基于边界跟踪的快速欧氏距离变换算法

提出了一种基于边界跟踪、剥离的快速二维欧氏距离变换算法.从目标区域的最外层边界开始,自外向内、逐层对目标区域进行边界跟踪、剥离,直至目标区域为空.每跟踪到一个边界像素点,即根据其邻域像素所传递的最短距离信息来计算与最近背景像素间的欧氏距离,并利用一个链表结构来完成对已经过距离变换的像素点的距离更新,以解决距离传递的路径可能改变的问题.实验结果表明,该算法能够得到准确的欧氏距离,并且算法时间不到3×3倒角近似欧氏距离变换算法的2倍,比基于桶排序的欧氏距离变换算法快几十至上千倍.     

近似欧氏距离变换的一种并行算法

提出了一种基于超大规模集成电路(VLSI)硬件结构的新型距离变换并行处理算法。距离变换是一种基于二值图像的全局操作，在骨架抽取、形状匹配、目标重建、机器人避障等图像分析与模式识别算法中有着广泛的应用。欧氏距离是精确的L2范数距离，但是由于欧氏距离的非线性，不利于各种并行算法和加速算法的设计与实现，因此在应用中各种变形的加权距离作为欧氏距离的近似得到了实际推广。本文算法是有别于传统近似欧氏距离的并行计算方法，可应用于传统IC硬件或数字信号处理芯片(DSP)。理论分析和实验结果表明，该方法具有算法简单、快速、误差小等特点，可以更好地近似欧氏距离，并同时得到图像的Voronoi图，是一种实际可行的升级算法。     

基于改进的等距离映射算法的人脸识别

针对等距离映射(Isomap)算法在处理扰动图像时拓扑结构不稳定的缺点,提出了一种改进算法。改进算法将图像欧氏距离(IMED)嵌入到等距离映射算法之中。首先引入坐标度量系数计算图像的坐标度量矩阵,通过线性变换将原始图像从欧氏距离(ED)空间转换到图像欧氏距离空间;然后计算变换空间中样本的欧氏距离矩阵,并在此基础上构建样本邻域图,得到近似测地距离矩阵;最后采用多维标度(MDS)分析算法构造样本的低维表示。对ORL和Yale人脸数据库降维并结合最近邻分类器进行实验,基于改进算法的识别率平均分别提高了5.57%和3.95%,表明与原算法相比,改进算法在人脸识别中对图像扰动具有较好的鲁棒性。     

一种新的完全欧氏距离变换算法

论文提出了一种基于边界剥离的二维完全欧氏距离变换算法。该算法从物体目标的最外层边界开始,自外向内、逐层对物体目标区域进行边界跟踪、剥离。在跟踪过程中,根据当前边界像素点的已获得距离变换结果或为背景的邻域像素信息,计算其与最近背景像素间的欧氏距离,从而实现距离变换。和已有算法相比,文中算法具有简单快速、容易实现,得到的是完全欧氏距离的优点,在分离粘连物体的应用中,取得了良好分离效果。     

基于围线扫描的快速完全欧氏距离变换算法

欧几里德距离变换（EDT）是为由黑白像素构成的二值图像中所有像素找到距离其最近的黑色像素,并计算它们之间的欧几里德距离,目前广泛地应用于图像分析和计算机视觉等领域.本文采用基于围线扫描的思想,提出了一个在二值图像中进行完全欧氏距离变换的算法.算法首先将二值图像中的像素进行分类,对那些本身既不是特征像素且其4-邻域内也没有特征像素的点作上标记,然后对这些标记的像素自内向外进行围线扫描,搜索与它最近的黑点并计算它们的欧氏距离.算法能够计算精确的欧氏距离.同时对算法的时间复杂度进行了简单的分析,并给出了程序实现中得到的一些实验数据,结果表明该算法运算速度快,时空需求在当前的硬件环境下令人满意,是一种有效的和有着巨大实际应用价值的距离变换算法.     

