In this article, accumulated sudden infant death syndrome (SIDS) data, from 1974–1978 and 1979–1984 for the counties of North Carolina, are analyzed. After a spatial exploratory data analysis, Markov random-field models are fit to the data. The (spatial) trend is meant to capture the large-scale variation in the data, and the variance and spatial dependence are meant to capture the small-scale variation. The trend could be a function of other explanatory variables or could simply be modeled as a function of spatial location. Both models are fit and compared. The results give an excellent illustration of a phenomenon already well-known in time series, that autocorrelation in data can be due to an undiscovered explanatory variable. Indeed, for 1974–1978 we confirm a dependence of SIDS rate on proportion of nonwhite babies born, along with insignificant spatial correlation. Without this regressor variable, however, the spatial correlation is significant. In 1979–1984, perhaps due to reporting bias o...

Spatial modeling of regional variables

This thesis presents extensions to the local binary pattern (LBP) texture analysis operator. The operator is defined as a gray-scale invariant texture measure, derived from a general definition of texture in a local neighborhood. It is made invariant against the rotation of the image domain, and supplemented with a rotation invariant measure of local contrast. The LBP is proposed as a unifying texture model that describes the formation of a texture with micro-textons and their statistical placement rules. The basic LBP is extended to facilitate the analysis of textures with multiple scales by combining neighborhoods with different sizes. The possible instability in sparse sampling is addressed with Gaussian low-pass filtering, which seems to be somewhat helpful. Cellular automata are used as texture features, presumably for the first time ever. With a straightforward inversion algorithm, arbitrarily large binary neighborhoods are encoded with an eight-bit cellular automaton rule, resulting in a very compact multi-scale texture descriptor. The performance of the new operator is shown in an experiment involving textures with multiple spatial scales. An opponent-color version of the LBP is introduced and applied to color textures. Good results are obtained in static illumination conditions. An empirical study with different color and texture measures however shows that color and texture should be treated separately. A number of different applications of the LBP operator are presented, emphasizing real-time issues. A very fast software implementation of the operator is introduced, and different ways of speeding up classification are evaluated. The operator is successfully applied to industrial visual inspection applications and to image retrieval.

The local binary pattern approach to texture analysis — extensions and applications

Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modeling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behavior of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.

A survey of cellular automata: types, dynamics, non-uniformity and applications

Matrix algebraic formulae concerning some exceptional rules of two-dimensional cellular automata

In the past, Cellular Automata based models and machines [1] have been proposed for simulation of physical systems without any analytical insight into the behaviour of the underlying simulation machine. This paper makes a significant departure from this traditional approach. An elegant mathematical model using simple matrix algebra is reported in this paper for characterizing the behaviour of two-dimensional nearest neighbourhood linear cellular automata with null and periodic boundary conditions. Based on this mathematical model, a VLSI architecture of a Cellular Automata Machine (CAM) has been proposed. Interesting applications of CAM in the fields of image analysis and fractal image generation are also reported.

VLSI architecture of a cellular automata machine

This paper presents an elegant mathematical model using simple matrix algebra for characterising the behaviour of two-dimensional nearest neighbourhood linear cellular automata with periodic boundary conditions. Based on this mathematical model, the VLSI architecture of a Cellular Automata Machine (CAM) has been proposed for text compression. Experimental results of comparisons with adaptive Huffman coding scheme also presented.

Text compression using two-dimensional cellular automata

Nowadays, one-dimensional (1D) cellular automata (CA) based models and machines were demonstrated for various applications [1–7]. 2D CA based machines have not yet been used fruitfully mainly due to the lack of analytical insight into the behaviour of the underlying evolutionary process. The set of papers [8–11] dealt with the behaviour of the uniform 2D CAs. In the present paper, for the first time an attempt has been made to characterize a particular hybrid linear 2D CA transformation in GF (2) using matrix algebra. Also we deal with the synthesis problem of this particular hybrid transformation.

Characterisation of a particular hybrid transformation of two-dimensional cellular automata

It is difficult to obtain trustworthy data on stigmatizing matters like habits of tax evasion, drunken driving, etc., through direct queries. To overcome this difficulty, Warner introduced randomized response techniques to estimate the proportion of people bearing such a stigmatizing or sensitive characteristic in a given community. For simplicity in estimation he restricted to SRSWR and since then, several researchers have extended and applied this technique in various ways. All these results involve sampling with a pre-fixed number of draws. In this paper we employ inverse sampling with equal probabilities with replacement and show certain advantages in estimation using randomized response data by Warner’s device gathered through such a simple inverse sampling scheme.

Kajal Dihidar

Papers

VLSI architecture of a cellular automata machine

Matrix algebraic formulae concerning some exceptional rules of two-dimensional cellular automata

Text compression using two-dimensional cellular automata

Characterisation of a particular hybrid transformation of two-dimensional cellular automata

Estimation of a sensitive proportion by Warner’s randomized response data through inverse sampling