Metric

Matching a pair of affine invariant regions between images results in estimation of the affine transformation between the regions. However, the parameters of the affine transformations are rarely used directly for matching images, mainly due to the lack of an appropriate error metric of the distance between them. In this paper we derive a novel metric for measuring the distance between affine transformations: Given an image region, we show that minimization of this metric is equivalent to the minimization of the mean squared distance between affine transformations of a point, sampled uniformly on the image region. Moreover, the metric of the distance between affine transformations is equivalent to the l ₂ norm of a linear transformation of the difference between the six parameters of the affine transformations. We employ the metric for estimating homographies and for estimating the fundamental matrix between images. We show that both homography estimation and fundamental matrix estimation methods, based on the proposed metric, are superior to current linear estimation methods as they provide better accuracy without increasing the computational complexity.     

一种新的分割式比例仿射投影算法

针对自适应算法收敛速度和计算复杂度之间的矛盾．提出一种基于集员滤波的分割式比例仿射投影算法（SM-SPAPA）。该算法中只有当参数估计误差大于给定的误差门限时滤波器系数才进行迭代更新,从而能有效地减少滤波器系数的迭代次数。仿真结果表明,由于每次迭代将对误差性能贡献最大的输入信号筛选出来作为输入,从而能加快收敛速度,同时还能够减少算法的运算量。     

一种改进的变步长仿射投影算法

变步长的仿射投影算法因具有较传统仿射投影算法收敛快、失调小等优点而受到广泛重视。但是因计算量较大,限制了其在实际中的应用。为降低计算的复杂性和减少计算量,该文根据权值部分更新和步长间歇更新的思想提出一种改进方案,即根据某些原则仅选择部分权值进行更新以及每L次迭代只更新一次步长。文中通过一个具有有色输入的线性系统的辩识验证了改进方法的性能。仿真结果表明,改进算法在保证计算收敛性和计算精度的情况下,可有效地减少计算量。     

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.     

一种颜色仿射变换下的局部特征描述子

提出一种颜色仿射变换下局部特征的描述子,它分别处理特征点邻域内每个像素的RGB 3个颜色通道,并利用仿射不变量计算每个颜色通道的仿射梯度;为控制特征点处描述子的维数,根据邻域内像素到特征点的距离和相对特征点主方向的角度对特征点邻域内的仿射梯度进行累加,构成局部特征点的特征描述子.所提出的特征描述子增强了特征点对光度变化和仿射变换的不变性,提高了图像局部特征匹配的准确度;并通过一组典型图像的特征点匹配实验验证了其有效性.     

仿射不变参数化

仿射不变技术的目的是指图形在经历各种仿射变换后,它的某些性质保持不变,即这些性质本身不受变换的影响。将仿射不变技术用于参数化,由此得到的参数在各种仿射变换前后都保持不变。用这种参数做曲线插值时,可为实际应用带来很大的方便。以三次样条函数实现参数曲线,并通过计算实例对新方法与目前常用的参数化方法的插值结果进行了比较,在效率和显示结果上,新的方法是令人满意的。     

Extension of Affine Shape

In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to more general sets. It turns out to be possible to generalize most of the theory. The extension makes it possible to reconstruct, for example, 3D-curves up to projective transformations, from a number of their 2D-projections. An algorithm is presented, which is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that a solution is given to the aperture problem of finding point correspondences between curves.