On a Linear Gromov-Wasserstein Distance.

Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal transport (LOT), was successfully used in practice, there does not exist a notion of linear Gromov-Wasserstein distances so far. In this paper, we propose a definition of linear Gromov-Wasserstein distances.

Lagrangian Motion Magnification with Landmark-Prior and Sparse PCA for Facial Microexpressions and Micromovements.

Video motion magnification methods are motion visualization techniques that aim to magnify subtle and imper-ceptibly small motions in videos. They fall into two main groups where Eulerian methods work on the pixel grid with implicit motion information and Lagrangian methods use explicitly estimated motion and modify point trajectories. The motion in high framerate videos of faces can contain a wide variety of information that ranges from microexpressions over pulse or respiratory rate to cues on speech and affective state.

Robust PCA via Regularized Reaper with a Matrix-Free Proximal Algorithm.

Principal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called reaper, aims to find the principal components by solving a convex optimization problem. Usually the number of principal components must be determined in advance and the minimization is performed over symmetric positive semi-definite matrices having the size of the data, although the number of principal components is substantially smaller.

Spectral imaging based on 2D diffraction patterns and a regularization model.

We present a variational approach to reconstruct a multispectral image from an array of diffraction patterns captured in one monochromatic image. The mathematical model relies on the superposition of wavelength dependent calibration diffraction patterns and a spectral regularization with second order differences. The necessary preprocessing steps which influence the mathematical setting are discussed in detail.

Fast ordering algorithm for exact histogram specification.

This paper provides a fast algorithm to order in a meaningful, strict way the integer gray values in digital (quantized) images. It can be used in any exact histogram specification-based application. Our algorithm relies on the ordering procedure based on the specialized variational approach.

Fast Hue and Range Preserving Histogram: Specification: Theory and New Algorithms for Color Image Enhancement.

Color image enhancement is a complex and challenging task in digital imaging with abundant applications. Preserving the hue of the input image is crucial in a wide range of situations. We propose simple image enhancement algorithms which conserve the hue and preserve the range (gamut) of the R, G, B channels in an optimal way.

Nonlocal two dimensional denoising of frequency specific chirp evoked ABR single trials.

Recently, we have shown that denoising evoked potential (EP) images is possible using two dimensional diffusion filtering methods. This restoration allows for an integration of regularities over multiple stimulations into the denoising process. In the present work we propose the nonlocal means (NLM) method for EP image denoising.

Exploiting the self-similarity in ERP images by nonlocal means for single-trial denoising.

Event related potentials (ERPs) represent a noninvasive and widely available means to analyze neural correlates of sensory and cognitive processing. Recent developments in neural and cognitive engineering proposed completely new application fields of this well-established measurement technique when using an advanced single-trial processing. We have recently shown that 2-D diffusion filtering methods from image processing can be used for the denoising of ERP single-trials in matrix representations, also called ERP images.

Diffusion tensors for processing sheared and rotated rectangles.

Image restoration and simplification methods that respect important features such as edges play a fundamental role in digital image processing. However, known edge-preserving methods like common nonlinear diffusion methods tend to round vertices for large diffusion times. In this paper, we adapt the diffusion tensor for anisotropic diffusion to avoid this effects in images containing rotated and sheared rectangles, respectively.