霍夫变换等价于倍频程
Hough Transform Equivalent in Octave
我在下面的 MATLAB 中附上了 霍夫变换 的代码：
%Hough Transform to find lines
%Load an Image and Convert to Grayscale to apply canny Filter
im = imread('lines.jpg');
im_gray = rgb2gray(im);
im_edge = edge(im_gray, 'canny');
figure, imshow(im), title('Original Image');
figure, imshow(im_gray), title('Grayscale Image');
figure, imshow(im_edge), title('Canny Filter Edge');
%Apply Hough Transform to Find the Candidate Lines
[accum theta rho] = hough(im_edge);
figure, imagesc(accum, 'xData', theta, 'ydata', rho), title('Hough Accumulator');
peaks = houghpeaks(accum, 100, 'Threshold', ceil(0.6 * max(accum(:))),'NHoodSize', [5,5]);
size(peaks);
%Finding the line segments in the image
line_segs = houghlines(edges, theta, rows, peaks, 'FillGap', 50,'MinLength', 100);
%Plotting
figure, imshow(im), title('Line Segments');
hold on;
for k=1:length(line_segs)
endpoints = [line_segs(k).point1; line_segs(k).point2];
plot(endpoints(:,1), endpoints(:,2), 'LineWidth', 2, 'Color','green');
end
hold off;
当我尝试通过更改 'hough into houghtf'、'houghlines to hough_line' 在 OCTAVE 中实现相同功能时和 'houghpeaks into immaximas' 如下：
%Hough Transform to find lines
pkg load image;
%Load an Image and Convert to Grayscale to apply canny Filter
im = imread('lines.jpg');
im_gray = rgb2gray(im);
im_edge = edge(im_gray, 'canny');
figure, imshow(im), title('Original Image');
figure, imshow(im_gray), title('Grayscale Image');
figure, imshow(im_edge), title('Canny Filter Edge');
%Apply Hough Transform to Find the Candidate Lines
[accum theta rho] = houghtf(im_edge); %In Octave and 'hough' in MATLAB
figure, imagesc(accum, 'xData', theta, 'ydata', rho), title('Hough Accumulator');
peaks = immaximas(accum, 100, 'Threshold', ceil(0.6 * max(accum(:))),'NHoodSize', [5,5]);
size(peaks);
%Finding the line segments in the image
line_segs = hough_line(edges, theta, rows, peaks, 'FillGap', 50, 'MinLength', 100);
%Plotting
figure, imshow(im), title('Line Segments');
hold on;
for k=1:length(line_segs)
endpoints = [line_segs(k).point1; line_segs(k).point2];
plot(endpoints(:,1), endpoints(:,2), 'LineWidth', 2, 'Color', 'green');
end
hold off;
执行时出现以下错误：
error: element number 3 undefined in return list
error: called from
HoughTransformLines at line 14 column 18
我收到错误消息，指出 'rho' 未定义。
我对 MATLAB 和 Octave 完全陌生。谁能帮我在 Octave 中实现霍夫变换？
Octave 告诉您 rho 未定义的原因是因为 Matlab 的 hough function and Octave's houghtf 函数不是完全等价的。
这是相应 Mathwork 网页上 hough 返回的输出参数的描述：
The function returns rho, the distance from the origin to the line
along a vector perpendicular to the line, and theta, the angle in
degrees between the x-axis and this vector. The function also returns
the Standard Hough Transform, H, which is a parameter space matrix
whose rows and columns correspond to rho and theta values
respectively.
Octave的houghtf，另一方面，只有returns矩阵H:
The result H is an N by M matrix containing the Hough transform. Here,
N is the number different values of r that has been attempted. This is
computed as 2*diag_length - 1, where diag_length is the length of the
diagonal of the input image. M is the number of different values of
theta. These can be set through the third input argument arg. This
must be a vector of real numbers, and is by default pi*(-90:90)/180.
