基于高斯平滑的自适应角点检测

文中算法首先在曲线尺度空间中通过高斯平滑以消除噪声；然后再基于自适应弯曲度计算和角点筛选准则确定角点，该算法不需要预先输入参数，具有较好的抗干扰性，实现简单有效。     

Robust image corner detection through curvature scale space

This paper describes a novel method for image corner detection based on the curvature scale-space (CSS) representation. The first step is to extract edges from the original image using a Canny detector (1986). The corner points of an image are defined as points where image edges have their maxima of absolute curvature. The corner points are detected at a high scale of the CSS and tracked through multiple lower scales to improve localization. This method is very robust to noise, and we believe that it performs better than the existing corner detectors An improvement to Canny edge detector's response to 45° and 135° edges is also proposed. Furthermore, the CSS detector can provide additional point features (curvature zero-crossings of image edge contours) in addition to the traditional corners     

Scale-Space Behavior of Planar-Curve Corners

The curvature scale-space (CSS) technique is suitable for extracting curvature features from objects with noisy boundaries. To detect corner points in a multiscale framework, Rattarangsi and Chin investigated the scale-space behavior of planar-curve corners. Unfortunately, their investigation was based on an incorrect assumption, viz., that planar curves have no shrinkage under evolution. In the present paper, this mistake is corrected. First, it is demonstrated that a planar curve may shrink nonuniformly as it evolves across increasing scales. Then, by taking into account the shrinkage effect of evolved curves, the CSS trajectory maps of various corner models are investigated and their properties are summarized. The scale-space trajectory of a corner may either persist, vanish, merge with a neighboring trajectory, or split into several trajectories. The scale-space trajectories of adjacent corners may attract each other when the corners have the same concavity, or repel each other when the corners have opposite concavities. Finally, we present a standard curvature measure for computing the CSS maps of digital curves, with which it is shown that planar-curve corners have consistent scale-space behavior in the digital case as in the continuous case.     

Scale-based detection of corners of planar curves

A technique for detecting and localizing corners of planar curves is proposed. The technique is based on Gaussian scale space, which consists of the maxima of absolute curvature of the boundary function presented at all scales. The scale space of isolated simple and double corners is first analyzed to investigate the behavior of scale space due to smoothing and interactions between two adjacent corners. The analysis shows that the resulting scale space contains line patterns that either persist, terminate, or merge with a neighboring line. Next, the scale space is transformed into a tree that provides simple but concise representation of corners at multiple scales. Finally, a multiple-scale corner detection scheme is developed using a coarse-to-fine tree parsing technique. The parsing scheme is based on a stability criterion that states that the presence of a corner must concur with a curvature maximum observable at a majority of scales. Experiments were performed to show that the scale space corner detector is reliable for objects with multiple-size features and noisy boundaries and compares favorably with other corner detectors tested     

基于曲率尺度空间的VOP形状编码算法

首先对曲率尺度空间（CSS）算法进行改进，并用改进的CSS算法对任意形状物体的形状信息进行特征点的分层提取；其次，用自适应算术编码算法对固定长度的八分圆编码算法进行改进，并对所提取的特征点进行算术编码，实验结果表明，这种新的基于特征点提取的形状编码方法比MPEG-4校验模型中基于上下文的算术形状编码算法，在Dn相同的条件下，主观质量更好，且压缩比更高。     

一种基于曲率尺度空间的自适应角点检测方法

角点是图像处理中的重要特征,基于曲率尺度空间技术,提出一种自适应角点检测方法.首先提取图像的轮廓,采用一个固定的低尺度计算所有轮廓点的曲率,并根据曲率得到候选角点集,然后用由自适应支持区域确定的角点角度和一个动态曲率阙值代替固定的阙值筛选出正确角点.实验结果证实该方法应用于复杂图像的精确性和稳定性.     

Silhouette-based isolated object recognition through curvaturescale space

A complete, fast and practical isolated object recognition system has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and local deformations of shape (due to perspective projection, segmentation errors and non-rigid material used in some objects). The system has been tested on a wide variety of three-dimensional objects with different shapes and material and surface properties. A light-box setup is used to obtain silhouette images which are segmented to obtain the physical boundaries of the objects which are classified as either convex or concave. Convex curves are recognized using their four high-scale curvature extrema points. Curvature scale space (CSS) representations are computed for concave curves. The CSS representation is a multi-scale organization of the natural, invariant features of a curve (curvature zero-crossings or extrema) and useful for very reliable recognition of the correct model since it places no constraints on the shape of objects. A three-stage, coarse-to-fine matching algorithm prunes the search space in stage one by applying the CSS aspect ratio test. The maxima of contours in CSS representations of the surviving models are used for fast CSS matching in stage two. Finally, stage three verifies the best match and resolves any ambiguities by determining the distance between the image and model curves. Transformation parameter optimization is then used to find the best fit of the input object to the correct model     

A theory of multiscale, curvature-based shape representation forplanar curves

A shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented. The method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve. Three different ways of computing the representation are described. They result in three different representations: the curvature scale space image, the renormalized curvature scale space image, and the resampled curvature scale space image. The process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve. Several evolution and arc length evolution properties of planar curves are discussed     

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.     

