Numerical Geometry of Images: Theory, Algorithms, and Applications
Numerical Geometry of Images: Theory, Algorithms, and Applications
Handbook of Mathematical Models in Computer Vision
Handbook of Mathematical Models in Computer Vision
Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
A Metric Approach to nD Images Edge Detection with Clifford Algebras
Journal of Mathematical Imaging and Vision
A general framework for low level vision
IEEE Transactions on Image Processing
A Class of Generalized Laplacians on Vector Bundles Devoted to Multi-Channel Image Processing
Journal of Mathematical Imaging and Vision
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We propose a new mathematical model for color images taking into account that color pixels change under transformation of the light source. For this, we deal with (ρ,G)-equivariant functions on principal bundles, where ρ is a representation of a Lie group G on the color space RGB. We present an application to image regularization, by minimization of the Polyakov action associated to the graph of such functions. We test the groups ${\rm I\!R}^{+\ast}$ , DC(3) of contractions and dilatations of ${\rm I\!R}^3$ and SO(3) with their natural matrix representations, as well as ${\rm I\!R}^{+\ast}$ with its trivial representation. We show that the regularization has denoising properties if the representation is unitary and segmentation properties otherwise.