SYMMETRY DETECTION FROM GRAY-SCALE IMAGES:

Segmentation of shapes from gray level images is a difficult task mainly due to gaps or weak contrast edges arising from figure-ground blending, partial occlusion,  specularity highlights, etc, suggesting symmetry detection directly from gray level images.

Such an extraction, however, faces a number of difficulties as object symmetries are distorted due to :

• (i) gaps in the bounding contour of a shape due to figure-ground blending, weak contrast edges,highlights, noise, etc.;
• (ii) an introduction of parts and occluders, and
• (iii) spurious edge elements due to surface markings, texture, etc.

In analogy with Blums' grassfire, such symmetries from real images can be detected as the quench points of a wave propagation, or constant speed waves initiated at the contour segments extracted by low-level processes.

These quench points can be viewed as the shocks, or singularities of the waves carrying geometric descriptions about the contour segments.

In addition, labeling of shocks based on whether the colliding wavefronts carry true orientation information (regular vs. rarefaction waves) allows a division of shocks into 3 sets:

• Regular shocks are the partial shocks of partial contours as they remain invariant to the completion of the contour.
• Semi-degenerate and degenerate shocks depict potential parts and gaps.
• Finally, shocks altered due to spurious edges, occlusion, and gaps are recovered via a simulation of inter-penetrating waves generated at select shock groups which with the aid of the above shock labels leads to second and further generations of shocks.

Examples:

     1. Shocks From Images:

     2. Shape Decomposition:

     3. Grouping: