Visual stimuli contain a limited amount of information that could potentially be used to perform a given visual task. At successive stages of visual processing, some of this information is lost and some is transmitted to higher stages. This article describes a new analysis, based on the concept of the ideal observer in signal detection theory, that allows one to trace the (low of discrimination information through the initial physiological stages of visual processing, for arbitrary spatio-chromatic stimuli. This ideal-observer analysis provides a rigorous means of measuring the information content of visual stimuli and of assessing the contribution of specific physiological mechanisms to discrimination performance. Here, the analysis is developed for the physiological mechanisms up to the level of the photoreceptor. It is shown that many psychophysical phenomena previously attributed to neural mechanisms may be explained by variations in the information content of the stimuli and by preneural mechanisms. The purpose of vision is to extract and represent information about the physical environment from the light that is emitted, transmitted, or reflected by objects and surfaces. In order to extract useful information, a visual system must be able to encode

Rank-order based filters such as stack filters, multilevel and multistage median filters, morphological filters, and order statistic filters have all proven to be very effective at enhancing and restoring images. Perhaps the primary reason for their success is that they can suppress noise without destroying important image details such as edges and lines. Two approaches have been used in the past to design rank-order based nonlinear filters to enhance or restore images. They may be called the structural approach and the estimation approach. The first approach requires structural descriptions of the image and the process which has altered it, while the second requires statistical descriptions. The many different classes of rank-order based filters that have been developed over the last few decades are reviewed in the context of these two approaches. One of these filter classes, stack filters, then becomes the focus of the rest of the paper. These filters, which are defined by a weak superposition property and an ordering property, contain all compositions of 2-D rank-order operations. The recently developed theory of minimum mean absolute error (MMAE) stack filtering is reviewed and extended to two dimensions. Then, a theory of optimal stack filtering under structural constraints and goals is developed for the structural approach to image processing. These two optimal stack filtering theories are then combined into a single design theory for rank-order based filters.

Uma rede estatística é uma cole,cão de nós representando variáveis aleatórias e um conjunto de arestas que ligam os nós. Um modelo estocástico por isso e chamado um modelo gráfico. Estes modelos, de gráficos e redes, sáo particularmente úteis para examinar as dependéncias estatísticas baseadas em condi,coes do tipo das que ocorrem frequentemente em economia e estatística. Neste artigo as variáveis aleatórias dos nós serão séries temporais ou processos pontuais. Os casos de gráfos direcionados e não-direcionados são apresentados. A statistical network is a collection of nodes representing random variables and a set of edges that connect the nodes. A probabilistic model for such is called a graphi-cal model. These models, graphs and networks are particularly useful for examining statistical dependencies based on conditioning as often occurs in economics and statis-tics. In this paper the nodal random variables will be time series or point proceses. The cases of undirected and directed graphs are focussed on.

A framework for the regularized and robust estimation of non-uniform dimensionality and density in high dimensional noisy data is introduced in this work. This leads to learning stratifications, that is, mixture of manifolds representing different characteristics and complexities in the data set. The basic idea relies on modeling the high dimensional sample points as a process of Translated Poisson mixtures, with regularizing restrictions, leading to a model which includes the presence of noise. The Translated Poisson distribution is useful to model a noisy counting process, and it is derived from the noise-induced translation of a regular Poisson distribution. By maximizing the log-likelihood of the process counting the points falling into a local ball, we estimate the local dimension and density. We show that

The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning. 1

The time histogram method is the most basic tool for capturing a timedependent rate of neuronal spikes. Generally in the neurophysiological literature, the bin size that critically determines the goodness of the fit of the time histogram to the underlying spike rate has been subjectively selected by individual researchers. Here, we propose a method for objectively selecting the bin size from the spike count statistics alone, so that the resulting bar or line graph time histogram best represents the unknown underlying spike rate. For a small number of spike sequences generated from a modestly fluctuating rate, the optimal bin size may diverge, indicating that any time histogram is likely to capture a spurious rate. Given a paucity of data, the method presented here can nevertheless suggest how many experimental trials should be added in order to obtain a meaningful time-dependent histogram with the required accuracy.

2. Wavelets for time series functions and moments. Wavelet analysis provides a means of parameterizing such quantities in the nonstationary case. By wavelet jk=ZT

Absrract-A recurrence relation is obtained for the counting distribu-tion, as well as the probability density of waiting time, for a doubly stochastic Poisson point process driven by nonstationary shot noise (SNDP). For a stimulus of short duration, the counting distribution approximately reduces to the Neyman Type-A. The SNDP is an important special Neyman-Scott cluster process. I.

The time-histogram method is a handy tool for capturing the instantaneous rate of spike occurrence. In most of the neurophysiological literature, the bin size that critically determines the goodness of the fit of the time-histogram to the underlying rate has been selected by individual researchers in an unsystematic manner. We propose an objective method for selecting the bin size of a time-histogram from the spike data, so that the time-histogram best approximates the unknown underlying rate. The resolution of the histogram increases, or the optimal bin size decreases, with the number of spike sequences sampled. It is notable that the optimal bin size diverges if only a small number of experimental trials are available from a moderately fluctuating rate process. In this case, any attempt to characterize the underlying spike rate will lead to spurious results. Given a paucity of data, our method can also suggest how many more trials are needed until the set of data can be analyzed with the required resolution. 1

We propose a vector representation approach to contour estimation from noisy data. Images are modeled as random fields composed of a set of homogeneous regions: contours (boundaries of homogeneous regions) are assumed to be vectors of a subspace of L²(T) generated by a given finite basis; B-splines, Sinc-type, and Fourier bases are considered. The main contribution...