Transcript Jonathan and Krzys

3D Skeletons Using Graphics
Hardware
Jonathan Bilodeau
Chris Niski
Outline
• Background
• Goal
• Method
– Find points that lie on the graph
– Extract vertices/edges from points
• Results
• Problems
• Future Work
Background
• Two general techniques for computing shape
descriptors
– Statistical shape descriptors
– Structural shape descriptors
• Statistical shape descriptors work well when
comparing objects that cannot be deformed
• Also need to potentially store large amounts
of data
Background
• Structural shape descriptors are simple
geometrical descriptions of a more complex
model
• Generally the structural shape descriptor
takes the form of a skeleton of the mesh
• Skeleton representation is efficient if properly
computed as it takes up little space, and can
compare deformed objects, as well as
perform partial matching
Computing the skeleton
• In 2D the traditional method of
computing the skeleton is to use the
Euclidian Distance Transform
– Basically find the center line of a 2d
contour
– Another method is to use waves
propagating inward from the surface
Surface
EDT
• Example borrowed from Mishas class notes
• The EDT is expensive to compute
– On2m for 2D
– On3m for 3D
• No good/fast 3D equivalent
– Usually mesh thinning is used to calculate
the skeleton
Goal
• Using graphics hardware, create a 3D graph
of a model
–
–
–
–
Slice the model along each coordinate axis
Find 2D skeleton with GH, merge them
Find intersection
Extract graph
• Capture 3d axis information
• Intersection will remove random noise
• Simple transition to a graph
– only vertices and edges
– No sheets
Method
• Voxelize the model
• Consider each slice of the volume along
each axis
– Gives you a 2D contour
• Compute the skeleton of each 2D
contour
Method – Finding 2D skeleton
• Using Graphics
hardware
– For each point on the
contour draw a code
centered on the
point, pointing at the
viewer.
– Read back the depth
buffer
– Analogous to a
distance transform
Method – Finding 2D skeleton
• Look for
discontinuities in the
EDT
– Scan columns/rows
looking for points
where both
neighbors are
smaller
– Every point that
passes is marked
true
Method
• Output is a 2D skeleton
• Merge the 2D skeletons into a volume
again
• Intersect each volume
– One from each axis
Method – Noise
• Noise around the
perimeter
Method – Noise
• Red dots
indicate points
that allowed a
skeleton point in
the center of
this circle
Method – Noise Removal
• Angle between
blue lines is
small
• Remove points
that have a
small angle
Method – Noise Removal
• Keep points
above 90
degrees
• D < Sqrt(2)*R
Method
• Once the EDT of the mesh is calculated
we need to fit a skeleton to the
resulting points
• The EDT voxel grid is not necessarily
connected, ie. Voxels may not have
neighbours
Fitting Skeleton
• Start by assigning an edge to each point that
has several neighbours
• Begin merging the edges based on several
criteria
– Distance between the two edges
– Length of the edges
– The angle between the two edges
• Stop merging when no suitable candidates
are present
Fitting Skeleton
• We also discard some of the edges
– If they are short and do not have an edge
to merge with
– Not attached to the rest of the graph
Results
• We can extract a voxel grid containing
the mesh skeleton
• Filter the grid to remove some of the
noise
• Fit a skeleton onto the grid to
compactly represent the grid points
Sample results
Problems - Voxelation
• Still can’t remove
all the noise
– Have to be
conservative with
the noise test or
else you throw
out large chunks
of the valid
skeleton
Problems - Orientation
• Objects that aren’t axis aligned don’t
work.
• Results in sheets
– Traditional 3D MA has sheets
– Contradicts one of our goals
Problems
• General problems with skeleton based
approach:
– The skeleton is not very descriptive
– Can be very susceptible to noise
– If connectivity changes after deformation,
comparison becomes very difficult
– Hard to capture just the right amount of
detail
• Problems with our approach:
– Our version of the EDT still creates noise
around the surface of the mesh
– Noise on the surface of the mesh creates
false edges which can merge with good
edges
Future Work
• Try other methods for finding 2D
skeleton that are less prone to noise
– Before voxelation?
– High resolution 2D images that get down
sampled?
• Can’t keep high resolution for 3D
• What affect would aliasing have?
Future Work
• Orientation problem
– Instead of using the coordinate axis, find
the EGI with a relatively small number of
bins.
• Flip any normals with –z components
– Find axis volume relative to the dominant
normals
• Problem lining up volumes with arbitrary
rotations