Hierarchical conditional random fields for parts based models matching

A parts based model is a parametrization of an object class using a collection of landmarks following the object structure. The matching of parts based models is one of the problems where pairwise Conditional Random Fields have been successfully applied. The main reason of their effectiveness is tractable inference and learning due to the simplicity of involved graphs, usually trees. However, these models do not consider possible patterns of statistics among sets of landmarks, and thus they sufffer from using too myopic information. To overcome this limitation, we propoese a novel structure based on a hierarchical Conditional Random Fields, which we explain in the first part of this memory. We build a hierarchy of combinations of landmarks, where matching is performed taking into account the whole hierarchy. To preserve tractable inference we effectively sample the label set. We test our method on facial feature selection and human pose estimation on two challenging datasets: Buffy and MultiPIE. In the second part of this memory, we present a novel approach to multiple kernel combination that relies on stacked classification. This method can be used to evaluate the landmarks of the parts-based model approach. Our method is based on combining responses of a set of independent classifiers for each individual kernel. Unlike earlier approaches that linearly combine kernel responses, our approach uses them as inputs to another set of classifiers. We will show that we outperform state-of-the-art methods on most of the standard benchmark datasets.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

On the inclusion of channel's time dependence in a hidden Markov model for blind channel estimation

In this paper, the theory of hidden Markov models (HMM) isapplied to the problem of blind (without training sequences) channel estimationand data detection. Within a HMM framework, the Baum–Welch(BW) identification algorithm is frequently used to find out maximum-likelihood (ML) estimates of the corresponding model. However, such a procedureassumes the model (i.e., the channel response) to be static throughoutthe observation sequence. By means of introducing a parametric model fortime-varying channel responses, a version of the algorithm, which is moreappropriate for mobile channels [time-dependent Baum-Welch (TDBW)] isderived. Aiming to compare algorithm behavior, a set of computer simulationsfor a GSM scenario is provided. Results indicate that, in comparisonto other Baum–Welch (BW) versions of the algorithm, the TDBW approachattains a remarkable enhancement in performance. For that purpose, onlya moderate increase in computational complexity is needed.

Blind channel estimation and data detection using hidden Markov models theory

In this correspondence, we propose applying the hiddenMarkov models (HMM) theory to the problem of blind channel estimationand data detection. The Baum–Welch (BW) algorithm, which is able toestimate all the parameters of the model, is enriched by introducingsome linear constraints emerging from a linear FIR hypothesis on thechannel. Additionally, a version of the algorithm that is suitable for timevaryingchannels is also presented. Performance is analyzed in a GSMenvironment using standard test channels and is found to be close to thatobtained with a nonblind receiver.

Sistema de reconeixement de cares basat en múltiples vistes

En aquest projecte es proposa un algorisme de detecció de pell que introdueix el veïnatge a l’hora de classificar píxels. Partim d’un espai de color invariant après a partir de múltiples vistes i introduïm la influència del veïnatge mitjançant camps aleatoris de Markov. A partir dels experiments realitzats podem concloure que la inclusió del veïnatge en el procés de classificació de píxels millora significativament els resultats de detecció.

Sound Texture Modelling

In the PhD thesis “Sound Texture Modeling” we deal with statistical modelling or textural sounds like water, wind, rain, etc. For synthesis and classification. Our initial model is based on a wavelet tree signal decomposition and the modeling of the resulting sequence by means of a parametric probabilistic model, that can be situated within the family of models trainable via expectation maximization (hidden Markov tree model ). Our model is able to capture key characteristics of the source textures (water, rain, fire, applause, crowd chatter ), and faithfully reproduces some of the sound classes. In terms of a more general taxonomy of natural events proposed by Graver, we worked on models for natural event classification and segmentation. While the event labels comprise physical interactions between materials that do not have textural propierties in their enterity, those segmentation models can help in identifying textural portions of an audio recording useful for analysis and resynthesis. Following our work on concatenative synthesis of musical instruments, we have developed a pattern-based synthesis system, that allows to sonically explore a database of units by means of their representation in a perceptual feature space. Concatenative syntyhesis with “molecules” built from sparse atomic representations also allows capture low-level correlations in perceptual audio features, while facilitating the manipulation of textural sounds based on their physical and perceptual properties. We have approached the problem of sound texture modelling for synthesis from different directions, namely a low-level signal-theoretic point of view through a wavelet transform, and a more high-level point of view driven by perceptual audio features in the concatenative synthesis setting. The developed framework provides unified approach to the high-quality resynthesis of natural texture sounds. Our research is embedded within the Metaverse 1 European project (2008-2011), where our models are contributting as low level building blocks within a semi-automated soundscape generation system.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Class of correlated random networks with hidden variables

We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.

Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization

The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions

Numerical signs fos a transition in the 2d Random Field Ising Model at T=0

Intensive numerical studies of exact ground states of the two-dimensional ferromagnetic random field Ising model at T=0, with a Gaussian distribution of fields, are presented. Standard finite size scaling analysis of the data suggests the existence of a transition at ¿c=0.64±0.08. Results are compared with existing theories and with the study of metastable avalanches in the same model.

First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

Structural disorder in two-dimensional random magnets: Very thin films of rare earths and transition metals

The low-temperature isothermal magnetization curves, M(H), of SmCo4 and Fe3Tb thin films are studied according to the two-dimensional correlated spin-glass model of Chudnovsky. We have calculated the magnetization law in approach to saturation and shown that the M(H) data fit well the theory at high and low fields. In our fit procedure we have used three different correlation functions. The Gaussian decay correlation function fits well the experimental data for both samples.

LSB Matching Steganalysis Based on Patterns of Pixel Differences and Random Embedding

Peer-reviewed