Boosting confidence in detecting time-dependent ultradian rhythms using wavelet analysis

Recently, biologists have shown fractal and oscillatory characteristics in animal behaviortime series. Aspects so different can be explained by a model with added components thatinclude deterministic cycles (ultradian and circadian rhythms), polynomial tendencies, and anunderlying nonlinear process with stationary increments. Such components can be extractedfrom the data using wavelet analysis by selecting the transformation appropriately. In this talk, we will discuss a five-step method that describes the data without making any parametric assumptions about trends in the frequency or amplitude of the components signals and is resilient to noise.1. Visual inspection by Continuous wavelet transform based on real Gaussian motherwavelet in the Cartesian time scale plane2. Visual inspection by Continuous wavelet transform based on complex Morlet motherwavelet in the Polar time scale plane.3. Modal frequency detection by Synchrosqueezed wavelet transform, a linear timescale analysis followed by a synchrosqueezing technique.4. Modal frequency corroboration by Empirical wavelet transform, a wavelet analysis in theFourier domain followed by frequency segmentation to extract the modal components.5- Quantification of coherence and phase difference between different series.Fil: Flesia, Ana Georgina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaSMB 2021 Annual MeetingRiversideEstados UnidosSociety for Mathematical BiologyUniversity of Californi

Unsupervised edge map scoring: a statistical complexity approach

We propose a new Statistical Complexity Measure (SCM) to qualify edge maps without Ground Truth (GT) knowledge. The measure is the product of two indices, an \emph{Equilibrium} index $\mathcal{E}$ obtained by projecting the edge map into a family of edge patterns, and an \emph{Entropy} index $\mathcal{H}$, defined as a function of the Kolmogorov Smirnov (KS) statistic. This new measure can be used for performance characterization which includes: (i)~the specific evaluation of an algorithm (intra-technique process) in order to identify its best parameters, and (ii)~the comparison of different algorithms (inter-technique process) in order to classify them according to their quality. Results made over images of the South Florida and Berkeley databases show that our approach significantly improves over Pratt's Figure of Merit (PFoM) which is the objective reference-based edge map evaluation standard, as it takes into account more features in its evaluation

Accuracy of MAP segmentation with hidden Potts and Markov mesh prior models via Path Constrained Viterbi Training, Iterated Conditional Modes and Graph Cut based algorithms

In this paper, we study statistical classification accuracy of two different Markov field environments for pixelwise image segmentation, considering the labels of the image as hidden states and solving the estimation of such labels as a solution of the MAP equation. The emission distribution is assumed the same in all models, and the difference lays in the Markovian prior hypothesis made over the labeling random field. The a priori labeling knowledge will be modeled with a) a second order anisotropic Markov Mesh and b) a classical isotropic Potts model. Under such models, we will consider three different segmentation procedures, 2D Path Constrained Viterbi training for the Hidden Markov Mesh, a Graph Cut based segmentation for the first order isotropic Potts model, and ICM (Iterated Conditional Modes) for the second order isotropic Potts model. We provide a unified view of all three methods, and investigate goodness of fit for classification, studying the influence of parameter estimation, computational gain, and extent of automation in the statistical measures Overall Accuracy, Relative Improvement and Kappa coefficient, allowing robust and accurate statistical analysis on synthetic and real-life experimental data coming from the field of Dental Diagnostic Radiography. All algorithms, using the learned parameters, generate good segmentations with little interaction when the images have a clear multimodal histogram. Suboptimal learning proves to be frail in the case of non-distinctive modes, which limits the complexity of usable models, and hence the achievable error rate as well. All Matlab code written is provided in a toolbox available for download from our website, following the Reproducible Research Paradigm

On segmentation with Markovian models

This paper addresses the image modeling problem under the assumption that images can be represented by 2d order, hidden Markov random fields models. The modeling applications we have in mind com- prise pixelwise segmentation of gray-level images coming from the field of Oral Radiographic Differential Diagnosis. Segmentation is achieved by approximations to the solution of the maximum a posteriori equation (MAP) when the emission distribution is assumed the same in all models and the difference lays in the Neighborhood Markovian hypothesis made over the labeling random field. For two algorithms, 2d path-constrained Viterbi training and Potts-ICM we investigate goodness of fit by study- ing statistical complexity, computational gain, extent of automation, and rate of classification measured with kappa statistic. All code written is provided in a Matlab toolbox available for download from our website, following the Reproducible Research Paradigm.Sociedad Argentina de Informática e Investigación Operativ

