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A comprehensive framework for detection and characterization
of partial intrinsic symmetry over 3D shapes is
proposed. To identify prominent symmetric regions which overlap
in space and vary in form, the proposed framework is decoupled
into a Correspondence Space Voting (CSV) procedure followed
by a Transformation Space Mapping (TSM) procedure. In the
CSV procedure, significant symmetries are first detected by
identifying surface point pairs on the input shape that exhibit
local similarity in terms of their intrinsic geometry while simultaneously
maintaining an intrinsic distance structure at a global
level. To allow detection of potentially overlapping symmetric
shape regions, a global intrinsic distance-based voting scheme is
employed to ensure the inclusion of only those point pairs that
exhibit significant intrinsic symmetry. In the TSM procedure,
the Functional Map framework is employed to generate the final
map of symmetries between point pairs. The TSM procedure
ensures the retrieval of the underlying dense correspondence map
throughout the 3D shape that follows a particular symmetry. The
TSM procedure is also shown to result in the formulation of a
metric symmetry space where each point in the space represents
a specific symmetry transformation and the distance between
points represents the complexity between the corresponding
transformations. Experimental results show that the proposed
framework can successfully analyze complex 3D shapes that
possess rich symmetries.
A novel multi-criteria optimization framework for matching of partially visible shapes in multiple images using joint geometric graph embedding is proposed. The proposed framework achieves matching of partial shapes in images that exhibit extreme variations in scale, orientation, viewpoint and illumination and also instances of occlusion; conditions which render impractical the use of global contour-based descriptors or local pixel-level features for shape matching. The proposed technique is based on optimization of the embedding distances of geometric features obtained from the eigenspectrum of the joint image graph, coupled with regularization over values of the mean pixel intensity or histogram of oriented gradients. It is shown to obtain successfully the correspondences denoting partial shape similarities as well as correspondences between feature points in the images. A new benchmark dataset is proposed which contains disparate image pairs with extremely challenging variations in viewing conditions when compared to an existing dataset [18]. The proposed technique is shown to significantly outperform several state-of-the-art partial shape matching techniques on both datasets.