The Nonlinear Statistics of High-Contrast Patches in Natural Images

Recently, there has been a great deal of interest in modeling the non-Gaussian structures of natural images. However, despite the many advances in the direction of sparse coding and multi-resolution analysis, the full probability distribution of pixels values in a neighborhood has not yet been described. In this study, we explore the space of data points representing the values of 3 × 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely “sparse” with the majority of the data points concentrated in clusters and non-linear low-dimensional manifolds. Furthermore, a detailed study of probability densities allows us to systematically distinguish between images of different modalities (optical versus range), which otherwise display similar marginal distributions. Our work indicates the importance of studying the full probability distribution of natural images, not just marginals, and the need to understand the intrinsic dimensionality and nature of the data. We believe that object-like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space. Our study of natural image statistics accounts for local geometries (such as edges) in natural scenes, but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases.Mathematic

Automatic segmentation of overlapping cervical smear cells based on local distinctive features and guided shape deformation

Automated segmentation of cells from cervical smears poses great challenge to biomedical image analysis because of the noisy and complex background, poor cytoplasmic contrast and the presence of fuzzy and overlapping cells. In this paper, we propose an automated segmentation method for the nucleus and cytoplasm in a cluster of cervical cells based on distinctive local features and guided sparse shape deformation. Our proposed approach is performed in two stages: segmentation of nuclei and cellular clusters, and segmentation of overlapping cytoplasm. In the rst stage, a set of local discriminative shape and appearance cues of image superpixels is incorporated and classi ed by the Support Vector Machine (SVM) to segment the image into nuclei, cellular clusters, and background. In the second stage, a robust shape deformation framework is proposed, based on Sparse Coding (SC) theory and guided by representative shape features, to construct the cytoplasmic shape of each overlapping cell. Then, the obtained shape is re ned by the Distance Regularized Level Set Evolution (DRLSE) model. We evaluated our approach using the ISBI 2014 challenge dataset, which has 135 synthetic cell images for a total of 810 cells. Our results show that our approach outperformed existing approaches in segmenting overlapping cells and obtaining accurate nuclear boundaries. Keywords: overlapping cervical smear cells, feature extraction, sparse coding, shape deformation, distance regularized level set

Centralized Cell-Free Massive MIMO with Low-Resolution Fronthaul

The increasingly new data-hungry applications in our digital society now might no longer be handled efficiently by the current cellular networks. Cell-free massive MIMO network comes to resolve the traditional way of deploying wireless networks by blurring the cell boundaries. The network comprises a large number of access points (APs) which connect the users to a central processing unit (CPU) via fronthauls for coherent transmission and reception. It is expected that this network can provide a uniformly high data rate per user and per unit area. In this thesis, we study a centralized approach to cell-free massive MIMO that can further exploit its potential with considering a practical issue of limited-capacity fronthauls. We develop different schemes as well as strategies that make the centralized approach feasible. Thereby, we propose the use of low-resolution fronthauls and analyse its performance by making use of Bussgang theorem. The first part of this thesis considers a cell-free network with single-antenna APs, where a coarse scalar uniform quantizer is devised as an interface to the fronthauls. In the second part of this thesis, we extend the network to the case of multi-antenna APs, where two different processing schemes at the APs are studied: individual processing and joint processing. For each part, two strategies for acquiring the channel state information (CSI) under low-resolution fronthaul constraint are developed: estimate-and-quantize (EQ) and quantize-and-estimate (QE). We analyse the performance of both strategies and take them into account for deriving the achievable rate of the systems. Moreover, the scalability of the centralized approach is also discussed in terms of fronthaul load and AP processing. In the last part, we propose the use of a lattice vector quantizer at multi-antenna APs for the high-mobility and high-density scenario, in which two procedures for constructing the lattice codebook are developed

The stellar halos of ETGs in the IllustrisTNG simulations: the photometric and kinematic diversity of galaxies at large radii

We characterize the photometric and kinematic properties of simulated early-type galaxy (ETG) stellar halos, and compare them to observations. We select a sample of ~1200 ETGs in the TNG100 and TNG50 simulations, spanning a stellar mass range of $10^{10.3}-10^{12}M_{\odot}$ and within the range of (g-r) colour and lambda-ellipticity diagram populated by observed ETGs. We determine photometric parameters, intrinsic shapes, and kinematic observables in their extended stellar halos. We study the variation in kinematics from center to halo and connect it to a change in the intrinsic shape of the galaxies. We find that the simulated galaxy sample reproduces the diversity of kinematic properties observed in ETG halos. Simulated fast rotators (FRs) divide almost evenly in one third having flat lambda profiles and high halo rotational support, a third with gently decreasing profiles, and another third with low halo rotation. Slow rotators (SRs) tend to have increased rotation in the outskirts, with half of them exceeding lambda=0.2. For $M_{*}>10^{11.5}M_{\odot}$ halo rotation is unimportant. A similar variety of properties is found for the stellar halo intrinsic shapes. Rotational support and shape are deeply related: the kinematic transition to lower rotational support is accompanied by a change towards rounder intrinsic shape. Triaxiality in the halos of FRs increases outwards and with stellar mass. Simulated SRs have relatively constant triaxiality profiles. Simulated stellar halos show a large variety of structural properties, with quantitative but no clear qualitative differences between FRs and SRs. At the same stellar mass, stellar halo properties show a gradual transition and significant overlap between the two families, despite the clear bimodality in the central regions. This is in agreement with observations of extended photometry and kinematics. [abridged]Comment: accepted for publication in A&A, 25 pages, 22 figure

