算子比较
比较常见的边缘检测算子有Roberts、Prewitt和Sobel。这里给出一些简单比较：
- Roberts算子：边缘定位准，但是对噪声敏感。适用于边缘明显且噪声较少的图像分割。Roberts边缘检测算子是一种利用局部差分算子寻找边缘的算子,Robert算子图像处理后结果边缘不是很平滑。经分析，由于Robert算子通常会在图像边缘附近的区域内产生较宽的响应，故采用上述算子检测的边缘图像常需做细化处理，边缘定位的精度不是很高。
- Prewitt算子：对噪声有抑制作用，抑制噪声的原理是通过像素平均，但是像素平均相当于对图像的低通滤波，所以Prewitt算子对边缘的定位不如Roberts算子。
- Sobel算子：Sobel算子和Prewitt算子都是加权平均，但是Sobel算子认为，邻域的像素对当前像素产生的影响不是等价的，所以距离不同的像素具有不同的权值，对算子结果产生的影响也不同。一般来说，距离越远，产生的影响越小。
- Isotropic Sobel算子：加权平均算子，权值反比于邻点与中心点的距离，当沿不同方向检测边缘时梯度幅度一致，就是通常所说的各向同性。
简单定义
|∇f|≈|Gx| |Gy| |nabla f|approx|G_x| |G_y|
当 |∇f|>T |nabla f|>T大于阀值的时候判定此像素点为边缘。
代码实现：
在主文件中进行了手动给出阀值T 和 不给出阀值T，让函数自动迭代生成。 prewittee.m
代码语言：javascript复制function prewittee(FILENAME)
%prewittee(FILENAME) takes a gray scale image with filename FILENAME.
% Read the image.
Im = im2double(imread(FILENAME));
% Show the image in a new window.
figure;imshow(Im, [min(min(Im)) max(max(Im))]);title('Original Image');
disp('Original image is read and displayed successfully.');
%
% Generate the corresponding binary edge image of the given image Im.
T = double(max(max(Im)))*0.2;
direction = 'all';
g = myprewittedge(Im,T,direction);
% Show the image in a new window.
figure;imshow(g, [0 1]);title('Binary Edge Image 1');
disp('The corresponding binary edge image is computed and displayed successfully.');
%
% Generate the corresponding binary edge image of the given image Im
% without specifying the threshold
direction = 'all';
f = myprewittedge(Im,[],direction);
% Show the image in a new window.
figure;imshow(f, [0 1]);title('Binary Edge Image 2');
disp('The corresponding binary edge image is computed and displayed successfully.');myprewittedge.m
代码语言：javascript复制% myprewittedge computes a binary edge image from the given image.
%
% g = myprewittedge(Im,T,direction) computes the binary edge image from the
% input image Im.
%
% The function myprewittedge, with the format g=myprewittedge(Im,T,direction),
% computes the binary edge image from the input image Im. This function takes
% an intensity image Im as its input, and returns a binary image g of the
% same size as Im (mxn), with 1's where the function finds edges in Im and 0's
% elsewhere. This function finds edges using the Prewitt approximation to the
% derivatives with the assumption that input image values outside the bounds
% are zero and all calculations are done using double-precision floating
% point. The function returns g with size mxn. The image g contains edges at
% those points where the absolute filter response is above or equal to the
% threshold T.
%
% Input parameters:
% Im = An intensity gray scale image.
% T = Threshold for generating the binary output image. If you do not
% specify T, or if T is empty ([ ]), myprewittedge(Im,[],direction)
% chooses the value automatically according to the Algorithm 1 (refer
% to the assignment descripton).
% direction = A string for specifying whether to look for
% 'horizontal' edges, 'vertical' edges, positive 45 degree 'pos45'
% edges, negative 45 degree 'neg45' edges or 'all' edges.
function g = myprewittedge(Im,T,direction)
if isempty(T)
T = (max(max(Im)) min(min(Im))) / 2;
for i = 1:10
G1 = Im .* (Im > T);
G2 = Im .* (Im < T);
m1 = mean(G1(G1~=0));
m2 = mean(G2(G2~=0));
T = (m1 m2) / 2;
end
end
[m, n] = size(Im);
% temp = Im;
prewittNum = 0;
for j = 2:m-1
for k = 2:n-1
prewittNum = abs(Im(j-1,k 1)-Im(j 1,k 1) Im(j-1,k)-Im(j 1,k) Im(j-1,k-1)-Im(j 1,k-1)) abs(Im(j-1,k 1) Im(j,k 1) Im(j 1,k 1)-Im(j-1,k-1)-Im(j,k-1)-Im(j 1,k-1));
if (prewittNum > T)
temp(j,k) = 255;
else
temp(j,k) = 0;
end
end
end
g = temp;示例输入与输出
输入文件
手动给出阀值T
自动生成阀值T
