API Reference

Welcome to the official API reference for pyxu-diffops. This API documentation is intended to serve as a comprehensive guide to the library’s various modules, classes, functions, and interfaces. It provides detailed descriptions of each component’s role, relations, assumptions, and behavior.

To use this plugin, users can instantiate the class corresponding to the desired diffusion operator. Such classes rely on private modules implementing the building blocks composing each operator; only advanced users wanting to implement new operators should look into them. The code for such private modules is available on the repository but no compiled documentation is provided. All diffusion operators are daughter classes of the private base class _Diffusion.

Remark

Diffusion operators are implemented as differentiable functionals DiffFunc. However, they are atypical differentiable functionals. Indeed, the apply() method is not necessarily defined, in the case of implicitly defined functionals. The key method is grad(), necessary to perform gradient flow optimization. The apply() method raises a NotImplementedError unless the diffusion term is known to derive from a variational formulation.

The Pyxu-diffops plug-in implements the following diffusion operators.

Diffusion operators

pyxu_diffops.operator

MfiDiffusion(dim_shape[, extra_term, beta, ...])	Minimum Fisher Information (MFI) diffusion operator, featuring an inhomogeneous isotropic diffusion tensor.
PeronaMalikDiffusion(dim_shape[, beta, ...])	Perona-Malik diffusion operator, featuring an inhomogeneous isotropic diffusion tensor with Perona-Malik diffusivity.
TikhonovDiffusion(dim_shape[, sampling])	Tikhonov diffusion operator, featuring a homogeneous isotropic diffusion tensor with constant diffusivity.
TotalVariationDiffusion(dim_shape[, beta, ...])	Total variation (TV) diffusion operator, featuring an inhomogeneous isotropic diffusion tensor.
CurvaturePreservingDiffusionOp(dim_shape[, ...])	Curvature preserving diffusion operator [Tschumperle].
AnisEdgeEnhancingDiffusionOp(dim_shape[, ...])	Anisotropic edge-enhancing diffusion operator, featuring an inhomogeneous anisotropic diffusion tensor defined as in [Weickert].
AnisCoherenceEnhancingDiffusionOp(dim_shape)	Anisotropic coherence-enhancing diffusion operator, featuring an inhomogeneous anisotropic diffusion tensor defined as in [Weickert].
AnisDiffusionOp(dim_shape[, alpha, ...])	Anisotropic diffusion operator, featuring an inhomogeneous anisotropic diffusion tensor.