Sunday, July 09, 2006
Shape Completion Experiments (part 2)
More text from an email:
-------------------------------------------
i just finished running some more shape completion experiments with single
partial contours and unknown correspondences. results were good for partial
contours very similar to the mean shape, as the algorithm tries to
find correspondences from the partial contour to the mean shape. results
for partial contours sufficiently different from the mean shape were not
good.
it seems to me that what we have here is a classic hidden variable problem:
we assume the completed shape should be a mix of principle components in our
shape model (i.e. the completed shape lies in eigenspace), and the
difficulty in finding correspondences is that we don't know a priori the
mixing coefficients (principle component coordinates) of the completed
shape. if we knew the mixing coefficients, we could use the resulting shape
(rather than the mean shape, as we are currently doing) to find
correspondences to the partial contour.
i don't know if it's worth the time to write this out as an EM problem, but
i just thought i'd point it out that the problem exists. for now, we could
try a sampling technique, for example:
1) sample 50 full shapes from the tangent space shape distribution.
2) for each sample, find the best correspondences to the partial shape.
3) use these correspondences and the sample full shape to sample several
orientations and scales.
4) complete the shapes for each (full shape sample, orientation, scale)
combination, and take the best one.
-------------------------------------------
Here is the data I was referring to; once again we use the occluded tools contour:
We again hand-segment out the following two partial contours:
For the partial contour on the right, results were almost identical (even slightly improved) to the previous experiment where correspondences from the partial shape to the mean shape were estimated by hand. Here is the best completion (in green) shown against the mean shape (in blue):
For the partial contour on the left, however, the situation was much worse. As is explained in the text from the email above, this is likely due to the fact that the partial contour was generated from a full contour which is significantly different from the mean shape, so finding correspondences to the mean shape is the wrong thing to do. Here is the best completion (the rest were just as bad):
-------------------------------------------
i just finished running some more shape completion experiments with single
partial contours and unknown correspondences. results were good for partial
contours very similar to the mean shape, as the algorithm tries to
find correspondences from the partial contour to the mean shape. results
for partial contours sufficiently different from the mean shape were not
good.
it seems to me that what we have here is a classic hidden variable problem:
we assume the completed shape should be a mix of principle components in our
shape model (i.e. the completed shape lies in eigenspace), and the
difficulty in finding correspondences is that we don't know a priori the
mixing coefficients (principle component coordinates) of the completed
shape. if we knew the mixing coefficients, we could use the resulting shape
(rather than the mean shape, as we are currently doing) to find
correspondences to the partial contour.
i don't know if it's worth the time to write this out as an EM problem, but
i just thought i'd point it out that the problem exists. for now, we could
try a sampling technique, for example:
1) sample 50 full shapes from the tangent space shape distribution.
2) for each sample, find the best correspondences to the partial shape.
3) use these correspondences and the sample full shape to sample several
orientations and scales.
4) complete the shapes for each (full shape sample, orientation, scale)
combination, and take the best one.
-------------------------------------------
Here is the data I was referring to; once again we use the occluded tools contour:
We again hand-segment out the following two partial contours:
For the partial contour on the right, results were almost identical (even slightly improved) to the previous experiment where correspondences from the partial shape to the mean shape were estimated by hand. Here is the best completion (in green) shown against the mean shape (in blue):
For the partial contour on the left, however, the situation was much worse. As is explained in the text from the email above, this is likely due to the fact that the partial contour was generated from a full contour which is significantly different from the mean shape, so finding correspondences to the mean shape is the wrong thing to do. Here is the best completion (the rest were just as bad):
# posted by Jared @ 12:05 AM 