Considering correlation properties on statistical simulation of clutter

Statistical properties of image data are of paramount importance in the design of pattern recognition technics and the interpretation of their outputs. Image simulation allows quantification of method?s error and accuracy. In the case of SAR images, the contamination they suffer from a particular kind of noise, called speckle, which does not follow the classical hypothesis of entering the signal in an additive manner and obeying the Gaussian law, make them require a more careful treatment. Since the seminal work of Frery et al. (1997) a great variety of studies have been made targeting the specification of statistical properties of SAR data beyond classical assumptions. The G distribution family proposed by Frery has been proved a flexible tool for the design of pattern recognition algorithms based on statistical modeling. Nevertheless, most of such work does not consider correlation present in the data as significant, which introduces an error in the model of particular regions of the imagery. The autocorrelation function can represent the structure of sea waves and the random variation made by the height and width of trees, along with the variability introduced in forests by the variation of wind intensity. Using the roughness parameter of the G family for target discrimination alleviates this modeling error, since it was shown by Frery et al. (1997) that it characterizes heterogeneity in data. Classification accuracy is then tied to parameter estimation, which in this case it has been proved difficult, Lucini (2002), Bustos et al. (2002). In this paper we review some of our own simulation techniques to generate SAR clutter with pre-specified correlation properties, Flesia (1999), Bustos et al. (2001), Bustos et al. (2009), and release a new set of routines in R for simulation studies based on such techniques. We give an example of the code versatility studying the change in accuracy of non-parametric techniques when correlated data is classified, compared with classification of uncorrelated data simulated with the same parameters. All code is available for download from AGF?s Reproducible Research website, Flesia (2014).This work was financially supported by grants from SeCyT-UNC, Argentina. AGF, MML are careermembers of CONICET.Fil: Flesia, Ana Georgina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Flesia, Ana Georgina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Estudios de Matemática; Argentina.Fil: Pérez, Darío Javier. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Pérez, Darío Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Estudios de Matemática; Argentina.Fil: Lucini, María Magdalena. Universidad Nacional de Nordeste. Facultad de Ciencias Exactas, Naturales y Agrimensura; Argentina.Fil: Lucini, María Magdalena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Ciencias de la Información y Bioinformática (desarrollo de hardware va en 2.2 "Ingeniería Eléctrica, Electrónica y de Información" y los aspectos sociales van en 5.8 "Comunicación y Medios"

A new approach to image segmentation with two-dimensional hidden Markov models

Image segmentation is one of the fundamental problems in computer vision. In this work, we present a new segmentation algorithm that is based on the theory of twodimensional hidden Markov models (2D-HMM). Unlike most 2DHMM approaches we do not apply the Viterbi Algorithm, instead we present a computationally efficient algorithm that propagates the state probabilities through the image. This approach can easily be extended to higher dimensions. We compare the proposed method with a 2D-HMM standard algorithm and Iterated Conditional Modes using real world images like a radiography or a satellite image as well as synthetic images. The experimental results show that our approach is highly capable of condensing image segments. This gives our algorithm a significant advantage over the standard algorithm when dealing with noisy images with few classes.Fil: Baumgartner, Josef. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales; Argentina.Fil: Flesia, Ana Georgina. Universidad Tecnológica Nacional; Argentina.Fil: Flesia, Ana Georgina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Flesia, Ana Georgina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Gimenez, Javier. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Pucheta, Julián. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales; Argentina.Sistemas de Automatización y Contro

Estimación paralela de parámetros texturales

En este trabajo se presenta un estimador del vector de parámetros asociado con un modelo Auto-Binomial (MAB) basado en el estimador de mínimos cuadrados condicional (MCC). Este método admite programación paralela con el fin de optimizar el rendimiento en términos de velocidad del proceso de estimación. El MAB es un modelo estocástico entre los Campos Aleatorios de Gibbs- Markov que permite describir en forma robusta la información espacial de la imagen a través del vector de parámetros de su función de energía.Sociedad Argentina de Informática e Investigación Operativ