fitting the curve or line in 3d data and extendng the curve the end

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prashant singh
prashant singh 2017-12-28
评论： Eric Chadwick 2018-6-18
I have the 3d data(attached), where the first two columns represent the xy coordinate of point in a image and third column is my image number. These images are slices of one volumetric image. I want to fit a straight line through these points and then extend the line in that direction. For instance my image starts from image number 36 and end at 128. i want to fit a line for these image points and then extend the line so that i ca get the coordinate of images from image 35 to 0.

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回答（2 个）

Image Analyst
Image Analyst 2017-12-28
Parameterize your equation on slice, then fit for x and y separately:
s = load('data.mat')
data = s.data
x = data(:, 1);
y = data(:, 2);
sliceNumber = data(:, 3);
coefficientsX = polyfit(sliceNumber, x, 1);
coefficientsY = polyfit(sliceNumber, y, 1);
sFitted = 1 : max(sliceNumber);
xFitted = polyval(coefficientsX, sFitted);
yFitted = polyval(coefficientsY, sFitted);
plot(sliceNumber, x, 'b*');
hold on;
plot(sliceNumber, y, 'c*');
plot(sFitted, xFitted, 'm-', 'LineWidth', 2);
plot(sFitted, yFitted, 'r-', 'LineWidth', 2);
grid on;
xlabel('Slice Number', 'FontSize', 20);
ylabel('x or y', 'FontSize', 20);
legend('x data', 'y data', 'x fit', 'yFit');
Image Analyst
Image Analyst 2017-12-28
If you want to ignore what seem to be like bad data with y < 3, then do this:
s = load('data.mat')
data = s.data
x = data(:, 1);
y = data(:, 2);
sliceNumber = data(:, 3);
goodRows = y > 3;
x = x(goodRows);
y = y(goodRows);
sliceNumber = sliceNumber(goodRows);
coefficientsX = polyfit(sliceNumber, x, 1);
coefficientsY = polyfit(sliceNumber, y, 1);
sFitted = 1 : max(sliceNumber);
xFitted = polyval(coefficientsX, sFitted);
yFitted = polyval(coefficientsY, sFitted);
plot(sliceNumber, x, 'b*');
hold on;
plot(sliceNumber, y, 'c*');
plot(sFitted, xFitted, 'm-', 'LineWidth', 2);
plot(sFitted, yFitted, 'r-', 'LineWidth', 2);
grid on;
xlabel('Slice Number', 'FontSize', 20);
ylabel('x or y', 'FontSize', 20);
legend('x data', 'y data', 'x fit', 'y Fit');
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Image Analyst
Image Analyst 2018-6-15
I think he did, using my code. There is no reason that the code I gave should not work for his attached image once it has been segmented to give the (x,y) coordinates of the interface/boundary between the two regions. Now, finding that interface is a completely separate question than this one which regarded fitting/regression and extrapolation.
Eric Chadwick
Eric Chadwick 2018-6-18
I understand that, but what I don't understand is how to fit just one line instead of two since I want the line of best fit in 3D (i.e. using x,y,z that than just x OR y and z.

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