Incorporating uncertainty in environmental models informed by imagery

In this thesis, the issue of incorporating uncertainty for environmental modelling informed by imagery is explored by considering uncertainty in deterministic modelling, measurement uncertainty and uncertainty in image composition. Incorporating uncertainty in deterministic modelling is extended for use with imagery using the Bayesian melding approach. In the application presented, slope steepness is shown to be the main contributor to total uncertainty in the Revised Universal Soil Loss Equation. A spatial sampling procedure is also proposed to assist in implementing Bayesian melding given the increased data size with models informed by imagery. Measurement error models are another approach to incorporating uncertainty when data is informed by imagery. These models for measurement uncertainty, considered in a Bayesian conditional independence framework, are applied to ecological data generated from imagery. The models are shown to be appropriate and useful in certain situations. Measurement uncertainty is also considered in the context of change detection when two images are not co-registered. An approach for detecting change in two successive images is proposed that is not affected by registration. The procedure uses the Kolmogorov-Smirnov test on homogeneous segments of an image to detect change, with the homogeneous segments determined using a Bayesian mixture model of pixel values. Using the mixture model to segment an image also allows for uncertainty in the composition of an image. This thesis concludes by comparing several different Bayesian image segmentation approaches that allow for uncertainty regarding the allocation of pixels to different ground components. Each segmentation approach is applied to a data set of chlorophyll values and shown to have different benefits and drawbacks depending on the aims of the analysis.

Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

Towards automatic object segmentation with sequential multiple views

Object segmentation is one of the fundamental steps for a number of robotic applications such as manipulation, object detection, and obstacle avoidance. This paper proposes a visual method for incorporating colour and depth information from sequential multiview stereo images to segment objects of interest from complex and cluttered environments. Rather than segmenting objects using information from a single frame in the sequence, we incorporate information from neighbouring views to increase the reliability of the information and improve the overall segmentation result. Specifically, dense depth information of a scene is computed using multiple view stereo. Depths from neighbouring views are reprojected into the reference frame to be segmented compensating for imperfect depth computations for individual frames. The multiple depth layers are then combined with color information from the reference frame to create a Markov random field to model the segmentation problem. Finally, graphcut optimisation is employed to infer pixels belonging to the object to be segmented. The segmentation accuracy is evaluated over images from an outdoor video sequence demonstrating the viability for automatic object segmentation for mobile robots using monocular cameras as a primary sensor.

Variational Bayes and the reduced dependence approximation for the autologistic model on an irregular grid with applications

Discrete Markov random field models provide a natural framework for representing images or spatial datasets. They model the spatial association present while providing a convenient Markovian dependency structure and strong edge-preservation properties. However, parameter estimation for discrete Markov random field models is difficult due to the complex form of the associated normalizing constant for the likelihood function. For large lattices, the reduced dependence approximation to the normalizing constant is based on the concept of performing computationally efficient and feasible forward recursions on smaller sublattices which are then suitably combined to estimate the constant for the whole lattice. We present an efficient computational extension of the forward recursion approach for the autologistic model to lattices that have an irregularly shaped boundary and which may contain regions with no data; these lattices are typical in applications. Consequently, we also extend the reduced dependence approximation to these scenarios enabling us to implement a practical and efficient non-simulation based approach for spatial data analysis within the variational Bayesian framework. The methodology is illustrated through application to simulated data and example images. The supplemental materials include our C++ source code for computing the approximate normalizing constant and simulation studies.

Automatic object segmentation of unstructured scenes using colour and depth maps

This study presents a segmentation pipeline that fuses colour and depth information to automatically separate objects of interest in video sequences captured from a quadcopter. Many approaches assume that cameras are static with known position, a condition which cannot be preserved in most outdoor robotic applications. In this study, the authors compute depth information and camera positions from a monocular video sequence using structure from motion and use this information as an additional cue to colour for accurate segmentation. The authors model the problem similarly to standard segmentation routines as a Markov random field and perform the segmentation using graph cuts optimisation. Manual intervention is minimised and is only required to determine pixel seeds in the first frame which are then automatically reprojected into the remaining frames of the sequence. The authors also describe an automated method to adjust the relative weights for colour and depth according to their discriminative properties in each frame. Experimental results are presented for two video sequences captured using a quadcopter. The quality of the segmentation is compared to a ground truth and other state-of-the-art methods with consistently accurate results.

Bayesian computational methods for spatial analysis of images

This thesis introduces a new way of using prior information in a spatial model and develops scalable algorithms for fitting this model to large imaging datasets. These methods are employed for image-guided radiation therapy and satellite based classification of land use and water quality. This study has utilized a pre-computation step to achieve a hundredfold improvement in the elapsed runtime for model fitting. This makes it much more feasible to apply these models to real-world problems, and enables full Bayesian inference for images with a million or more pixels.

Scalable Bayesian Computation for intractable likelihoods in image analysis

The inverse temperature hyperparameter of the hidden Potts model governs the strength of spatial cohesion and therefore has a substantial influence over the resulting model fit. The difficulty arises from the dependence of an intractable normalising constant on the value of the inverse temperature, thus there is no closed form solution for sampling from the distribution directly. We review three computational approaches for addressing this issue, namely pseudolikelihood, path sampling, and the approximate exchange algorithm. We compare the accuracy and scalability of these methods using a simulation study.

Hydraulic conductivity fields: Gaussian or not?

Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high-resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales.

