Digital cultural heritage imaging via osmosis filtering

In Cultural Heritage (CH) imaging, data acquired within different spectral regions are often used to inspect surface and sub-surface features. Due to the experimental setup, these images may suffer from intensity inhomogeneities, which may prevent conservators from distinguishing the physical properties of the object under restoration. Furthermore, in multi-modal imaging, the transfer of information between one modality to another is often used to integrate image contents. In this paper, we apply the image osmosis model proposed in [4, 10, 12] to solve correct these problems arising when diagnostic CH imaging techniques based on reflectance, emission and fluorescence mode in the optical and thermal range are used. For an efficient computation, we use stable operator splitting techniques to solve the discretised model. We test our methods on real artwork datasets: the thermal measurements of the mural painting “Monocromo” by Leonardo Da Vinci, the UV-VIS-IR imaging of an ancient Russian icon and the Archimedes Palimpsest dataset

Nonlinear spectral image fusion

In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and edge-preserving spectral TV decomposition allows to select frequencies of a certain image to transfer particular features, such as wrinkles in a face, from one image to another. We illustrate the effectiveness of the proposed approach in several numerical experiments, including a comparison to the competing techniques of Poisson image editing, linear osmosis, wavelet fusion and Laplacian pyramid fusion. We conclude that the proposed spectral TV image decomposition framework is a valuable tool for semi- and fully-automatic image editing and fusion

Patient-specific computational modeling of Cortical Spreading Depression via Diffusion Tensor Imaging

Cortical Spreading Depression (CSD), a depolarization wave originat- ing in the visual cortex and traveling towards the frontal lobe, is com- monly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in sup- porting or contrasting the propagation of CSD. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisa- tion in the grey matter. In this paper we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from Diffusion Tensor Imaging data.This work was supported by the Bizkaia Talent and European Commission through COFUND under the grant BRAhMS - Brain Aura Mathematical Sim- ulation (AYD-000-285), by the Basque Government through the BERC 2014- 2017 program, and by the Spanish Ministry of Economics and Competitiveness MINECO through the BCAM Severo Ochoa excellence accreditation SEV-2013- 0323 and the Spanish "Plan Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad" under Grant BELEMET - Brain ELEctro- METabolic modeling and numerical approximation (MTM2015-69992-R). JMC acknowledges financial support from Ikerbasque: The Basque Foundation for Science and Euskampus at UPV/EHU

Linear scale-spaces in image processing: drift-diffusion and connections to mathematical morphology

Auf Skalenräumen basierende Ideen sind aus dem heutigen Alltag nicht mehr wegzudenken. Wir beginnen mit einem auf der homogenen Diffusionsgleichung aufbauenden Skalenraum und verfolgen zwei Strategien zur Konstruktion neuer Skalenräume. Als erstes beweisen wir, dass der lineare Osmosefilter, welcher auf einer Drift-Diffusionsgleichung beruht, eine Reihe von wichtigen Skalenraumeigenschaften erfüllt. Der zusätzliche Driftterm ermöglicht einen großen Freiraum in der Modellierung und hat sich bereits als vielversprechend in der Bildverarbeitung etabliert. Allerdings sorgt er auch dafür, dass der stationäre Zustand nicht konstant ist, im Gegensatz zu bisher untersuchten Skalenräumen. Bei dem Beweis von Vereinfachungseigenschaften im Sinne von Lyapunov-Funktionalen führt dies zu einer Reihe von Problemen. Während der erste Teil der Arbeit einen neuen Skalenraum einführt, werden wir uns im zweiten Teil den beiden meist studierten Klassen von Skalenräumen widmen: den linearen shift-invarianten und den morphologischen Skalenräumen. Mithilfe der neu eingeführten Cramer-Fourier-Transformation zeigen wir, wie sich beide Klassen sowohl auf struktureller Ebene als auch auf der Ebene der Evolutionsgleichungen verbinden lassen. Dieses Resultat erweitert ein Ergebnis über die strukturelle Gleichheit des Gaußschen Skalenraumes mit seinem morphologischen Gegenstück. Weiterhin beweisen wir, dass die entscheidenden Eigenschaften der bisher verwendeten Cramer-Transformation erhalten bleiben.Scale-space ideas are ubiquitous and indispensable for modern image analysis. Starting from a linear scale-space based on a homogeneous diffusion equation we pursue two strategies to create new scale-spaces. First, we rigorously prove that the linear osmosis filtering, which is based on a drift-diffusion equation, fulfils several important scale-space properties. The additional drift term introduces a modelling choice that has proved valuable in the past for image processing applications. However, in contrast to previously analysed scale-spaces, the steady state is non-constant. This leads to a number of challenges when aiming for image simplification properties in terms of Lyapunov functionals. Whereas we analyse a new scale-space in the first part, the second part picks up the two most studied classes of scale-spaces: linear shift-invariant and morphological scale-spaces. By introducing the Cramer-Fourier transform, we can connect these classes both on a structural level and on the level of evolution equations. This extends a structural similarity result between the Gaussian scale-space and its morphological counterpart. While the decisive properties of the previously used Cramer transform are preserved, our new transformation has many benefits in an image processing context. We use the Cramer-Fourier transform to construct not yet discovered scale-spaces

Brownian motion near an elastic cell membrane: A theoretical study

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.Comment: 16 pages, 7 figures and 161 references. Contributed chapter to the flowing matter boo