MATLAB: Volume enclosed by isosurface

isosurface volume

How can I calculate the volume enclosed by an isosurface, in this case my isosufaces are generally irregular cylinders.

I've attached an image to give you and idea of the tubes (although its not a great one!)

Convex hull method over estimates due to its curvature, but could possibly work for small segments and summation over the whole tube. However, there must be a simpler way!?

Many thanks, Will

Best Answer

Cleaned up image and counted the data points which represent voxels (of known value)..... easy

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I would recommend voxelizing it and then just summing the resulting three dimensional volumetric image. There are a few utilities on the FEX that do this:

MATLAB: How to perform batch image thresholding with variable threshold for each image

I figured out how to do this based on the second peak in the histogram. It feels kind of hackish and unwieldy, but it works.

Assuming MZ is your two dimensional image:

     hist = imhist(MZ);
     % Get counts and bins for histogram
     [counts, binlocs] = imhist(MZ);
     % Find peaks of histogram
     [peaks,locs] = findpeaks(hist);
     % Get 2nd peak by sorting in descending order and choosing second index
     peaks_sorted = sort(peaks,'descend');
     second_peak = peaks_sorted(2);
     %Find index of 2nd max
     second_peak_index = find(counts==second_peak);
     second_peak_index = max(second_peak_index); 
     % If multiple instances of intensity of second_peak exist, we want the 
     % highest index.  There is probably a better way to do this.
     %Determine intensity value of second peak
     second_peak_intensity = binlocs(second_peak_index);
     %Choose threshold value based on second peak
     thresh_value = second_peak_intensity + 0.01;
     %Create image segmentation based on dynamic threshold value
     BW = MZ > thresh_value;         
     seg = MZ;
     seg(~BW) = 0;

Best Answer

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MATLAB: How to get the volume of a 3D concave shape

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