一种基于曲率尺度空间的图像拼接算法

提出了一种基于曲率尺度空间的图像拼接算法。该算法利用曲率尺度空间（CSS）角点检测法提取特征点,通过比较各特征点圆形邻域Zernike矩的欧式距离得到匹配点对,然后利用正确的映射模型计算出变换参数,最后采用加权平均法得到图像的拼接结果。实验表明,该算法在图像间存在旋转、平移及噪声干扰的情况下,仍能得到很好的拼接结果。     

Space corner smoothing of CNC machine tools through developing 3D general clothoid

Tool paths defined by G01/G02/G03 commands need to be smoothed to eliminate the discontinuities of velocity, acceleration and jerk at the junction points. Because of inherent problems of curve fillets, traditional corner smoothing strategies are limited to the smoothing of corners in plane. This article presents a method to smooth the space corners through blending the position, tangent, curvature and sharpness of the adjacent trajectory segments based on 3D general clothoid splines, which are analytically developed by proposing 3D clothoid with G³ continuity. The 3D general clothoid realizes extending the traditional clothoid from 2-dimension to 3-dimension, and reserves some good properties of the traditional clothoid, i.e. the curve length parameterization and the analytically expressed curvature. It can also achieve higher degree of continuity compared to the traditional 2D clothoid. Based on the proposed 3D general clothoid, a corner smoothing algorithm, which is suitable for the smoothing of any planar or space line-line, line-arc or arc-arc pairs with G³ continuity, is proposed. At the same time, a smoothing-error-constraining-algorithm is developed to constrain the smoothing error within the tolerance. Simulation and experimental results, which are obtained from the smoothing of trajectories containing space corners, trajectories containing planar corners with G02/G03 commands, and trajectories containing planar corners with only G01 commands, demonstrate that the proposed corner smoothing algorithm can effectively increase the machining quality and efficiency.     

利用非线性滤波进行多尺度拐角检测

对灰度图进行一般线性和非线性平滑会极大程度地模糊拐角,使得多尺度方法难以用于拐角检测.由于非线性多尺度CB(contour-based)形态滤波算子具有很好的拐角保持特性,而且能使拐角满足单调性,即当尺度增大时拐角数不增加.用CB形态滤波器对灰度图进行滤波,构成CB形态学尺度空间,以实现对拐角的多尺度检测.理论分析和实验结果证明了这种分析方法的有效性.     

SIFER: Scale-Invariant Feature Detector with Error Resilience

We present a new method to extract scale-invariant features from an image by using a Cosine Modulated Gaussian (CM-Gaussian) filter. Its balanced scale-space atom with minimal spread in scale and space leads to an outstanding scale-invariant feature detection quality, albeit at reduced planar rotational invariance. Both sharp and distributed features like corners and blobs are reliably detected, irrespective of various image artifacts and camera parameter variations, except for planar rotation. The CM-Gaussian filters are approximated with the sum of exponentials as a single, fixed-length filter and equal approximation error over all scales, providing constant-time, low-cost image filtering implementations. The approximation error of the corresponding digital signal processing is below the noise threshold. It is scalable with the filter order, providing many quality-complexity trade-off working points. We validate the efficiency of the proposed feature detection algorithm on image registration applications over a wide range of testbench conditions.     

Restoration of a feature closed class of two-dimensional images

A restoration principle is proposed and demonstrated for a feature closed class of two-dimensional images. Any member of this class of images can be represented as an intersection of unions of half planes in R2. Images with corners as well as images with continuous curvature can be generated under this algebraic representation. All resulting images have a well-defined interior and a nonintersecting boundary. Knowledge that the image to be restored comes from this closed class of images allows for an image restoration algorithm that is superior to a point-thickening algorithm. The proposed restoration algorithm produces a restored image that lies within the image to be restored. For a random sample of n points known to lie within the image to be restored, the expected value of the residual area for the image with corners is of order (In n/n) and is proportional to the number of outside corners. For images with continuous curvature, the residual area is of order 1/?n and is proportional to a geometric constant associated with the curvature of the boundary. The restoration algorithm offers insight into the consideration of the shape of the boundary in image restoration.     

基于多尺度曲率乘积的鲁棒图像角点检测

为了更好地进行图像角点检测,在曲率尺度空间(CSS)框架下,提出了一种基于多尺度乘积的角点检测技术,其中曲率尺度积函数被定义为各个尺度下轮廓曲率的乘积,而角点则被定义为曲率乘积的局部极值点。这种尺度积不仅能显著地增强角点曲率极值点的峰值,同时能抑制噪声影响,而且不改变角点的位置,为了说明该技术的优点,根据角点数一致性(CCN)准则证明了该技术优于其他的角点检测算法。实验结果表明,该方法不仅具备优越的检测效果,并对噪声有较强的鲁棒性。