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

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.

[Matt J]

Didn't we cover this in your previous post?

https://www.mathworks.com/matlabcentral/answers/374590-svd-line-fitting-or-ransac-line-fitting-in-multidimensionl-image

I thought the problem was how to view the results.

Answer 1

[Image Analyst]

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');

Answer 2

[Image Analyst]

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');

[prashant singh]

it works perfectly but I don't need to plot straight line or curve on x and y separately. X and Y are the coordinates of the single point in 2d image. These 2d images then combined to for volume image. The direction of line should be decided both by x and y coordinates. Attached one such image for reference.

[Eric Chadwick]

I have the same problem as you. Did you figure out how to do it?

[Image Analyst]

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]

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.