Total variation denoising in l1l^1 anisotropy

We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a naturally defined class of functions piecewise constant on rectangles (PCR). This class forms a strictly dense subset of the space of functions of bounded variation with an anisotropic norm. The main result shows that if the given noisy image is a PCR function, then solutions to both considered problems also have this property. For PCR data the problem of finding the solution is reduced to a finite algorithm. We discuss some implications of this result, for instance we use it to prove that continuity is preserved by both considered problems.Comment: 34 pages, 9 figure

Constructing phase diagrams for defects by correlated atomic-scale characterization

Phase transformations and crystallographic defects are two essential tools to drive innovations in materials. Bulk materials design via tuning chemical compositions has been systematized using phase diagrams. We show here that the same thermodynamic concept can be applied to understand the chemistry at defects. We present a combined experimental and modelling approach to scope and buildphase diagrams for defects. The discovery was enabled by triggering phase transformations of individual defects through local alloying, and sequentially imaging the structural and chemical changes using atomic-resolution scanning transmission electron microscopy. Byobserving atomic-scale phase transformations of a Mg grain boundary through Ga alloying, we exemplified the method to construct a grainboundary phase diagram using ab initio simulations and thermodynamic principles. The methodology enables a systematic development of defect phase diagrams to propel a new paradigm for materials designutilizing chemical complexity and phase transformations at defects

Polar space based shape averaging for star-shaped biological objects

In this paper, we propose an averaging method for expert segmentation proposals of microbial organisms, resulting in a smooth, naturally looking segmentation ground truth. The approach exploits a geometrical property of the majority of the organisms - star-shapedness - and is based on contour averaging in polar space. It is robust and computationally efficient, where robustness is due to the absence of tuneable parameters. Moreover, the algorithm preserves the uncertainty (in terms of the standard deviation) of the experts' opinion, which allows to introduce an uncertainty-aware metric for estimation of the segmentation quality. This metric emphasizes the influence of ground truth regions with low variance. We study the performance of the proposed averaging method on time-lapse microscopy data of Corynebacterium glutamicum and the uncertainty-aware metric on synthetic data

Non-local Means for Scanning Transmission Electron Microscopy Images and Poisson Noise based on Adaptive Periodic Similarity Search and Patch Regularization

High-Angle Annular Darkfield Scanning Transmission Electron Microscopy (HAADF-STEM) allows to take images at atomic scale with a contrast proportional to the atomic number. STEM acquires an image line-by-line, pixel-by-pixel leading to characteristic distortions. Furthermore, STEM images of beam sensitive materials have to be taken with short exposure times, leading to low contrast images with Poisson noise. In this paper, we propose an extension of Non-local Means (NLM) tailored to STEM images of crystalline structures. To find similar patches, we introduce an adaptive non-local search strategy that exploits the periodic structure of the crystal images. Furthermore, we extend the patch similarity measure to take into account the horizontal distortions typical for STEM images. Moreover, we discuss the Anscombe transform and the Poisson likelihood ratio to deal with Poisson noise. Finally, the resulting methods are compared to BM3D with Anscombe tranform and PURE-LET on simulated and real data.Vision, Modeling & Visualizatio

Deformable image registration with automatic non-correspondence detection

Image registration aims at establishing pointwise correspondences between given images. However, in many practical applications, no correspondences can be established in certain parts of the images. A typical example is the tumor resection area in pre- and post-operative medical images. In this paper, we introduce a novel variational framework that combines registration with an automatic detection of non-correspondence regions. The formulation of the proposed approach is simple but efficient, and compatible with a large class of image registration similarity measures and regularizers. The resulting minimization problem is solved numerically with a non-alternating gradient flow scheme. Furthermore, the method is validated on synthetic data as well as axial slices of pre-, post- and intra-operative MR T1 head scans