matthijs van eede university of toronto august 22nd, 2006
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Matthijs van Eede University of Toronto August 22nd, 2006 Joint work with Diego Macrini, Alex Telea, Cristian Sminchisescu, and Sven Dickinson. - PowerPoint PPT PresentationTRANSCRIPT
Matthijs van EedeUniversity of Toronto
August 22nd, 2006
Joint work with Diego Macrini, Alex Telea, Cristian Sminchisescu, and Sven Dickinson
The skeleton of a shape yields a symmetry-based parts decomposition (e.g., a shock graph) which can support effective object indexing and recognition, e.g., Siddiqi et al. (1999), Sebastian et al. (2004).
But, they suffer from two forms of instability…
Ligature branch
Ligature segment
Blum (1973)
• “Smooth” these structural instabilities while retaining the object’s salient shape structure.
• Two exemplar shapes drawn from the same category should therefore yield two graphs with the same structure.
• Prune skeletal branches that don’t contribute to the salient shape structure of the object.
• Simpler graphs with fewer unstable nodes lead to more efficient and more effective indexing and matching.
• But how do we measure branch saliency and when do we stop pruning?
Reconstructionerror
Saliency favors elongated and thick parts
External branches rank-ordered by saliency:
1
2
3
4
5
6
7
8
910
11
12
Strong SmoothingMild SmoothingNo Smoothing
The cost of external branch smoothing: increased reconstruction error
Intuitively: create similar topologies in the skeletons by pruning short (low saliency) ligature
segments and branches
Ligature branch
Ligature segment
Fit piecewise linear skeleton fragments subject to endpoint and tangent constraints
No Smoothing
Strong SmoothingMild Smoothing
The cost of internal branch smoothing: altering the shape’s appearance
• Fact the medial axis transform of a shape is unique; skeleton changes introduce reconstruction error
• Goal minimize a cost function that promotes simpler skeletons with low reconstruction error
# branches Reconstruction error
p
spR(sp)
1. Rank-order external branches by saliency2. Iteratively prune low-saliency external
branches until cost function is minimized3. For internal branches, identify the
ligature branches as candidates for pruning, and rank-order them by saliency
4. Iteratively prune low-saliency candidate internal branches until cost function is minimized
Three hand shapes and their skeletons using no simplifications
Three hand shapes and their skeletons using both externalas well as internal simplifications
Notice the isomorphic graph structure
• Shock graphs are computed for 15 views of 8 three dimensional CAD models. A total of 120 shapes in the database.
• Each object view is removed from the database and used as a query
• Successful object recognition best ranked view belongs to the same object as query view
• Successful pose estimation neighbouring view of query is among top ranked views
• Noise is simulated by adding random “bumps” and “notches” to the query.
Results when using simplifications
- Object recognition performance increased up to 16%- Pose estimation performance increased up to 20%- (r5) = having a radius of 5 pixels
Results without usingsimplifications
• Skeletal descriptions of a shape offer a powerful shape representation for object recognition, yet their structural instability has long been an obstacle to their widespread use.
• Our structural simplification framework isolates this instability at both external and internal branches, and removes non-salient branches.
• The removal of internal branches requires a proper smoothing of neighboring branches so that the resulting skeleton is a MAT and reconstruction error is minimized.
• Results on a shock graph recognition experiment indicate a significant improvement in recognition and pose estimation performance when both query and database are structurally simplified prior to recognition.