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    <p>Linearize the voxel coordinates, and put them into two scipy.sparse.sparse.csc matrices. </p> <p>Let v be the number of voxels, m the number of masks, and t the number of tracks.<br> Let M be the mask csc matrix, size (m x v), where a 1 at (i,j) means mask i overlaps voxel j.<br> Let T be the track csc matrix, size (t x v), where a 1 at (k,j) means track k overlaps voxel j. </p> <pre><code>Overlap = (M * T.transpose() &gt; 0) # track T overlaps mask M Connected = (Overlap * Overlap.tranpose() &gt; 0) # Connected masks Density[mask_idx] = numpy.take(T, nonzero(Overlap[mask_idx, :])[0], axis=0).sum(axis=0) </code></pre> <p>I might be wrong on the last one, and I'm not sure css_matrices can be operated on by nonzero &amp; take. You might need to pull out each column in a loop and convert it to a full matrix.</p> <hr> <p>I ran some experiments trying to simulate what I thought was a reasonable amount of data. The code below takes about 2 minutes on a 2-year old MacBook. If you use csr_matrices, it takes about 4 minutes. There is probably a tradeoff depending on how long each track is. </p> <pre><code>from numpy import * from scipy.sparse import csc_matrix nvox = 1000000 ntracks = 300000 nmask = 100 # create about 100 entries per track tcoords = random.uniform(0, ntracks, ntracks * 100).astype(int) vcoords = random.uniform(0, nvox, ntracks * 100).astype(int) d = ones(ntracks * 100) T = csc_matrix((d, vstack((tcoords, vcoords))), shape=(ntracks, nvox), dtype=bool) # create around 10000 entries per mask mcoords = random.uniform(0, nmask, nmask * 10000).astype(int) vcoords = random.uniform(0, nvox, nmask * 10000).astype(int) d = ones(nmask * 10000) M = csc_matrix((d, vstack((mcoords, vcoords))), shape=(nmask, nvox), dtype=bool) Overlap = (M * T.transpose()).astype(bool) # mask M overlaps track T Connected = (Overlap * Overlap.transpose()).astype(bool) # mask M1 and M2 are connected Density = Overlap * T.astype(float) # number of tracks overlapping mask M summed across voxels </code></pre>
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    1. COIf the dtype of the matrices is set to bool, I don't think the "> 0" bits are necessary anymore.
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    2. COactually, not true. at least for sparse matrices, multipltication promotes them to a byte. (?) I hope that doesn't mean there are wraparound issues, as well.
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    3. COThanks for this, sped me up to under one minute with the average track length around 10 and the average mask size around 500.
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