二次式距离上基于SVD的高维图像索引方法

向量近似方法（vector approximation file）是解决高维索引中维数灾难问题的一种有效方法，但是它不能直接支持二次式距离上的近邻搜索，为此，提出一种基于奇异值分解（SVD）的二次式距离上的向量近似方法，通过奇异值分解技术将二次式距离变换为欧氏距离形式，对变换后的特征向量进行近似得到近似向量。进行近邻搜索时采用低维过滤算法，先在较高能量的低维子空间内计算近似距离进行过滤，再对过滤结果进行高维距离计算。实验结果表明，低维过滤算法可以过滤掉大部分特征向量，而只有小部分数据需要进行高维距离运算，该方法可以显著提高大型高维图像数据库的近邻搜索性能。     

统一化的快速距离变换

距离变换是图象处理和分析的有效工具，是关于图象是全局操作，为了避免庞大的计算量，人们通常采用将全局操作分解成局部操作的策略，但是这种分解策略只能产生近似的欧氏距离，本文提出了一种统一的化的距离变换算法，它不需要并行处理硬件的支持就能快速实现距离变换心最近特征变变换，对于使用不同的距离测度函数，仅需要调整距离查找表，而算法本身不用做任何改动，本文最后给出算法分析和实验结果。     

基于围线分层扫描的完全欧氏距离变换算法

围线扫描欧氏距离变换算法是一种快速的完全欧氏距离变换算法,其时间复杂度达到最优,但需在围线区域进行全局搜索,计算时间并未优化。针对此问题,提出了一种基 于围线分层扫描的完全欧氏距离算法。该算法首先根据中心像素的围线性质对二值图像像素点进行重新分类,然后按照围线区域像素与中心像素的空间关系,对中心像素的围线区 域进行分层搜索,并给出了搜索的终止条件。该算法保持了最优的时间复杂度,可通过定量分析单个像素的计算时间来证明其计算时间已得到优化。实验结果表明,该算法能够得到 准确的欧氏距离图像,且运行速度快。     

基于核的图像欧氏距离人脸识别

引进了两幅图像之间的一种新的距离度量方法——图像欧氏距离,该距离是利用核函数对传统的欧氏距离进行改进而得到的。在此基础上,设计了一种新的分类识别方法——基于核的图像欧氏距离人脸识别方法,并应用于人脸识别中。为验证该算法的可行性,对人脸图像进行DCT变换得到预处理样本,并在ORL和Yale人脸库上进行多角度的比较实验。分析实验结果表明,该方法优于其它距离分类器算法。     

基于欧氏距离变换的肺实质修补

在胸部CT图像的肺实质提取过程中,往往存在诸如过分割等问题,因此有必要对分割出的肺实质图像进行修补,论文提出了一种基于欧氏距离变换的肺实质修补算法.该算法是在初提取肺实质之后,利用欧氏距离变换将肺部边缘的血管和肺结节恢复,从而得到包含病灶区域在内的完整的肺实质.采用该算法对45个病人的胸部CT图像中缺失的肺实质进行了修补,结果显示该算法的正确率达90％以上,证明了该方法的可靠性和有效性.     

New sequential exact Euclidean distance transform algorithms based on convex analysis

We present several sequential exact Euclidean distance transform algorithms. The algorithms are based on fundamental transforms of convex analysis: The Legendre Conjugate or Legendre–Fenchel transform, and the Moreau envelope or Moreau-Yosida approximate. They combine the separability of the Euclidean distance with convex properties to achieve an optimal linear-time complexity.We compare them with a Parabolic Envelope distance transform, and provide several extensions. All the algorithms presented perform equally well in higher dimensions. They can naturally handle grayscale images, and their principles are generic enough to apply to other transforms.     

Parallel computation of the Euclidean distance transform on a three-dimensional image array

In a two- or three-dimensional image array, the computation of Euclidean distance transform (EDT) is an important task. With the increasing application of 3D voxel images, it is useful to consider the distance transform of a 3D digital image array. Because the EDT computation is a global operation, it is prohibitively time consuming when performing the EDT for image processing. In order to provide the efficient transform computations, parallelism is employed. We first derive several important geometry relations and properties among parallel planes. We then, develop a parallel algorithm for the three-dimensional Euclidean distance transform (3D-EDT) on the EREW PRAM computation model. The time complexity of our parallel algorithm is O(log/sup 2/ N) for an N/spl times/N/spl times/N image array and this is currently the best known result. A generalized parallel algorithm for the 3D-EDT is also proposed. We implement the proposed algorithms sequentially, the performance of which exceeds the existing algorithms (proposed by Yamada, 1984). Finally, we develop the corresponding parallel programs on both the emulated EREW PRAM model computer and the IBM SP2 to verify the speed-up properties of the proposed algorithms.     

