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 $\mathrm{\rho }=x\cos \left(\mathrm{\theta }\right)+y\sin \left(\mathrm{\theta }\right)$ is represented by the pair of values $\left(\mathrm{\rho }\,\mathrm{\theta }\right)$. 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 $\mathrm{\rho }$ (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 $\mathrm{\theta }$ (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 $\mathrm{\theta }$ are in the range $0$ to $\mathrm{\pi }$.

The implementation attempts to find such lines by varying $\mathrm{\rho }$ and $\mathrm{\theta }$ over a grid of values. The required arguments d_rho and d_theta specify the step size for $\mathrm{\rho }$ and $\mathrm{\theta }$, respectively, in this grid. For each line, the implementation counts the number of nonblack pixels. If this is greater than threshold, the line is included in the result.

img should be a binary image, so calling EdgeDetect and Threshold are usually necessary before calling HoughLine.

The option rhorange specifies the range of $\mathrm{\rho }$, so only the lines with $\mathrm{\rho }$ values in this range is returned. The default is from $-\mathrm{upperbound}\left(\mathrm{img}\,1\right)-\mathrm{upperbound}\left(\mathrm{img}\,2\right)$ to $\mathrm{upperbound}\left(\mathrm{img}\,1\right)+\mathrm{upperbound}\left(\mathrm{img}\,2\right)$.

The option thetarange specifies the range of $\mathrm{\theta }$, so only the lines with $\mathrm{\theta }$ values in this range is returned. The default is $0$ to $\mathrm{\pi }$.

$\mathrm{with}\left(\mathrm{ImageTools}\right)\:$

$\mathrm{img}≔\mathrm{Read}\left(\mathrm{cat}\left(\mathrm{kernelopts}\left(\mathrm{datadir}\right)\,''/images/Maplesoft.png''\right)\right)$

$\mathrm{edge}≔\mathrm{Threshold}\left(\mathrm{EdgeDetect}\left(\mathrm{img}\right)\,1.5\right)$

$\mathrm{Embed}\left(\mathrm{edge}\right)$

$\mathrm{line}≔\mathrm{HoughLine}\left(\mathrm{edge}\,1\,\frac{\mathrm{\pi }}{180}\,250\right)$

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]):
    end do;
end proc:

$\mathrm{DrawLine}\left(\mathrm{img}\,\mathrm{line}\right)$

$\mathrm{Embed}\left(\mathrm{img}\right)$

The ImageTools[HoughLine] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.