unknown parameters in Radon transform example

in https://www.mathworks.com/help/images/detect-lines-using-the-radon-transform.html line 31 of example code: [x1,y1] = pol2cart(deg2rad(1),5000) , where 5000 comes from? the same line 34, [x91,y91] = pol2cart(deg2rad(91),100) - where 100 comes from?

[SL: fixed URL by removing trailing comma]

Answer 1

[Star Strider]

Considering the complete example —

I = fitsread("solarspectra.fts");
I = rescale(I);

figure
imshow(I)
title("Original Image")

BW = edge(I);
figure
imshow(BW)
title("Edges of Original Image")

theta = 0:179;
[R,xp] = radon(BW,theta);

figure
imagesc(theta,xp,R)
colormap(hot)
xlabel("\theta (degrees)")
ylabel("x^{\prime} (pixels from center)")
title("R_{\theta} (x^{\prime})")
colorbar

figure
imagesc(theta,xp,R)
colormap(hot)
xlabel("\theta (degrees)")
ylabel("x^{\prime} (pixels from center)")
title("R_{\theta} (x^{\prime})")
colorbar

R_sort = sort(unique(R),"descend");

[row_peak,col_peak] = find(ismember(R,R_sort(1:5)));
xp_peak_offset = xp(row_peak);
theta_peak = theta(col_peak);

centerX = ceil(size(I,2)/2)

centerX = 96

centerY = ceil(size(I,1)/2)

centerY = 83

figure
imshow(I)
hold on
scatter(centerX,centerY,50,"bx",LineWidth=2)

[x1,y1] = pol2cart(deg2rad(1),5000)

x1 = 4.9992e+03

y1 = 87.2620

PlotArgsX = [centerX-x1 centerX+x1]

PlotArgsX = 1x2

1.0e+03 * -4.9032 5.0952

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PlotArgsY = [centerY+y1 centerY-y1]

PlotArgsY = 1x2

170.2620 -4.2620

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plot([centerX-x1 centerX+x1],[centerY+y1 centerY-y1],"r--",LineWidth=2)

[x91,y91] = pol2cart(deg2rad(91),100)

x91 = -1.7452

y91 = 99.9848

for i=1:3
    plot([centerX-x91+xp_peak_offset(i) centerX+x91+xp_peak_offset(i)], ...
        [centerY+y91 centerY-y91], ...
        "r",LineWidth=2)
end

plot([centerX-x91 centerX+x91],[centerY+y91 centerY-y91],"g--",LineWidth=2)

for i=4:5
plot([centerX-x1 centerX+x1], ...
    [centerY+y1-xp_peak_offset(i) centerY-y1-xp_peak_offset(i)], ...
    "g",LineWidth=2)
end

axlims = axis

axlims = 1x4

0.5000 192.5000 0.5000 165.5000

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The ‘5000’ value appears to me to be arbitrary, since (for whatever reason) it does not plot beyond the axes limits (coutrely provided by the added axis result) as I would normally expect it to, for example —

figure
plot([centerX-x1 centerX+x1],[centerY+y1 centerY-y1],"r--",LineWidth=2)
hold on
plot(axlims([1 2]), axlims(3)*[1 1], '-g')
plot(axlims([1 2]), axlims(4)*[1 1], '-g')
plot(axlims([1 2]), axlims(3)*[1 1], '-g')
plot(axlims(1)*[1 1], axlims([3 4]), '-g')
plot(axlims(2)*[1 1], axlims([3 4]), '-g')
hold off
grid
legend('Red Dashed Line', 'imshow Axes', 'Location','NE')

Experimenting with thee code and changing to ‘5000’ value to ‘500’ instead does not change the appearsnce of the red dashed line in the imshow plot.

The second pol2cart call seems to me to be more reasonable, in that its results are within the axis limits, however I suspect the ‘100’ is also arbitrary, although more appropriate to the axis scaling.

.

Answer 2

[Image Analyst]

"The page you were looking for does not exist. Use the search box or browse topics below to find the page you were looking for."

help pol2cart

 POL2CART Transform polar to Cartesian coordinates.
    [X,Y] = POL2CART(TH,R) transforms corresponding elements of data stored
    in polar coordinates (angle TH, radius R) to Cartesian coordinates X,Y.
    The arrays TH and R must have compatible sizes. In the simplest cases,
    they can be the same size or one can be a scalar. Two inputs have
    compatible sizes if, for every dimension, the dimension sizes of the
    inputs are either the same or one of them is 1. TH must be in radians.
 
    [X,Y,Z] = POL2CART(TH,R,Z) transforms corresponding elements of data
    stored in cylindrical coordinates (angle TH, radius R, height Z) to
    Cartesian coordinates X,Y,Z. The arrays TH, R, and Z must have
    compatible sizes.  TH must be in radians.
 
    Class support for inputs TH,R,Z:
       float: double, single
 
    See also CART2SPH, CART2POL, SPH2CART.

    Documentation for pol2cart
       doc pol2cart

    Other uses of pol2cart

       distributed/pol2cart

The 5000 and 100 were the radius they chose. I don't know why since the page you gave no longer exists.

For what it's worth, you can see my attached radon demo.