Diffusion indices on magnetic resonance imaging and neuropsychological performance in amnestic mild cognitive impairment

Background: Magnetic resonance diffusion tensor imaging (DTI) shows promise in the early detection of microstructural pathophysiological changes in the brain. Objectives: To measure microstructural differences in the brains of participants with amnestic mild cognitive impairment (MCI) compared with an age-matched control group using an optimised DTI technique with fully automated image analysis tools and to investigate the correlation between diffusivity measurements and neuropsychological performance scores across groups. Methods: 34 participants (17 participants with MCI, 17 healthy elderly adults) underwent magnetic resonance imaging (MRI)-based DTI. To control for the effects of anatomical variation, diffusion images of all participants were registered to standard anatomical space. Significant statistical differences in diffusivity measurements between the two groups were determined on a pixel-by-pixel basis using gaussian random field theory. Results: Significantly raised mean diffusivity measurements (p<0.001) were observed in the left and right entorhinal cortices (BA28), posterior occipital-parietal cortex (BA18 and BA19), right parietal supramarginal gyrus (BA40) and right frontal precentral gyri (BA4 and BA6) in participants with MCI. With respect to fractional anisotropy, participants with MCI had significantly reduced measurements (p<0.001) in the limbic parahippocampal subgyral white matter, right thalamus and left posterior cingulate. Pearson's correlation coefficients calculated across all participants showed significant correlations between neuropsychological assessment scores and regional measurements of mean diffusivity and fractional anisotropy. Conclusions: DTI-based diffusivity measures may offer a sensitive method of detecting subtle microstructural brain changes associated with preclinical Alzheimer's disease.

Exponentiated gradient algorithms for large-margin structured classification

We consider the problem of structured classification, where the task is to predict a label y from an input x, and y has meaningful internal structure. Our framework includes supervised training of Markov random fields and weighted context-free grammars as special cases. We describe an algorithm that solves the large-margin optimization problem defined in [12], using an exponential-family (Gibbs distribution) representation of structured objects. The algorithm is efficient—even in cases where the number of labels y is exponential in size—provided that certain expectations under Gibbs distributions can be calculated efficiently. The method for structured labels relies on a more general result, specifically the application of exponentiated gradient updates [7, 8] to quadratic programs.

Finding additional semantic entity information for search engines

Entity-oriented search has become an essential component of modern search engines. It focuses on retrieving a list of entities or information about the specific entities instead of documents. In this paper, we study the problem of finding entity related information, referred to as attribute-value pairs, that play a significant role in searching target entities. We propose a novel decomposition framework combining reduced relations and the discriminative model, Conditional Random Field (CRF), for automatically finding entity-related attribute-value pairs from free text documents. This decomposition framework allows us to locate potential text fragments and identify the hidden semantics, in the form of attribute-value pairs for user queries. Empirical analysis shows that the decomposition framework outperforms pattern-based approaches due to its capability of effective integration of syntactic and semantic features.

GrabCutSFM : how 3D information improves unsupervised object segmentation

In this paper, we present an unsupervised graph cut based object segmentation method using 3D information provided by Structure from Motion (SFM), called Grab- CutSFM. Rather than focusing on the segmentation problem using a trained model or human intervention, our approach aims to achieve meaningful segmentation autonomously with direct application to vision based robotics. Generally, object (foreground) and background have certain discriminative geometric information in 3D space. By exploring the 3D information from multiple views, our proposed method can segment potential objects correctly and automatically compared to conventional unsupervised segmentation using only 2D visual cues. Experiments with real video data collected from indoor and outdoor environments verify the proposed approach.

Joint 2D and 3D cues for image segmentation towards robotic applications

This thesis investigates the fusion of 3D visual information with 2D image cues to provide 3D semantic maps of large-scale environments in which a robot traverses for robotic applications. A major theme of this thesis was to exploit the availability of 3D information acquired from robot sensors to improve upon 2D object classification alone. The proposed methods have been evaluated on several indoor and outdoor datasets collected from mobile robotic platforms including a quadcopter and ground vehicle covering several kilometres of urban roads.

Brain decoding based on functional magnetic resonance imaging using machine learning : a comparative study

Brain decoding of functional Magnetic Resonance Imaging data is a pattern analysis task that links brain activity patterns to the experimental conditions. Classifiers predict the neural states from the spatial and temporal pattern of brain activity extracted from multiple voxels in the functional images in a certain period of time. The prediction results offer insight into the nature of neural representations and cognitive mechanisms and the classification accuracy determines our confidence in understanding the relationship between brain activity and stimuli. In this paper, we compared the efficacy of three machine learning algorithms: neural network, support vector machines, and conditional random field to decode the visual stimuli or neural cognitive states from functional Magnetic Resonance data. Leave-one-out cross validation was performed to quantify the generalization accuracy of each algorithm on unseen data. The results indicated support vector machine and conditional random field have comparable performance and the potential of the latter is worthy of further investigation.

Structure matters: Adoption of structured classification Approach in the context of cognitive presence classification

Within online learning communities, receiving timely and meaningful insights into the quality of learning activities is an important part of an effective educational experience. Commonly adopted methods – such as the Community of Inquiry framework – rely on manual coding of online discussion transcripts, which is a costly and time consuming process. There are several efforts underway to enable the automated classification of online discussion messages using supervised machine learning, which would enable the real-time analysis of interactions occurring within online learning communities. This paper investigates the importance of incorporating features that utilise the structure of on-line discussions for the classification of "cognitive presence" – the central dimension of the Community of Inquiry framework focusing on the quality of students' critical thinking within online learning communities. We implemented a Conditional Random Field classification solution, which incorporates structural features that may be useful in increasing classification performance over other implementations. Our approach leads to an improvement in classification accuracy of 5.8% over current existing techniques when tested on the same dataset, with a precision and recall of 0.630 and 0.504 respectively.