在CIELab颜色空间下使用八方向Sobel算子实现边缘检测

参考河北师范大学硕士学位论文——基于八方向Sobel算子的边缘检测算法研究。
由于自己实现滤波器运算，计算速度很慢，以后有能力再进行改进。

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算子定义如下：

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算法思路：
1.将RGB图像转化为CIELab颜色空间的图像。
2.计算不同方向上的梯度，乘以权值后取最大值当作输出值。

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效果如下：

运行时间：33.543444 秒。

运行时间：79.695009 秒。

跑的好慢QAQ

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代码如下：
CIELabEdge.m（算法的总入口）

%在CIELab颜色空间下对图片进行边缘检测(参数为待处理的RGB图像)
%使用论文中的八方向Sobel算子进行滤波
%论文引自--郑英娟. 基于八方向Sobel算子的边缘检测算法研究. 河北师范大学硕士学位论文. 2013.3.26

%From:Yinggang Wang
%Create Date:2018.3.30

function [] = CIELabEdge(img)

%颜色空间转换
Lab = RGB2Lab(img);

%滤波处理
Edge = MyFilter(Lab);

%输出结果
figure('NumberTitle','off','Name','边缘');
imshow(Edge,[]);

figure('NumberTitle','off','Name','边缘(负片)');
imshow(imcomplement(Edge),[]);

MyFilter.m（自己实现的滤波器）

%使用滤波器滤波(参数:CIELab颜色空间的三维矩阵)(图像输出大小比实际小一点)
%
%From:Yinggang Wang
%Create Date:2018.3.30

function im = MyFilter(ori)

s = size(ori);
im = zeros(s(1),s(1,2));

for i = 3:(s(1)-2)
    for j = 3:(s(2)-2)
        im(i-2,j-2) = getOutput(ori,i,j);
    end
end

getOutput.m（得到每一点的输出值）

%得到x,y坐标像素点的输出值
%
%From:Yinggang Wang
%Create Date:2018.3.30

function out = getOutput(ori,x,y)

%以下是八个方向的算子
D0 = [1,2,4,2,1];
D22_5 = [1,2,4,2,4];
D45 = [1,4,2,4,1];
D67_5 = [1,2,4,2,4];
D90 = [1,2,4,2,1];
D112_5 = [1,2,4,2,1];
D135 = [1,4,2,4,1];
D157_5 = [1,2,4,2,4];

a = zeros(1,8);
a(1) = sum(D0 .* [CD(ori(x-2,y-1),ori(x-2,y+1)),CD(ori(x-1,y-1),ori(x-1,y+1)),CD(ori(x,y-1),ori(x,y+1)),CD(ori(x+1,y-1),ori(x+1,y+1)),CD(ori(x+2,y-1),ori(x+2,y+1))]);
a(2) = sum(D22_5 .* [CD(ori(x-2,y),ori(x+2,y)),CD(ori(x-1,y+1),ori(x+1,y-1)),CD(ori(x,y-1),ori(x,y+1)),CD(ori(x-1,y-1),ori(x+1,y+1)),CD(ori(x-1,y),ori(x+1,y))]);
a(3) = sum(D45 .* [CD(ori(x+1,y-2),ori(x+2,y-1)),CD(ori(x,y-1),ori(x+1,y)),CD(ori(x-1,y-1),ori(x+1,y+1)),CD(ori(x-1,y),ori(x,y+1)),CD(ori(x-2,y+1),ori(x-1,y+2))]);
a(4) = sum(D67_5 .* [CD(ori(x,y-2),ori(x,y+2)),CD(ori(x-1,y-1),ori(x+1,y+1)),CD(ori(x-1,y),ori(x+1,y)),CD(ori(x-1,y+1),ori(x+1,y-1)),CD(ori(x,y+1),ori(x,y-1))]);
a(5) = sum(D90 .* [CD(ori(x-1,y-2),ori(x+1,y-2)),CD(ori(x-1,y-1),ori(x+1,y-1)),CD(ori(x-1,y),ori(x+1,y)),CD(ori(x-1,y-2),ori(x+1,y-2)),CD(ori(x-1,y+2),ori(x+1,y+2))]);
a(6) = sum(D112_5 .* [CD(ori(x,y-2),ori(x,y+2)),CD(ori(x-1,y-1),ori(x+1,y+1)),CD(ori(x-1,y),ori(x+1,y)),CD(ori(x-1,y+1),ori(x+1,y-1)),CD(ori(x,y+1),ori(x,y-1))]);
a(7) = sum(D135 .* [CD(ori(x-1,y-2),ori(x-2,y-1)),CD(ori(x,y-1),ori(x-1,y)),CD(ori(x+1,y-1),ori(x-1,y+1)),CD(ori(x+1,y),ori(x,y+1)),CD(ori(x+2,y+1),ori(x+1,y+2))]);
a(8) = sum(D157_5 .* [CD(ori(x-2,y),ori(x+2,y)),CD(ori(x-1,y+1),ori(x+1,y-1)),CD(ori(x,y-1),ori(x,y+1)),CD(ori(x-1,y-1),ori(x+1,y+1)),CD(ori(x-1,y),ori(x+1,y))]);

a(1) = a(1)/10.0;
a(2) = a(2)/13.0;
a(3) = a(3)/12.0;
a(4) = a(4)/13.0;
a(5) = a(5)/10.0;
a(6) = a(6)/13.0;
a(7) = a(7)/12.0;
a(8) = a(8)/13.0;

out = ((max(a)+0.5));

CD.m（求两点的欧式距离）

%求两点的欧式距离
%
%From:Yinggang Wang
%Create Date:2018.3.30

function dis = CD(a,b)
dis = sqrt((a-b)^2 + (a-b)^2 + (a-b)^2);

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