SVD line fitting or ransac line fitting in multidimensionl image

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prashant singh
prashant singh 2017-12-26
编辑： Matt J 2017-12-28
i have a multidimensional image of size 1024*512*128. For each slice(1024*512), I have single point from the mid slice of an image say from slice 40 to 128. So, i have 89 points in my multidimensional (volumetric) image. how can i fit the straight line using svd/ ransac or any other method and then extrapolate that line to the end of the volumetric image?

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Matt J
Matt J 2017-12-27
编辑：Matt J 2017-12-27
This will give you the equations Aeq*x=beq for the line,
Q=[X(:),Y(:),Z(:)];
m=mean(Q,1).';
Q=Q-m.';
[~,~,Z]=svd(Q,0);
Aeq=Z(:,2:3).';
beq=Aeq*m;
Because you know the vertices of the volume's bounding box (put them in the rows of a matrix V), you can then use intersectionHull (download here) to find the intersection points of the line with the box,
I=intersectionHull('vert',V,'lcon',[],[],Aeq,beq);
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prashant singh
prashant singh 2017-12-28
Done but please let me know if I can visualize the convex hull on my volumetric image to validate the result.
Matt J
Matt J 2017-12-28
编辑：Matt J 2017-12-28
I'm not sure how you would do that. Possibly you could use a slice viewer from the File Exchange, e.g.,
https://www.mathworks.com/matlabcentral/fileexchange/27983-slicer
and then add lines to the 3D axes using the line() command (with HOLD ON active).

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