How to get the same pixel points in an image using Euclidean Distance when the image is scaled up or down?

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Fego Etese 2020-4-9

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https://ww2.mathworks.cn/matlabcentral/answers/516723-how-to-get-the-same-pixel-points-in-an-image-using-euclidean-distance-when-the-image-is-scaled-up-or

评论： Adam Danz 2020-4-11

I have two images, image A is normal and the image B is scaled up and on the image A I have calculated the euclidean distance between two pixel coordinates (x and y) and i want to be able to find the location of x and y in the image B that is scaled up using the euclidean distance I calculated in the image A. Assuming i can find pixel x location in the scaled image B, how then can I find pixel y coordinate in the scaled image B using the distance from pixel x to y in normal image A?. Is this possible? and how can I go about it?

Thanks

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darova 2020-4-9

Can you make a simple drawing or something? THe question is hard

Fego Etese 2020-4-10

Please check the comment below Adam Danz answer for more clarification. I've put up a drawing there with the image.

Thanks

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Adam Danz 2020-4-9

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https://ww2.mathworks.cn/matlabcentral/answers/516723-how-to-get-the-same-pixel-points-in-an-image-using-euclidean-distance-when-the-image-is-scaled-up-or#answer_425088

编辑：Adam Danz 2020-4-9

在 MATLAB Online 中打开

Think of the line that connects two points P & Q as the hypotenuse of a right triangle where the length of leg-1 is the x-distance between the two points and the length of leg-2 is the y-distance (sign indicates direction). You can compute leg-1 and leg-2 lengths easily by subtracting the coordinates Q from coordinates P (assuming a linear scale).

Then you just have to rescale leg-1 and leg-2 lengths to the upscaled image scale. The scale conversion for the x axis is just the range of the x-limits of image-2 divided by the range of x-limits of image-1. Same for the y-axis. If the extent of image-2 is larger than image-1 the value should be larger than 1. Multiply that conversion factor by the lengths of leg-1 and leg-2 to get the new leg-lengths which can be added to the know coordinate to produce the 2nd coordinate.

Here's a demo where Q1, P1 and Q2 are known and the P2 is calculated.

P = [2,5]; 
Q = [9,7];
Q2 = [20, 45];
figure()
sp(1) = subplot(1,2,1);
plot([P(1),Q(1)],[P(2),Q(2)], 'bo')
xlim([0,12])
ylim([0,12])
text(2.5,5,'Q1')
text(9.5,7,'P1')
grid on
sp(2) = subplot(1,2,2);
plot(Q2(1), Q2(2), 'bo')
xlim([0,120])
ylim([0,150])
text(25, 45,'Q2')
grid on
% compute P
xFactor = range(sp(2).XLim)/range(sp(1).XLim); 
yFactor = range(sp(2).YLim)/range(sp(1).YLim);
legX = Q(1) - P(1); 
legY = Q(2) - P(2); 
P2(1) = legX * xFactor + Q2(1); 
P2(2) = legY * yFactor + Q2(2); 
% Add to plot
hold(sp(2), 'on')
plot(sp(2), P2(1), P2(2), 'bo')
text(P2(1)+5, P2(2), 'P2', 'Color', 'r')