Symmetry of Occluded Shapes

Here we address a problem which is commonly encountered in microscopy studies of particulate materials Given a collection of similar objects, such that the individual shapes occlude each other, how can the symmetry of these objects be extracted using methods of automated image analysis. The method we apply to solve the problem is to evaluate the symmetry of the occluded shapes, locate the center of symmetry, and reconstruct the symmetric shape most similar to the unoccluded original. 

The process of reconstructing the occluded shape can be improved by altering the method of evaluating the symmetry of a set of points. As described in Section III the symmetry of a set of points is evaluated by folding, averaging, and unfolding about the centroid of the points. We alter the method as follows  

The folding and unfolding (steps 1 and 3) will be performed about the center of selection rather than about the centroid of the points. 

This method improves both the shape and the localization of the reconstruction. 

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The symmetry of occluded shapes, such that appear in microscopy studies of materials. 

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