poster
2019-12-10, 20:30
使用霍夫线 (http://en.wikipedia.org/wiki/Hough_transform)检测图像中的线后 (http://en.wikipedia.org/wiki/Hough_transform) ，如何使用它来计算参考图像线的角度（旋转）变化？
回答：
读者注意：这是一个后续问题，请参考以下内容：
如何在MATLAB中的霍夫变换中选择最大强度？ (https://stackoverflow.com/questions/1975206/how-to-select-maximum-intensity-in-hough-transform-in-matlab/1975261#1975261)
计算在MATLAB中移动的位移 (https://stackoverflow.com/questions/2062760/calculating-displacement-moved-in-matlab)
该过程类似于我之前展示的过程。在下面，我使用的是上一个问题的图像 (http://i182.photobucket.com/albums/x11/veronicafmy/FYP/pict1.jpg) （由于您只提供了一个，所以我将第一个旋转10度来创建另一个图像）。
我们首先检测两个图像的线条。我们借助Hough (http://www.mathworks.com/help/images/ref/hough.html) 变换 (http://www.mathworks.com/help/images/ref/houghlines.html) 功能来完成此操作 (http://www.mathworks.com/help/images/ref/houghpeaks.html) 。这看起来适用于两个图像：
https://i.stack.imgur.com/cINnK.png
接下来，我们要使用线端点作为控制点执行图像配准。首先，我们确保两个图像中的点彼此对应。我通过使用convhull (http://www.mathworks.com/help/matlab/ref/convhull.html)计算凸包来做到这一点， convhull (http://www.mathworks.com/help/matlab/ref/convhull.html)自动将它们按逆时针顺序排序（或者是相反方向！）。上面显示的数字指示顺序。
最后，我们使用cp2tform (http://www.mathworks.com/help/images/ref/cp2tform.html)函数获取转换矩阵，该矩阵用于对齐图像并提取平移，旋转和缩放。
以下是完整的代码：
%% # Step 1: read and prepare images %# (since you provided only one, I created the other by rotating the first). I1 = imread('http://i.stack.imgur.com/Se6zX.jpg'); I1 = rgb2gray( imcrop(I1, [85 35 445 345]) ); %# Get rid of white border I2 = imrotate(I1, -10, 'bilinear', 'crop'); %# Create 2nd by rotating 10 degrees %% # Step 2: detect the cross sign endpoints (sorted in same order) p1 = getCross(I1); p2 = getCross(I2); %% # Step 3: perform Image Registration %# Find transformation that maps I2 to I1 using the 4 control points for each t = cp2tform(p2,p1,'affine'); %# Transform I2 to be aligned with I1 II2 = imtransform(I2, t, 'XData',[1 size(I1,2)], 'YData',[1 size(I1,1)]); %# Plot figure('menu','none') subplot(131), imshow(I1), title('I1') subplot(132), imshow(I2), title('I2') subplot(133), imshow(II2), title('I2 (aligned)') %# Recover affine transformation params (translation, rotation, scale) ss = t.tdata.Tinv(2,1); sc = t.tdata.Tinv(1,1); tx = t.tdata.Tinv(3,1); ty = t.tdata.Tinv(3,2); scale = sqrt(ss*ss + sc*sc) rotation = atan2(ss,sc)*180/pi translation = [tx ty] 这是提取线端点的函数：
function points = getCross(I) %# Get edges (simply by thresholding) I = imfilter(I, fspecial('gaussian', [7 7], 1), 'symmetric'); BW = imclearborder(~im2bw(I, 0.5)); %# Hough transform [H,T,R] = hough(BW); %# Detect peaks P = houghpeaks(H, 2); %# Detect lines lines = houghlines(BW, T, R, P); %# Sort 2D points in counterclockwise order points = [vertcat(lines.point1); vertcat(lines.point2)]; idx = convhull(points(:,1), points(:,2)); points = points(idx(1:end-1),:); end 结果：
https://i.stack.imgur.com/PoT9N.png
scale = 1.0025 rotation = -9.7041 translation = 32.5270 -38.5021 旋转几乎恢复了10度（有一些不可避免的误差），缩放比例实际上是1（表示没有缩放）。请注意，在上面的示例中有一个平移组件，因为未围绕十字符号的中心执行旋转。
更多&回答... (https://stackoverflow.com/questions/2062826)
回答：
读者注意：这是一个后续问题，请参考以下内容：
如何在MATLAB中的霍夫变换中选择最大强度？ (https://stackoverflow.com/questions/1975206/how-to-select-maximum-intensity-in-hough-transform-in-matlab/1975261#1975261)
计算在MATLAB中移动的位移 (https://stackoverflow.com/questions/2062760/calculating-displacement-moved-in-matlab)
该过程类似于我之前展示的过程。在下面，我使用的是上一个问题的图像 (http://i182.photobucket.com/albums/x11/veronicafmy/FYP/pict1.jpg) （由于您只提供了一个，所以我将第一个旋转10度来创建另一个图像）。
我们首先检测两个图像的线条。我们借助Hough (http://www.mathworks.com/help/images/ref/hough.html) 变换 (http://www.mathworks.com/help/images/ref/houghlines.html) 功能来完成此操作 (http://www.mathworks.com/help/images/ref/houghpeaks.html) 。这看起来适用于两个图像：
https://i.stack.imgur.com/cINnK.png
接下来，我们要使用线端点作为控制点执行图像配准。首先，我们确保两个图像中的点彼此对应。我通过使用convhull (http://www.mathworks.com/help/matlab/ref/convhull.html)计算凸包来做到这一点， convhull (http://www.mathworks.com/help/matlab/ref/convhull.html)自动将它们按逆时针顺序排序（或者是相反方向！）。上面显示的数字指示顺序。
最后，我们使用cp2tform (http://www.mathworks.com/help/images/ref/cp2tform.html)函数获取转换矩阵，该矩阵用于对齐图像并提取平移，旋转和缩放。
以下是完整的代码：
%% # Step 1: read and prepare images %# (since you provided only one, I created the other by rotating the first). I1 = imread('http://i.stack.imgur.com/Se6zX.jpg'); I1 = rgb2gray( imcrop(I1, [85 35 445 345]) ); %# Get rid of white border I2 = imrotate(I1, -10, 'bilinear', 'crop'); %# Create 2nd by rotating 10 degrees %% # Step 2: detect the cross sign endpoints (sorted in same order) p1 = getCross(I1); p2 = getCross(I2); %% # Step 3: perform Image Registration %# Find transformation that maps I2 to I1 using the 4 control points for each t = cp2tform(p2,p1,'affine'); %# Transform I2 to be aligned with I1 II2 = imtransform(I2, t, 'XData',[1 size(I1,2)], 'YData',[1 size(I1,1)]); %# Plot figure('menu','none') subplot(131), imshow(I1), title('I1') subplot(132), imshow(I2), title('I2') subplot(133), imshow(II2), title('I2 (aligned)') %# Recover affine transformation params (translation, rotation, scale) ss = t.tdata.Tinv(2,1); sc = t.tdata.Tinv(1,1); tx = t.tdata.Tinv(3,1); ty = t.tdata.Tinv(3,2); scale = sqrt(ss*ss + sc*sc) rotation = atan2(ss,sc)*180/pi translation = [tx ty] 这是提取线端点的函数：
function points = getCross(I) %# Get edges (simply by thresholding) I = imfilter(I, fspecial('gaussian', [7 7], 1), 'symmetric'); BW = imclearborder(~im2bw(I, 0.5)); %# Hough transform [H,T,R] = hough(BW); %# Detect peaks P = houghpeaks(H, 2); %# Detect lines lines = houghlines(BW, T, R, P); %# Sort 2D points in counterclockwise order points = [vertcat(lines.point1); vertcat(lines.point2)]; idx = convhull(points(:,1), points(:,2)); points = points(idx(1:end-1),:); end 结果：
https://i.stack.imgur.com/PoT9N.png
scale = 1.0025 rotation = -9.7041 translation = 32.5270 -38.5021 旋转几乎恢复了10度（有一些不可避免的误差），缩放比例实际上是1（表示没有缩放）。请注意，在上面的示例中有一个平移组件，因为未围绕十字符号的中心执行旋转。
更多&回答... (https://stackoverflow.com/questions/2062826)