现在，在您的脚本中，您调用 rho 的唯一地方是第 15 行，当试图显示 Hough 累加器时。
我建议您改为这样绘制累加器：
figure, imagesc(H),xlabel('xData'),ylabel('ydata'),title('Hough accumulator')
让我知道这是否适合您！
[H] = houghtf(edges);
您必须以这种方式传递参数，因为八度 returns 只是一个值矩阵。您不能将三个不同的变量分配给一个矩阵。
所以，给它分配一个变量，你就会得到结果。
我建议对原始代码进行以下更新：
%Hough Transform to find lines
pkg load image;
%Load an Image and Convert to Grayscale to apply canny Filter
im = imread('lines.jpg');
im_gray = rgb2gray(im);
im_edge = edge(im_gray, 'canny');
figure 1, imshow(im), title('Original Image');
figure 2, imshow(im_gray), title('Grayscale Image');
figure 3, imshow(im_edge), title('Canny Filter Edge');
%Apply Hough Transform to Find the Candidate Lines
accum = houghtf(im_edge);
theta = -90:90;
diag_length = (size(accum)(1) - 1) / 2;
rho = -diag_length:diag_length;
figure 4, imagesc(theta, rho, accum), title('Hough Accumulator');
peaks = houghpeaks(accum, 100, 'Threshold', ceil(0.6 * max(accum(:))), 'NHoodSize', [5,5]);
%Finding the line segments in the image
line_segs = houghlines(im_edge, theta, rho, peaks, 'FillGap', 50, 'MinLength', 100);
%Plotting
figure 5, imshow(im), title('Line Segments');
hold on;
for k=1:length(line_segs)
endpoints = [line_segs(k).point1; line_segs(k).point2];
plot(endpoints(:,1), endpoints(:,2), 'LineWidth', 2, 'Color', 'green');
end
hold off;
让我们浏览所有更新并查看它们：
%Hough Transform to find lines
pkg load image;
%Load an Image and Convert to Grayscale to apply canny Filter
im = imread('lines.jpg');
im_gray = rgb2gray(im);
im_edge = edge(im_gray, 'canny');
figure 1, imshow(im), title('Original Image');
figure 2, imshow(im_gray), title('Grayscale Image');
figure 3, imshow(im_edge), title('Canny Filter Edge');
只有很小的变化 - 添加了数字索引以将它们划分为一致的单独 windows（参见 Multiple Plot Windows）。
之后我们应用霍夫变换并恢复 Octave 中的 "lost" theta 和 rho 值：
%Apply Hough Transform to Find the Candidate Lines
accum = houghtf(im_edge);
theta = -90:90;
diag_length = (size(accum)(1) - 1) / 2;
rho = -diag_length:diag_length;
figure 4, imagesc(theta, rho, accum), title('Hough Accumulator');
根据 houghtf function's docs, it returns only an accumulator with rows corresponding to indices of rho values, and columns - to indices of theta values. How can we restore the original rho and theta values? Well, the number of rho values (rows in the accum matrix variable) goes up to 2*diag_length - 1, where diag_length is the length of the diagonal of the input image. Knowing this, we should restore the diagonal length (it is a reversed action): diag_length = (size(accum)(1) - 1) / 2. Then we can restore rho values, which go from minus diagonal to diagonal: rho = -diag_length:diag_length. With thetas everything is easier - they are in the range of pi*(-90:90)/180, but we will use degrees instead: theta = -90:90. I've added the index for figure as did before and changed the call to imagesc according to its docs - 它应该被称为 imagesc (x, y, img)。
之后我们使用houghpeaks函数得到峰值：
peaks = houghpeaks(accum, 100, 'Threshold', ceil(0.6 * max(accum(:))), 'NHoodSize', [5,5]);
然后我们使用 houghlines 来获取结果线段（猜测有一些带有变量名称的勘误表）：
line_segs = houghlines(im_edge, theta, rho, peaks, 'FillGap', 50, 'MinLength', 100);
最后是绘制代码 - 它根本没有改变，因为它工作正常。
我在下面的 MATLAB 中附上了 霍夫变换 的代码：
