Edge-Based Shape Matching
To avoid potentially exponential cost of matching nondistinctive local fragments:
- Increase the fragments’ distinctiveness by upgrading to semilocal descriptors
- sparse sampling: Representing shape at a coarse scale or with sparse sampling can further reduce the search space
To avoid an expensive search over deformations:
- first extract a higher level representation of the essential shape structure and match this: e.g., transfers shapes into skeletons represented via a graph or tree structure, Shape representations are matched by finding the largest isomorphic subgraph/subtree
- suffers from instability of the derived representation
cannot capture small shape differences well since the skeleton representation compresses the shape variability
For shapes with small distortion, shape matching is easier and the difficulty of finding high quality point-to-point shape correspondence decreases: Similarity – euclidean distance between edge points, so rely on edge detection, a hard classification decision which is sensitive to noise and illumination changes.
- Chamfer matching
- Hausdorff-distance matching
- HoG represents shapes as gradient orientation histograms over regions. Matching is done via histogram comparison.
1) focusing on orientations rather than gradient magnitudes, which gives a degree of photometric invariance;
2) softening the edge correspondence via histogram matching and allowing each edge point to be added in multiple histogram bins.
Region-Based Shape Matching
To avoid the local ambiguities of edge matching, one can instead match regions. Region matching gives contour matching (for closed contours) with no need for explicit edge correspondence.
Edge: local feature, easy to get, but their locality makes comparing them sensitive to spatial shifts and shape variations
Regions: global feature, matching is more robust to local-shape distortions and occlusions, but they can have complex shapes which may be difficult to extract reliably and hard to represent or match precisely.
intermediate between region and edge matching
associates edges with regions by representing shapes as edge orientation histograms over regions, which efficiently combines the advantages of local edge representations and global region robustness.
drawback: an information loss method edge histograms sacrifice shape description accuracy.
Probabilistic index maps (PIM): direct each pixel to an image-dependent palette,
efficiently capture the common structures underlying multiple images despite large appearance changes caused by feature variations, e.g., color or illumination changes. Since training images are required to learn the class structure model, PIM is not suitable for comparing images by their shape structures directly.
Using Segmentations for Recognition