边缘算子

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

Research emphasis is put on thefollowing aspects:First,study of multiwavelet basis(e.g.periodic vector,interpolation vector,multi-dimensional vector)suitable for different practical demands.Second,from perspective of operatorapproximation order,study of normal function approximation operator,contrast and comparison ofwavelet operator and multiwavelet operator and their respective applicable fields.And further,onbasis of the above,exploration of approaches of multiwavelet analysis application in function spacetheoretical research,and higher-lever,more convenient approaches for multi-function spaceapproximation theoretical research.Third,by fully employing unique features of multiwavelet,research action of multiwavelet analysis in the construction of L〓space non-conditionalbasis.Fourth,research such as transient signal analysis,image edge extraction,datacompression,fractal signal analysis.

其一，研究适宜于不同实际问题需要的向量小波基（如周期向量小波、插值向量小波、高维向量小波等）；其二，从算子逼近阶的角度研究一般函数逼近算子、小波算子和向量小波算子的异同点以及较优适用领域；在此基础上，探索将向量小波分析应用于函数空间理论研究的途径，寻找更高层次、更便捷地研究多元函数空间逼近理论的方法；其三，充分利用向量小波所独具的完美性质，探索在〓空间〓无条件基的构造中，向量小波分析的价值；其四，对向量小波适用的信号瞬态分析、图像边缘分析、数据压缩保真、分形信号分析等领域应给予特别的重视。

In image processing, method as follows will be introduced in this paper: a method combining image threshold iterative segmentation with threshold interpolation, edge detection operator Sobel and LoG, edge linking method using delation operator based on mathematical morphology, using boundary tracking and projection method in edge distill process. Through this method, measurement of wheelset will be met precision demand.

本文阐明了图像的分通道自动采集过程，以及对采集到的原始图像进行预处理过程，达到图像去噪声的目标，本课题采用了阈值分割中迭代阈值和阈值插值相结合的方法，Sobel算子、LoG算子边缘检测算法，基于数学形态学的膨胀运算子进行边缘断点连接以及目标提取中的投影法和边缘跟踪方法，使得提取轮对图像边缘达到测量精度的要求。

By analysis and comparison the algorithms, the dissertation presented an algorithm, based on the Sobel operator and frame difference method. Considering the characteristics of infrared image, the frame difference algorithm is simple and easy to be realized by hardware.

文中对多种边缘检测算子进行了分析比较，其中Sobel算子在处理该类图像时的速度与效果比较理想，且算法简单易于DSP硬件实现，所以最终采用了sobel算子。

For the sake of predicting the detection effect of differential operator s,the frequency features of common operators are analyzed from the view point of frequency domain.

为了预测微分算子边缘提取能达到的效果，从频域角度出发，分析了边缘检测中常用微分算子的频谱特性。

We studied the different kinds of the edge extractor and the criteria of how to evaluate the performance of different method.

一方面分析了不同类别的边缘提取算子的优缺点、评价边缘提取算子性能的准则，并对不同的算子进行了比较研究，给出了实验结果。

Linear edge detection operator can implement the one to one mapping of edge detection operator to edge type, that is, one kind of edge detector can only detect one kind of edge.

线性边缘检测算子，只能实现边缘检测算子到边缘类型的一一映射，即一种边缘检测算子只能检测一种边缘类型。

Edge detection is one of the important roles in the digital image processing, the Prewitt operator, LOG operator and Canny operator are adopted in the classical edge detection operator arithmetic in space domain.

边缘检测是数字图像处理的一个重要内容，讨论了经典的边缘检测算子算法，该算法更多地采用Prewitt算子、LOG算子、Canny算子等在空域中进行。

The ordinary edge detection methods such as Sobel and Canny operators are immune to noise, which result in cophasal axes discontinuity due to lack of edge information caused by noise.

由于边缘检测中常用的Sobel算子和Canny算子检测同相轴时对噪声免疫差，常因噪声因素引起边缘信息缺失导致同相轴提取不连续，本文采用中值滤波并对Sobel算子进行改进，对地震剖面图进行预处理，结合均方差自动确定阈值并进行异常检测，提取完整同相轴。

The ordinary edge detection methods such as Sobel and Canny operators are immune to noise, which result in cophasal axes discontinuity due to lack of edge information caused by noise. In order to extract cophasal axes more continuous and immune to noise, a novel approach is developed based on edge detection. Firstly, the median filter and improved Sobel method are used to preprocess seismic section images. Secondly, the threshold value is determined automatically based on variance to detect abnormal information. Finally, the complete cophasal axes are extracted after a post-processing.

由于边缘检测中常用的Sobel算子和Canny算子检测同相轴时对噪声免疫差，常因噪声因素引起边缘信息缺失导致同相轴提取不连续，本文采用中值滤波并对Sobel算子进行改进，对地震剖面图进行预处理，结合均方差自动确定阈值并进行异常检测，提取完整同相轴。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。