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Orthonormal vector sets regularization with PDE's and applications
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DOI：10.1023/A:1020870207168.png)
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摘要
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We are interested in regularizing fields of orthonormal vector sets, using constraint-preserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vectors or orthogonal matrices (among other examples). We first develop a general variational framework that solves this regularization problem, thanks to a constrained minimization of phi-functionals. This leads to a set of coupled vector-valued PDE's preserving the orthonormal constraints. Then, we focus on particular applications of this general framework, including the restoration of noisy direction fields, noisy chromaticity color images, estimated camera motions and DT-MRI (Diffusion Tensor MRI) datasets.
Keyword:
partial differential equations (PDE)
constrained vector-valued regularization
orientation features
anisotropic diffusion
orthogonal matrices
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