%Hough Transform to find lines
%Load an Image and Convert to Grayscale to apply canny Filter
im = imread('lines.jpg');
im_gray = rgb2gray(im);
im_edge = edge(im_gray, 'canny');
figure, imshow(im), title('Original Image');
figure, imshow(im_gray), title('Grayscale Image');
figure, imshow(im_edge), title('Canny Filter Edge');
%Apply Hough Transform to Find the Candidate Lines
[accum theta rho] = hough(im_edge);
figure, imagesc(accum, 'xData', theta, 'ydata', rho), title('Hough Accumulator');
peaks = houghpeaks(accum, 100, 'Threshold', ceil(0.6 * max(accum(:))),'NHoodSize', [5,5]);
size(peaks);
%Finding the line segments in the image
line_segs = houghlines(edges, theta, rows, peaks, 'FillGap', 50,'MinLength', 100);
%Plotting
figure, imshow(im), title('Line Segments');
hold on;
for k=1:length(line_segs)
endpoints = [line_segs(k).point1; line_segs(k).point2];
plot(endpoints(:,1), endpoints(:,2), 'LineWidth', 2, 'Color','green');
end
hold off;
当我尝试通过更改 'hough into houghtf'、'houghlines to hough_line' 在 OCTAVE 中实现相同功能时和 'houghpeaks into immaximas' 如下：
%Hough Transform to find lines
pkg load image;
%Load an Image and Convert to Grayscale to apply canny Filter
im = imread('lines.jpg');
im_gray = rgb2gray(im);
im_edge = edge(im_gray, 'canny');
figure, imshow(im), title('Original Image');
figure, imshow(im_gray), title('Grayscale Image');
figure, imshow(im_edge), title('Canny Filter Edge');
%Apply Hough Transform to Find the Candidate Lines
[accum theta rho] = houghtf(im_edge); %In Octave and 'hough' in MATLAB
figure, imagesc(accum, 'xData', theta, 'ydata', rho), title('Hough Accumulator');
peaks = immaximas(accum, 100, 'Threshold', ceil(0.6 * max(accum(:))),'NHoodSize', [5,5]);
size(peaks);
%Finding the line segments in the image
line_segs = hough_line(edges, theta, rows, peaks, 'FillGap', 50, 'MinLength', 100);
%Plotting
figure, imshow(im), title('Line Segments');
hold on;
for k=1:length(line_segs)
endpoints = [line_segs(k).point1; line_segs(k).point2];
plot(endpoints(:,1), endpoints(:,2), 'LineWidth', 2, 'Color', 'green');
end
hold off;
执行时出现以下错误：
error: element number 3 undefined in return list
error: called from
HoughTransformLines at line 14 column 18
我收到错误消息，指出 'rho' 未定义。 我对 MATLAB 和 Octave 完全陌生。谁能帮我在 Octave 中实现霍夫变换？
Octave 告诉您 rho 未定义的原因是因为 Matlab 的 hough function and Octave's houghtf 函数不是完全等价的。
这是相应 Mathwork 网页上 hough 返回的输出参数的描述：
The function returns rho, the distance from the origin to the line along a vector perpendicular to the line, and theta, the angle in degrees between the x-axis and this vector. The function also returns the Standard Hough Transform, H, which is a parameter space matrix whose rows and columns correspond to rho and theta values respectively.
Octave的houghtf，另一方面，只有returns矩阵H:
The result H is an N by M matrix containing the Hough transform. Here, N is the number different values of r that has been attempted. This is computed as 2*diag_length - 1, where diag_length is the length of the diagonal of the input image. M is the number of different values of theta. These can be set through the third input argument arg. This must be a vector of real numbers, and is by default pi*(-90:90)/180.
