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ImageTools

  

HoughLine

  

detect lines using Hough Transform

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

Calling Sequence

HoughLine(img, rho, theta, threshold)

Parameters

img

-

Image

d_rho

-

algebraic , radial increment

d_theta

-

algebraic , angular increment in radian

threshold

-

posint , minimum number of points required to detect a line

Options

• 

rhorange : list , contains minimum rho and maximum rho

• 

thetarange : list , contains minimum theta and maximum theta

Description

• 

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=xcosθ+ysinθ 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 upperboundimg,1upperboundimg,2 to upperboundimg,1+upperboundimg,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.

Examples

withImageTools:

imgReadcatkerneloptsdatadir,/images/Maplesoft.png

_rtable18446884427913793654

(5.1)

edgeThresholdEdgeDetectimg,1.5

_rtable18446884427776642454

(5.2)

Embededge

lineHoughLineedge,1,π180,250

_rtable18446884427776623550

(5.3)

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:

DrawLineimg,line

Embedimg

Compatibility

• 

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

• 

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

See Also

ImageTools[Draw][Line]

ImageTools[ProbabilisticHoughLine]