A versatile generic framework for parent grain reconstruction from fully or partially transformed child microstructures has been integrated into the open-source crystallographic toolbox MTEX. The framework extends traditional parent grain reconstruction, phase transformation and variant analysis to all parent–child crystal symmetry combinations. The inherent versatility of the universally applicable parent grain reconstruction methods and the ability to conduct in-depth variant analysis are showcased via example workflows that can be programmatically modified by users to suit their specific applications. This is highlighted by three applications, namely α′-to-γ reconstruction in a lath martensitic steel, α-to-β reconstruction in a Ti alloy, and a two-step reconstruction from α′ to ɛ to γ in a twinning and transformation-induced plasticity steel. Advanced orientation relationship discovery and analysis options, including variant analysis, are demonstrated via the add-on function library ORTools.

The paper addresses the generalization of the half-quadratic minimization method for the restoration of images having values in a complete, connected Riemannian manifold. We recall the half-quadratic minimization method using the notation of the $c$-transform and adapt the algorithm to our special variational setting. We prove the convergence of the method for Hadamard spaces. Extensive numerical examples for images with values on spheres, in the rotation group $SO(3)$, and in the manifold of positive definite matrices demonstrate the excellent performance of the algorithm. In particular, the method with $SO(3)$-valued data shows promising results for the restoration of images obtained from Electron Backscattered Diffraction which are of interest in material science.