3d skeletons using graphics hardware jonathan bilodeau chris niski
TRANSCRIPT
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
• 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
• Red dots indicate points that allowed a skeleton point in the center of this circle
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
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?