Zernike descriptors are HUGE

[binarybottle]

Email exchange between Brian Rossa, Arthur Mikhno, and Arno Klein (8/5-7/2013):

Brian Rossa (8/5/2013):
The Python results agree completely with the Octave results on my side, but my results do not agree with your results. The problem is that the function D_CV_orig expects "faces" to be 1-indexed -- think MATLAB -- rather than 0-indexed. We can add an "assert" to the code to check for this error mode in the future.
The size of the descriptor that you are seeing, 6, appears to be correct insofar as Arthur's code also gives a descriptor of size 6.
The descriptor for label22.vtk has some very large values. While this may seem dubious, the Arthur's code gives extremely high values as well.
Here are the "right" answers for your two examples according to Arthur and Octave:
[ 0.03978874 0.07597287 0.08322411 0.20233902 0.11730369 0.14579667]
[ 7.56275148e+03 1.43262240e+08 1.10767079e+06 2.84879089e+10 1.12922387e+08 1.02507341e+10]

Arthur Mikhno (8/7/2013):
The length of the descriptors exponentially increases with order. I don't recall the formula for calculating the number of descriptors from order but can look into that. For ex. order 20 yields 121 descriptors while order 35 yields 342.

Generally speaking, values should be < ~1, with values >> 1 a sign of instability in calculating descriptors. Instability could be due to the way the mesh is created or by trying to calculate at an order too high given the resolution/size of the object.

BTW. One way to tell if your descriptor values are reasonable is by reconstructing using zernike moments to see if the estimated object resembles the true object. I have recon. code ready if you want to give that a try.

Arno:
thank you for the explanation, arthur. i like the idea of reconstructing the mesh to see how well it estimated the moments. please do share your code for this so we may give it a try.

the surface patches i am running the code on have hundreds to thousands of vertices, and when i run the code with order 10 i get huge descriptor values. do you think that simplifying the mesh would lead to greater stability for the zernike code? is there any theoretical rationale for choosing a given order; for example, would a given mesh size demand a minimum order?

[satra]

i agree that recon is a good way to look at accuracy. in that regard take a look at:

doi:10.1109/TPAMI.2010.139

that paper describes an approximate form which runs much quicker but should be fairly good on dense meshes like the ones arno has.

[binarybottle]

Arthur Mikhno:

This is the algorithm we actually implemented!

[binarybottle]

yes, we would love to try it out. better still, could you first try it on the descriptors from the label22.vtk file i sent to you today?

here are the desciptors that i get for order 3:

>>> # Moments for label 22 (postcentral) in Twins-2-1:
>>> import os
>>> from mindboggle.shapes.zernike.zernike import zernike_moments_per_label
>>> path = os.environ['MINDBOGGLE_DATA']
>>> vtk_file = os.path.join(path, 'arno', 'labels', 'lh.labels.DKT25.manual.vtk')
>>> area_file = os.path.join(path, 'arno', 'shapes', 'lh.pial.area.vtk')
>>> order = 3
>>> exclude_labels = [0]
>>> largest_segment = True
>>> zernike_moments_per_label(vtk_file, order, exclude_labels, area_file,
>>>                           largest_segment)
([[7562.751480397972,
   143262239.5171249,
   1107670.7893994227,
   28487908892.820065,
   112922387.17238183,
   10250734140.30357]],
 [22])

[satra]

great. in that case that reference should be added to the docstring.

[binarybottle]

Arthur Mikhno:

Your descriptors don't look right, the values are way too high.

I loaded this label, it looks like a thin (1 pixel thick?) surface portion of a piece of a cortex. I am not sure my code will work a thin sheet like this, have only seen this applied to volumetric meshes. Can you confirm this? Is there a way to fill in the interior?

I would try filling it in, making it thicker, and running the code again and seeing the values are more reasonable.

[binarybottle]

do you mean that it has to be a closed mesh (like a beach ball) vs. a sheet, or that it needs to be a solid filled with triangles?

[binarybottle]

Arthur Mikhno:
A closed mesh or a solid, should give approx same results.

[binarybottle]

i start out with a closed mesh (hemisphere) and extract open patches (gyri, sulci). i will have to think about how to close it or thicken it. any suggestions?​

[satra]

close using white and pial surfaces.

[binarybottle]

do you know of a good way to close a mesh using two surfaces?

[satra]

just connect up the corresponding edge vertices of the patches. so every adjacent pair of edge vertices will have two triangular faces.

[binarybottle]

I have coded up a function called close_surfaces() to connect the corresponding boundary vertices of pial and gray-white surface patches. The zernike_moments_per_label() function now has the option to close each patch's surface and decimate the resulting mesh. Decimation does speed things up considerably, and the pre- and post-decimated zernike descriptors are similar. Unfortunately, the closed surfaces have values that are huge, just as before. One unfortunate aspect to connecting the surface patch boundaries is that the two surfaces are not parallel, so connecting the vertices leads to intersecting faces (see second figure).

[binarybottle]

Arthur Mikhno (8/27/2013):
The objects must be scaled to fit within a unit sphere first. I don't recall if the code you have does this or not.

You must normalize (scale and center) to a unit sphere before running ZK. To do this just shift the object to position 0,0,0 by subtracting the mean x,y,z values from each node. Then scale the object such that the max Euclidean distance between each node and origin is <=1.

[binarybottle]

i have added recentering and rescaling in zernike.py, and now things are looking more reasonable!
i'm even getting small values for open surface patches! perhaps i don't need to close them after all?
in fact, i'm even getting small values for a vtk file with two separate patches -- does this make sense?

these are the results for each of the example vtk files:
All are order=3

# Example 1: vtk_file = 'cube.vtk'
[0.0,
 1.5444366221695725e-21,
 0.0,
 2.081366518964347e-21,
 5.735003646768394e-05,
 2.433866250546253e-21]

# Example 2: vtk_file = 'test_one_surface.vtk'
[0.01566588675857814,
 0.012346130475603009,
 0.018993428582801408,
 0.022470635336483052,
 0.016625931229056885,
 0.014155674468859897]

# Example 3: vtk_file = 'test_two_surfaces.vtk'
[0.017618016083542545,
 0.014899667748084695,
 0.02071650549121894,
 0.025572906059619344,
 0.017558662051283647,
 0.014535574445816983]