现在，在您的脚本中，您调用 rho 的唯一地方是第 15 行，当试图显示 Hough 累加器时。
我建议您改为这样绘制累加器：
figure, imagesc(H),xlabel('xData'),ylabel('ydata'),title('Hough accumulator')
让我知道这是否适合您！
[H] = houghtf(edges);
您必须以这种方式传递参数，因为八度 returns 只是一个值矩阵。您不能将三个不同的变量分配给一个矩阵。
所以，给它分配一个变量，你就会得到结果。
我建议对原始代码进行以下更新：
%Hough Transform to find lines
pkg load image;
%Load an Image and Convert to Grayscale to apply canny Filter
im = imread('lines.jpg');
im_gray = rgb2gray(im);
im_edge = edge(im_gray, 'canny');
figure 1, imshow(im), title('Original Image');
figure 2, imshow(im_gray), title('Grayscale Image');
figure 3, imshow(im_edge), title('Canny Filter Edge');
%Apply Hough Transform to Find the Candidate Lines
accum = houghtf(im_edge);
theta = -90:90;
diag_length = (size(accum)(1) - 1) / 2;
rho = -diag_length:diag_length;
figure 4, imagesc(theta, rho, accum), title('Hough Accumulator');
peaks = houghpeaks(accum, 100, 'Threshold', ceil(0.6 * max(accum(:))), 'NHoodSize', [5,5]);
%Finding the line segments in the image
line_segs = houghlines(im_edge, theta, rho, peaks, 'FillGap', 50, 'MinLength', 100);
%Plotting
figure 5, imshow(im), title('Line Segments');
hold on;
for k=1:length(line_segs)
endpoints = [line_segs(k).point1; line_segs(k).point2];
plot(endpoints(:,1), endpoints(:,2), 'LineWidth', 2, 'Color', 'green');
end
hold off;
让我们浏览所有更新并查看它们：
%Hough Transform to find lines
pkg load image;
%Load an Image and Convert to Grayscale to apply canny Filter
im = imread('lines.jpg');
im_gray = rgb2gray(im);
im_edge = edge(im_gray, 'canny');
figure 1, imshow(im), title('Original Image');
figure 2, imshow(im_gray), title('Grayscale Image');
figure 3, imshow(im_edge), title('Canny Filter Edge');
只有很小的变化 - 添加了数字索引以将它们划分为一致的单独 windows（参见 Multiple Plot Windows）。
之后我们应用霍夫变换并恢复 Octave 中的 "lost" theta 和 rho 值：
%Apply Hough Transform to Find the Candidate Lines
accum = houghtf(im_edge);
theta = -90:90;
diag_length = (size(accum)(1) - 1) / 2;
rho = -diag_length:diag_length;
figure 4, imagesc(theta, rho, accum), title('Hough Accumulator');
根据 houghtf function's docs, it returns only an accumulator with rows corresponding to indices of rho values, and columns - to indices of theta values. How can we restore the original rho and theta values? Well, the number of rho values (rows in the accum matrix variable) goes up to 2*diag_length - 1, where diag_length is the length of the diagonal of the input image. Knowing this, we should restore the diagonal length (it is a reversed action): diag_length = (size(accum)(1) - 1) / 2. Then we can restore rho values, which go from minus diagonal to diagonal: rho = -diag_length:diag_length. With thetas everything is easier - they are in the range of pi*(-90:90)/180, but we will use degrees instead: theta = -90:90. I've added the index for figure as did before and changed the call to imagesc according to its docs - 它应该被称为 imagesc (x, y, img)。
之后我们使用houghpeaks函数得到峰值：
peaks = houghpeaks(accum, 100, 'Threshold', ceil(0.6 * max(accum(:))), 'NHoodSize', [5,5]);
然后我们使用 houghlines 来获取结果线段（猜测有一些带有变量名称的勘误表）：
line_segs = houghlines(im_edge, theta, rho, peaks, 'FillGap', 50, 'MinLength', 100);
最后是绘制代码 - 它根本没有改变，因为它工作正常。