detect lines using Hough Transform
HoughLine(img, rho, theta, threshold)
algebraic , radial increment
algebraic , angular increment in radian
posint , minimum number of points required to detect a line
rhorange : list , contains minimum rho and maximum rho
thetarange : list , contains minimum theta and maximum theta
The HoughLine command detects the lines in img, and returns the detected lines in an m by 2 Array, lines. A line given by the equation ρ=x⁢cos⁡θ+y⁢sin⁡θ is represented by the pair of values ρ,θ. This pair then forms a row of lines. The equation takes the origin of the coordinate system to be at the top left corner of the image, contrary to e.g. the ImageTools[Draw] subpackage which takes the origin a the lower left corner. The value ρ (in the first column) can be understood as the signed distance from the origin to the closest point on the line - the sign being negative if the line passes above the origin and positive otherwise. The value θ (in the second column) can be understood as the counterclockwise angle in radians of a normal to the line, starting from horizontal. By default, the values of θ are in the range 0 to π.
The implementation attempts to find such lines by varying ρ and θ over a grid of values. The required arguments d_rho and d_theta specify the step size for ρ and θ, respectively, in this grid.
img should be a binary image, so calling EdgeDetect and Threshold are usually necessary before calling HoughLine.
The option rhorange specifies the range of ρ, so only the lines with ρ values in this range is returned. The default is from −upperbound⁡img,1−upperbound⁡img,2 to upperbound⁡img,1+upperbound⁡img,2.
The option thetarange specifies the range of θ, so only the lines with θ values in this range is returned. The default is 0 to π.
DrawLine := proc(img, line)
local i, nRows, nCols, rho, theta, pixel, ctheta, stheta,
xMid, yMid, x1, y1, x2, y2;
nRows := upperbound(img, 1);
nCols := upperbound(img, 2);
pixel := evalf('sqrt'(nRows^2 + nCols^2));
for i to upperbound(line, 1) do
rho := line[i, 1];
theta := line[i, 2];
ctheta := cos(theta);
stheta := sin(theta);
xMid := rho * ctheta;
yMid := rho * stheta;
x1 := xMid + pixel * (-stheta);
y1 := yMid + pixel * ctheta;
x2 := xMid - pixel * (-stheta);
y2 := yMid - pixel * ctheta;
Draw:-Line(img, x1, nRows - y1, x2, nRows - y2, [255, 0, 0]):
The ImageTools[HoughLine] command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
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