Modeling spatial and temporal textures

Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1997.Includes bibliographical references (leaves 155-161).by Fang Liu.Ph.D

The Rank of the Covariance Matrix of an Evanescent Field

Evanescent random fields arise as a component of the 2-D Wold decomposition of homogenous random fields. Besides their theoretical importance, evanescent random fields have a number of practical applications, such as in modeling the observed signal in the space time adaptive processing (STAP) of airborne radar data. In this paper we derive an expression for the rank of the low-rank covariance matrix of a finite dimension sample from an evanescent random field. It is shown that the rank of this covariance matrix is completely determined by the evanescent field spectral support parameters, alone. Thus, the problem of estimating the rank lends itself to a solution that avoids the need to estimate the rank from the sample covariance matrix. We show that this result can be immediately applied to considerably simplify the estimation of the rank of the interference covariance matrix in the STAP problem

Two-dimensional minimum free energy autoregressive parametric modelling and spectral estimation

We present a new high resolution spectral estimation method. This method is a 2-D extension of the Minimum Free Energy (MFE) parameter estimation technique based on extension of the multidimensional Levinson method Our 2-D MFE technique determines autoregressive (AR) models for 2-D fields MFE-AR models may be used for 2-D spectral estimation. The performance of the technique for spectral estimation of closely spaced 2-D sinusoids in white noise is demonstrated by numerical example. Experimental results from tests on spectral resolution, estimator bias and variance, and tolerance to change in signal processing temperature are examined. The effects on spectral estimation of signal to noise ratio, data set size, model size, autocorrelation type, and dynamic range difference are illustrated. The spectral estimates from combmed and single quarter plane estimates are contrasted. The results illustrate that MFE provides accurate low model order spectral estimation. The performance of the method is compared to the multidimensional Levinson, conventional transform, modified covariance (MCV), hybrid, and maximum entropy methods. It is seen that our MFE method provides superior spectral estimation over that which can be achieved with the Levinson algorithm with equivalent computational burden Superior spectral resolution is achieved at lower data set size than that provided by the Fourier transform method. In terms of spectral resolution, the MFE method performs just as well as the MCV method for snapshot data. It is seen that MFE provides spectral estimates that are as good as if not better than that provided by hybrid and maximum entropy methods. The computational expense, stability, and accuracy of spectral estimation over a number of independent simulation trials are examined for both MFE and MCV methods. The bias and variance statistics for MFE are comparable to those for MCV. However, the computational expense is far less than that of MCV and maximum likelihood methods. Models generated by our method give rise to stable and causal systems that are recursively computable. Hence they may also be used for correlation extension and for field modelling applications such as texture generation

The Material Theory of Induction

The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it.The content of that logic and where it can be applied are determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference

Maximum Likelihood Parameter Estimation of the Harmonic, Evanescent and Purely Indeterministic Components of Discrete Homogeneous Random Fields

This paper presents a maximum-likelihood solution to the general problem of fitting a parametric model to observations from a single realization of a 2-D homogeneous random field with mixed spectral distribution. On the basis of a 2-D Wold-like decomposition, the field is represented as a sum of mutually orthogonal components of three types: purelyindeterministic, harmonic, and evanescent. The suggested algorithm involves a two-stage procedure. In the first stage we obtain a suboptimal initial estimate for the parameters of the spectral support of the evanescent and harmonic components. In the second stage we refine these initial estimates by iterative maximization of the conditional likelihood of the observed data, which is expressed as a function of only the parameters of the spectral supports of the evanescent and harmonic components. The solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the other unknown paramete..

The Material Theory of Induction

The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. The content of that logic and where it can be applied are determined by the facts prevailing in that domain

From uncertainty to adaptivity : multiscale edge detection and image segmentation

This thesis presents the research on two different tasks in computer vision: edge detection and image segmentation (including texture segmentation and motion field segmentation). The central issue of this thesis is the uncertainty of the joint space-frequency image analysis, which motivates the design of the adaptive multiscale/multiresolution schemes for edge detection and image segmentation. Edge detectors capture most of the local features in an image, including the object boundaries and the details of surface textures. Apart from these edge features, the region properties of surface textures and motion fields are also important for segmenting an image into disjoint regions. The major theoretical achievements of this thesis are twofold. First, a scale parameter for the local processing of an image (e.g. edge detection) is proposed. The corresponding edge behaviour in the scale space, referred to as Bounded Diffusion, is the basis of a multiscale edge detector where the scale is adjusted adaptively according to the local noise level. Second, an adaptive multiresolution clustering scheme is proposed for texture segmentation (referred to as Texture Focusing) and motion field segmentation. In this scheme, the central regions of homogeneous textures (motion fields) are analysed using coarse resolutions so as to achieve a better estimation of the textural content (optical flow), and the border region of a texture (motion field) is analysed using fine resolutions so as to achieve a better estimation of the boundary between textures (moving objects). Both of the above two achievements are the logical consequences of the uncertainty principle. Four algorithms, including a roof edge detector, a multiscale step edge detector, a texture segmentation scheme and a motion field segmentation scheme are proposed to address various aspects of edge detection and image segmentation. These algorithms have been implemented and extensively evaluated

An object-based approach to retrieval of image and video content

Promising new directions have been opened up for content-based visual retrieval in recent years. Object-based retrieval which allows users to manipulate video objects as part of their searching and browsing interaction, is one of these. It is the purpose of this thesis to constitute itself as a part of a larger stream of research that investigates visual objects as a possible approach to advancing the use of semantics in content-based visual retrieval. The notion of using objects in video retrieval has been seen as desirable for some years, but only very recently has technology started to allow even very basic object-location functions on video. The main hurdles to greater use of objects in video retrieval are the overhead of object segmentation on large amounts of video and the issue of whether objects can actually be used efficiently for multimedia retrieval. Despite this, there are already some examples of work which supports retrieval based on video objects. This thesis investigates an object-based approach to content-based visual retrieval. The main research contributions of this work are a study of shot boundary detection on compressed domain video where a fast detection approach is proposed and evaluated, and a study on the use of objects in interactive image retrieval. An object-based retrieval framework is developed in order to investigate object-based retrieval on a corpus of natural image and video. This framework contains the entire processing chain required to analyse, index and interactively retrieve images and video via object-to-object matching. The experimental results indicate that object-based searching consistently outperforms image-based search using low-level features. This result goes some way towards validating the approach of allowing users to select objects as a basis for searching video archives when the information need dictates it as appropriate