Entropie‐dominierte Selbstorganisationsprozesse birnenförmiger Teilchensysteme

The ambition to recreate highly complex and functional nanostructures found in living organisms marks one of the pillars of today‘s research in bio- and soft matter physics. Here, self-assembly has evolved into a prominent strategy in nanostructure formation and has proven to be a useful tool for many complex structures. However, it is still a challenge to design and realise particle properties such that they self-organise into a desired target configuration. One of the key design parameters is the shape of the constituent particles. This thesis focuses in particular on the shape sensitivity of liquid crystal phases by addressing the entropically driven colloidal self-assembly of tapered ellipsoids, reminiscent of „pear-shaped“ particles. Therefore, we analyse the formation of the gyroid and of the accompanying bilayer architecture, reported earlier in the so-called pear hard Gaussian overlap (PHGO) approximation, by applying various geometrical tools like Set-Voronoi tessellation and clustering algorithms. Using computational simulations, we also indicate a method to stabilise other bicontinuous structures like the diamond phase. Moreover, we investigate both computationally and theoretically(density functional theory) the influence of minor variations in shape on different pearshaped particle systems, including the stability of the PHGO gyroid phase. We show that the formation of the gyroid is due to small non-additive properties of the PHGO potential. This phase does not form in pears with a „true“ hard pear-shaped potential. Overall our results allow for a better general understanding of necessity and sufficiency of particle shape in regards to colloidal self-assembly processes. Furthermore, the pear-shaped particle system sheds light on a unique collective mechanism to generate bicontinuous phases. It suggests a new alternative pathway which might help us to solve still unknown characteristics and properties of naturally occurring gyroid-like nano- and microstructures.Ein wichtiger Bestandteil der heutigen Forschung in Bio- und Soft Matter Physik besteht daraus, Technologien zu entwickeln, um hoch komplexe und funktionelle Strukturen, die uns aus der Natur bekannt sind, nachzubilden. Hinsichtlich dessen ist vor allem die Methode der Selbstorganisation von Mikro- und Nanoteilchen hervorzuheben, durch die eine Vielzahl verschiedener Strukturen erzeugt werden konnten. Jedoch stehen wir bei diesem Verfahren noch immer vor der Herausforderung, Teilchen mit bestimmten Eigenschaften zu entwerfen, welche die spontane Anordnung der Teilchen in eine gewünschte Struktur bewirken. Einer der wichtigsten Designparameter ist dabei die Form der Bausteinteilchen. In dieser Dissertation konzentrieren wir uns besonders auf die Anfälligkeit von Flüssigkristallphasen bezüglich kleiner Änderungen der Teilchenform und nutzen dabei das Beispiel der Selbstorganisation von Entropie-dominierter Kolloide, die dem Umriss nach verjüngten Ellipsoiden oder "Birnen" ähneln. Mit Hilfe von geometrischen Werkzeugen wie z.B. Set-Voronoi Tessellation oder Cluster-Algorithmen analysieren wir insbesondere die Entstehung der Gyroidphase und der dazugehörigen Bilagenformation, welche bereits in Systemen von harten Birnen, die durch das pear hard Gaussian overlap (PHGO) Potential angenähert werden, entdeckt wurden. Des Weiteren zeigen wir durch Computersimulationen eine Strategie auf, um andere bikontinuierliche Strukturen, wie die Diamentenphase, zu stabilisieren. Schlussendlich betrachten wir sowohl rechnerisch (durch Simulationen) als auch theoretisch (durch Dichtefunktionaltheorie) die Auswirkungen kleiner Abweichungen der Teilchenform auf das Verhalten des kolloiden, birnenförmigen Teilchensystems, inklusive der Stabilität der PHGO Gyroidphase. Wir zeigen, dass die Entstehung des Gyroids auf kleinen nicht-additiven Eigenschaften des PHGO Birnenmodells beruhen. In ''echten'' harten Teilchensystemen entwickelt sich diese Struktur nicht. Insgesamt ermöglichen unsere Ergebnisse einen besseren Einblick auf das Konzept von notwendiger und hinreichender Teilchenform in Selbstorganistationsprozessen. Die birnenförmigen Teilchensysteme geben außerdem Aufschluss über einen ungewöhnlichen, kollektiven Mechanismus, um bikontinuierliche Phasen zu erzeugen. Dies deutet auf einen neuen, alternativen Konstruktionsweg hin, der uns möglicherweise hilft, noch unbekannte Eigenschaften natürlich vorkommender, gyroidähnlicher Nano- und Mikrostrukturen zu erklären