Abstract
In this article, we present an original unified framework for analyzing, describing, and encoding 3D facial surfaces. This framework allows the derivation of topologically ordered structures from triangular mesh surfaces, addressing thus the lack of ordered structure in such a modality. After describing the foundations of the framework and highlighting its advantages with respect to close representations, we show its adaptability to a variety of facial mesh surface processing tasks which includes mesh regularity assessment, facial surface cropping, facial surface compression, and facial surface alignment. In addition, it can be used for the extraction of a rich variety of local and global face descriptors. We validate this framework by testing it with raw 3D facial mesh surfaces.
Highlights
3D face image modality has been receiving increasing attention in applications related to people identification
Contributions and structure In this article, we propose a topological framework for encoding a 3D facial mesh surface
We propose two methods, which we call face grid alignment (FGA) and Ordered Concentric Discrete Contours (OCDC) alignment (OCDCA)
Summary
The algorithm ConcentricRings contains one loop having NumberOfRings iterations. The number of iterations in the first loop (For each pair (fouti, fout(i+1)%n)) is equal to the number of Fout facets in a ring, whereas in the second loop (While(gf = f 2)), located within the procedure Bridge, it is equal to the number of Fgap facets between each pair of consecutive Fout facets. The number of instructions in GetRing is a linear function of the number of facets in the ith ring. Let call ni this number, the number of instructions at each iteration of ConcentricRings can be expressed by ani + b, where a and b are constants. The number of instructions in ConcentricRings can be expressed by Number i=1
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