Texture representation using autoregressive models

Abstract

Texture is a fundamental characteristic in many natural images that plays an important role in human visual perception and in turn provides information for image understanding and scene interpretation. The textured image can be modeled to describe, analyze and synthesize the texture. The model parameters capture the essential perceived qualities of texture. One of the important characteristics of texture data is the statistical dependence of the gray level at a lattice point on those of its neighbors. The spatial-interaction models characterize this statistical dependency by representing the intensity of a pixel, as a 2-D linear combination of the intensity of its neighbors and an additive noise. One way of specifying this interaction is simultaneous autoregressive (SAR) models. This is one of the most traditional methods used for modeling in the area of image processing. This paper presents the work done by the authors on parameter estimation and synthesis of textured images using Simultaneous Autoregressive (SAR) modeling. Different programs are developed in MATLAB to implement the parameter estimation and synthesis and are tested for their performance. The scope of this work includes the use of causal and noncausal methods for modeling and synthesizing natural textures. Simultaneous or spatial autoregressive models with causal and noncausal neighborhoods are used for parameter estimation and texture pattern generation. Parameter estimation is done by two different methods: The least square error (LSE) and maximum likelihood estimation (MLE). LSE method is preferred for causal models. MLE method is used for noncausal autoregressive models and it uses iterative algorithm. The synthesis procedure is based on generating a two dimensional autoregressive random field driven by a two dimensional zero mean white noise field with unit variance. Two different algorithms are used for synthesis of causal and noncausal AR models. Different image textures are synthesized using a given set of neighborhoods and parameters. Different patterns of synthetic images can be generated using various sets of parameters. A number of images from Brodatz album are tested for parameter estimation and synthesis. The synthesized image retains the pattern in the original image like vertical or horizontal streaks. An interactive graphical user interface (GUI) is developed using MATLAB that allows user to select one image from Brodatz album. The user can choose between causal or noncausal neighborhood and select number of elements in the neighborhood or choose any one set of neighborhood from different sets stored, and find out SAR model parameters by one of the methods of parameter estimation. The user can synthesize the image using these parameters. Both original and synthesized image are displayed side by side on the screen and the user can easily compare the two images. Thus the GUI offers an interactive platform for implementation of parameter estimation using different neighborhoods for the images from Brodatz album and synthesis of the image from these estimated parameters.