Disconnected Skeleton: Shape at its Absolute Scale

We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale. Our motivation is to rely on the stable properties of the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of traditional connected skeletons, and the matching process gives quite successful results on a diverse database of 2D shapes. An important difference of our approach from the conventional use of the skeleton is that we replace the local coordinate frame with a global Euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations. As a result, we can produce descriptions that are sensitive to any combination of changes in scale, position, orientation and articulation, as well as invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV: Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape Recognition. Masters thesis, Department of Computer Engineering, Middle East Technical University, May 200

Високошвидкісний метод класифікації зображень

В роботі представлені методи для розпізнавання об’єктів на основі геометричної відповідності розподілів точок, що належать об’єкту в геометричних фігурах, які окреслюють об’єкт. Метод працює через розбивання області знаходження об’єкта на частини, та обробку статистичної інформації, яку містять ці частини.В работе представлены методы для распознавания объектов на основе геометрического соответствия делений точек, которые принадлежат объекту в геометрических фигурах, которые очерчивают объект. Метод работает через разбивание области нахождения объекта на части, и обработку статистической информации, которую содержат эти части.In this work methods for objects recognition on the basis of geometrical accordance of points’ distribution, which belong to the object in geometrical figures outlining the object, are presented. Methods work through dividing area of object’s layout to pieces, and statistical information processing that is aggregated using these parts

Hunting French Ducks in a Noisy Environment

We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations, consisting of alternating large- and small-amplitude oscillations. We quantify the effect of noise and obtain critical noise intensities above which the small-amplitude oscillations become hidden by fluctuations. Furthermore we prove that the noise can cause sample paths to jump away from so-called canard solutions with high probability before deterministic orbits do. This early-jump mechanism can drastically influence the local and global dynamics of the system by changing the mixed-mode patterns.Comment: 60 pages, 9 figure

Statistical mechanics of non equilibrium matter: from minimal models to morphogen gradients

Living systems are by definition far from thermodynamic equilibrium, a condition that can be maintained only at the cost of a continuous injection of energy at the microscale, e.g. via cellular metabolic processes, and dissipation into the surrounding environment. The absence of thermodynamic equilibrium, formalised in the breaking of the global detailed balance condition, allows for a wealth of exotic and often counterintuitive phenomena. Our understanding of the capabilities and limitations of living matter has been greatly informed by thermodynamic approaches, which have to be generalised with respect to their traditional counterparts in order to deal with systems subject to strong random fluctuations. The resulting toolkit of stochastic thermodynamics, in particular the concept of entropy production, gives us a quantitative handle on the degree of "non-equilibriumness" of such stochastic processes. Recently, stochastic thermodynamics has benefitted from cross-contamination with the field-theoretic literature and the techniques developed in the latter for the study of collective behaviour have opened the doors to the thermodynamic characterisation of increasingly complex systems. Starting from minimal mathematical models of single active particles and moving up across scales to the level of morphogenetic processes in real organisms (in particular, the formation of morphogen gradients), this thesis contributes to laying the foundations for a bridge between physical understanding and biological insight. While the focus is here on generic mechanisms and on the development of theoretical tools, the applicability to specific experimental scenarios will be pointed out where relevant.Open Acces

A Computational Model of the Short-Cut Rule for 2D Shape Decomposition

We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible cuts. We propose and implement a computational model for the short-cut rule and apply it to the problem of shape decomposition. The model we proposed generates a set of cut hypotheses passing through the points on the silhouette which represent the negative minima of curvature. We then show that most part-cut hypotheses can be eliminated by analysis of local properties of each. Finally, the remaining hypotheses are evaluated in ascending length order, which guarantees that of any pair of conflicting cuts only the shortest will be accepted. We demonstrate that, compared with state-of-the-art shape decomposition methods, the proposed approach achieves decomposition results which better correspond to human intuition as revealed in psychological experiments.Comment: 11 page

Inference on Riemannian Manifolds: Regression and Stochastic Differential Equations

Statistical inference for manifolds attracts much attention because of its power of working with more general forms of data or geometric objects. We study regression and stochastic differential equations on manifolds from the intrinsic point of view. Firstly, we are able to provide alternative parametrizations for data that lie on Lie group in the problem of fitting a regression model, by mapping this space intrinsically onto its Lie algebra, while we explore the behaviour of fitted values when this base point is chosen differently. Due to the nature of our data in the application of soft tissue artefacts, we employ two correlation structures, namely Matern and quasi-periodic correlation functions when using the generalized least squares, and show that some patterns of the residuals are removed. Secondly, we construct a generalization of the Ornstein-Uhlenbeck process on the cone of covariance matrices SP(n) endowed with two popular Riemannian metrics, namely Log-Euclidean (LE) and Affine-Invariant (AI) metrics. We show that the Riemannian Brownian motion on SP(n) has infinite explosion time as on the Euclidean space and establish the calculation for the horizontal lifts of smooth curves. Moreover, we provide Bayesian inference for discretely observed diffusion processes of covariance matrices associated with either the LE or the AI metrics, and present a novel diffusion bridge sampling method using guided proposals when equipping SP(n) with the AI metric. The estimation algorithms are illustrated with an application in finance, together with a goodness-of-fit test comparing models associated with different metrics. Furthermore, we explore the multivariate volatility models via simulation study, in which covariance matrices in the models are assumed to be unobservable

Forest point processes for the automatic extraction of networks in raster data

International audienceIn this paper, we propose a new stochastic approach for the automatic detection of network structures in raster data. We represent a network as a set of trees with acyclic planar graphs. We embed this model in the probabilistic framework of spatial point processes and determine the most probable configuration of trees by stochastic sampling. That is, different configurations are constructed randomly by modifying the graph parameters and by adding or removing nodes and edges to/ from the current trees. Each configuration is evaluated based on the probabilities for these changes and an energy function describing the conformity with a predefined model. By using the Reversible jump Markov chain Monte Carlo sampler, an approximation of the global optimum of the energy function is iteratively reached. Although our main target application is the extraction of rivers and tidal channels in digital terrain models, experiments with other types of networks in images show the transferability to further applications. Qualitative and quantitative evaluations demonstrate the competitiveness of our approach with respect to existing algorithms

AUTOMATED ANALYSIS OF NEURONAL MORPHOLOGY: DETECTION, MODELING AND RECONSTRUCTION

Ph.DDOCTOR OF PHILOSOPH