An efficient and exact dynamic programming algorithm is introduced to quantise a continuous random variable into a discrete random variable that maximises the likelihood of the quantised probability distribution for the original continuous random variable. Quantisation is often useful before statistical analysis and modelling of large discrete network models from observations of multiple continuous random variables. The quantisation algorithm is applied to genomic features including the recombination rate distribution across the chromosomes and the non-coding transposable element LINE-1 in the human genome. The association pattern is studied between the recombination rate, obtained by quantisation at genomic locations around LINE-1 elements, and the length groups of LINE-1 elements, also obtained by quantisation on LINE-1 length. The exact and density-preserving quantisation approach provides an alternative superior to the inexact and distance-based univariate iterative k-means clustering algorithm for discretisation.
During the past decade a number of multiimage picture processing software packages have been put together. However, only a few of the references to picture processing systems discuss image data structure or input/output routines. This correspondence is a first step in a direction toward getting a communication process started by suggesting some specifications for a multiimage data format and standard input/output interface routines to access the image data.
The goals of this thesis are to develop a system to perform maximally stable interpretations of scenes of line drawings by utilizing the perspective projection geometry and to optimally estimate the pose from line-to-line correspondences. Both goals are critical to an object recognition system.
In the first part of the thesis we develop a Bayesian approach to pose estimation from line-to-line correspondences. The Bayesian approach is different from other traditional least squares approaches in several respects. First, we introduce the Fisher distribution as an underlying noise model of the observations, which consists of directional data. The underlying model allows us to perform a consistent estimation of the unknown parameters. Second, the Bayesian approach estimates the rotation matrix and translation vector simultaneously. As a result, it gives an optimal solution. Finally, the objective function derived from the Bayesian approach is different from the least squares approaches. We define an experimental protocol to evaluate the performance of the Bayesian approach and the least squares approach proposed by Liu et al. The experimental results show that the Bayesian approach has a better accuracy and is thus a better technique.
In the second part of the thesis we start constructing a perspective projection knowledge-based system. In order to effectively utilize the perspective projection algorithms we encapsulate and organize the existing and newly developed perspective projection algorithm into the knowledge-based system. The knowledge-based system can adapt to different input relationships and infer a wide variety of geometrical relationships. Before perspective projection algorithms are embedded in the perspective projection geometry knowledge-based system, we evaluate their performance. This is especially important when different algorithms infer the same geometric information. We demonstrate the important of this task by applying the performance characterization to the three-point pose estimation problem based on numerical stability.
Finally, we employ a dynamic probabilistic inference network as a framework for interpreting a scene, dealing with any uncertainty occurring in the scene and updating the belief from a sequence of evidence. We give a unified formulation for how the probabilistic inference network works for scene interpretation.
In image processing literature, thus far researchers have assumed the perturbation in the data to be white (or uncorrelated) having a covariance matrix σ2I, i.e., assumption of equal variance for all the data samples and that no correlation exists between the data samples. However, there has been very little attempt to estimate noise characteristics under the assumption that there is correlation between data samples. We develop a new and novel approach for the estimation of the unknown colored noise covariance matrix. We use the facet model to describe the noise free image, because of its simple, yet elegant mathematical formulation.
Original contributions of this dissertation include: (1) Development of a new and novel approach for the simultaneous estimation of the unknown colored (or correlated) noise covariance matrix and the hyperparameters of the covariance model using the facet model . We also estimate, simultaneously, coefficients of the facet model. (2) Introduction of the Generalized Inverted Wishart ( GJW ) distribution to the image processing and computer vision community. (3) Formulation of the problem solution in a Bayesian framework using an improper uniform prior distribution for the facet model coefficients (i.e. a flat prior) and a Generalized Inverted Wishart ( GJW ) prior distribution for the unknown noise covariance matrix that is to be estimated. (4) Placing a structure on the hypercovariance matrix of GJW distribution, such that its elements are a function of the coefficients of a correlation filter. These filter coefficients in addition to the number of degrees of freedom parameter of the GJW distribution are called the hyperparameters. (5) Hyperparameters have constraints placed on them so that the resulting hypercovariance matrix remains positive definite. Therefore, we designed a new extension of the expectation maximization algorithm called the generalized constrained expectation maximization (GCEM) algorithm for the estimation of the hyperparameters using the sequential unconstrained minimization technique (SUMT) via barrier functions to incorporate the constraints. (6) Development of a new ridge operator called the integrated second directional derivative ridge operator (ISDDRO) based on the facet model. Our main focus here is the optimal estimation of ridge orientation. The orientation bias and orientation standard deviation are the measures of performance. The latter measures the noise sensitivity. (7) Comparison of ISDDRO using the noise covariance matrix estimation (ISDDRO-CN) with the same ridge operator under white noise assumption (ISDDRO-WN) and also with the most competing ridge operator multilocal level set extrinsic curvature (MLSEC) [5]. ISDDRO-CN has superior noise sensitivity characteristics compared to both ISDDRO-WN and MLSEC.
Photointerpreters employ a variety of implicit spatial models to provide interpretations from remotely sensed aerial or satellite imagery. In this paper one application is illustrated: how ridges and valleys can be automatically interpreted from Landsat imagery of a mountainous area, and how a relative elevation terrain model can be constructed from this interpretation. How to examine valleys for the possible presence of streams or rivers is shown, and how a spatial relational model can be set up to make a final interpretation of the river drainage network is explored.
This paper describes a technique for transforming a twodimensional shape into a binary relation whose clusters represent the intuitively pleasing simple parts of the shape. The binary relation can be defined on the set of boundary points of the shape or on the set of line segments of a piecewise linear approximation to the boundary. The relation includes all pairs of vertices (or segments) such that the line segment joining the pair lies entirely interior to the boundary of the shape. The graph-theoretic clustering method first determines dense regions, which are local regions of high compactness, and then forms clusters by merging together those dense regions having high enough overlap. Using this procedure on handdrawn colon shapes copied from an X-ray and on handprinted characters, the parts determined by the clustering often correspond well to decompositions that a human might make.