On the Euclidean distance of images

We present a new Euclidean distance for images, which we call image Euclidean distance (IMED). Unlike the traditional Euclidean distance, IMED takes into account the spatial relationships of pixels. Therefore, it is robust to small perturbation of images. We argue that IMED is the only intuitively reasonable Euclidean distance for images. IMED is then applied to image recognition. The key advantage of this distance measure is that it can be embedded in most image classification techniques such as SVM, LDA, and PCA. The embedding is rather efficient by involving a transformation referred to as standardizing transform (ST). We show that ST is a transform domain smoothing. Using the face recognition technology (FERET) database and two state-of-the-art face identification algorithms, we demonstrate a consistent performance improvement of the algorithms embedded with the new metric over their original versions.     

基于矩-傅里叶描述子人脸图像识别

本文介绍了在Radon变换下的图像矩特征的抽取方法，并得到图像的矩特征矩阵；进而对矩特征矩阵按行向量进行傅里叶变换组成矩－傅里叶描述子特征矩阵，采用矩阵的加权欧氏距离作为人脸图像的匹配识别的算法，产生较好的结果。     

基于提升小波的图像检索算法

提升小波具有高效性和多分辨率等优点,本文提出了基于提升小波的图像检索算法。该算法首先对图像进行提升小波变换,得到每层的低频子图像和高频子图像;然后分别提取低频子图像的形状特征和高频子图像的纹理特征;最后通过计算特征向量之间的欧式距离,检索出相似的图像。实验结果表明,此算法的检索效率高于其他算法,具有一定的优越性和通用性。     

基于断层间切片图像的插值方法研究

断层间图像插值是三维重建的一个关键步骤,研究了传统的插值方法,并对其进行了分析。在此基础上提出了一种基于距离变换的目标图像插值方法,该方法首先对断层图像进行阈值分割得到目标图像并对图像进行中心配准,然后运用欧几里德距离变换法求取目标图像的距离图像,采用加权平均线性插值方法得到目标图像间的插值图像;对ICT切片图像进行了实验研究,取得了令人满意的效果。     

A Euclidean distance transform using grayscale morphologydecomposition

A fast and exact Euclidean distance transformation using decomposed grayscale morphological operators is presented. Applied on a binary image, a distance transformation assigns each object pixel a value that corresponds to the shortest distance between the object pixel and the background pixels. It is shown that the large structuring element required for the Euclidean distance transformation can be easily decomposed into 3×3 windows. This is possible because the square of the Euclidean distance matrix changes uniformly both in the vertical and horizontal directions. A simple extension for a 3D Euclidean distance transformation is discussed. A fast distance transform for serial computers is also presented. Acting like thinning algorithms, the version for serial computers focuses operations only on the potential changing pixels and propagates from the boundary of objects, significantly reducing execution time. Nonsquare pixels can also be used in this algorithm. An example application, shape filtering using arbitrary sized circular dilation and erosion, is discussed. Rotation-invariant basic morphological operations can be done using this example application     

Comparison of Distance Measures for Planar Curves

The Hausdorff distance is a very natural and straightforward distance measure for comparing geometric shapes like curves or other compact sets. Unfortunately, it is not an appropriate distance measure in some cases. For this reason, the Fréchet distance has been investigated for measuring the resemblance of geometric shapes which avoids the drawbacks of the Hausdorff distance. Unfortunately, it is much harder to compute. Here we investigate under which conditions the two distance measures approximately coincide, i.e., the pathological cases for the Hausdorff distance cannot occur. We show that for closed convex curves both distance measures are the same. Furthermore, they are within a constant factor of each other for so-called κ-straight curves, i.e., curves where the arc length between any two points on the curve is at most a constant κ times their Euclidean distance. Therefore, algorithms for computing the Hausdorff distance can be used in these cases to get exact or approximate computations of the Fréchet distance, as well.