Linear and Nonlinear Generative Probabilistic Class Models for Shape Contours

We introduce a robust probabilistic approach to modeling shape contours based on a low- dimensional, nonlinear latent variable model. In contrast to existing techniques that use objective functions in data space without ex- plicit noise models, we are able to extract complex shape variation from noisy data. Most approaches to learning shape models slide observed data points around fixed con- tours and hence, require a correctly labeled ‘reference shape’ to prevent degenerate so- lutions. In our method, unobserved curves are reparameterized to explain the fixed data points, so this problem does not arise. The proposed algorithms are suitable for use with arbitrary basis functions and are applicable to both open and closed shapes; their effec- tiveness is demonstrated through illustrative examples, quantitative assessment on bench- mark data sets and a visualization task

Dynamical models and machine learning for supervised segmentation

This thesis is concerned with the problem of how to outline regions of interest in medical images, when the boundaries are weak or ambiguous and the region shapes are irregular. The focus on machine learning and interactivity leads to a common theme of the need to balance conflicting requirements. First, any machine learning method must strike a balance between how much it can learn and how well it generalises. Second, interactive methods must balance minimal user demand with maximal user control. To address the problem of weak boundaries,methods of supervised texture classification are investigated that do not use explicit texture features. These methods enable prior knowledge about the image to benefit any segmentation framework. A chosen dynamic contour model, based on probabilistic boundary tracking, combines these image priors with efficient modes of interaction. We show the benefits of the texture classifiers over intensity and gradient-based image models, in both classification and boundary extraction. To address the problem of irregular region shape, we devise a new type of statistical shape model (SSM) that does not use explicit boundary features or assume high-level similarity between region shapes. First, the models are used for shape discrimination, to constrain any segmentation framework by way of regularisation. Second, the SSMs are used for shape generation, allowing probabilistic segmentation frameworks to draw shapes from a prior distribution. The generative models also include novel methods to constrain shape generation according to information from both the image and user interactions. The shape models are first evaluated in terms of discrimination capability, and shown to out-perform other shape descriptors. Experiments also show that the shape models can benefit a standard type of segmentation algorithm by providing shape regularisers. We finally show how to exploit the shape models in supervised segmentation frameworks, and evaluate their benefits in user trials

Globally-Coordinated Locally-Linear Modeling of Multi-Dimensional Data

This thesis considers the problem of modeling and analysis of continuous, locally-linear, multi-dimensional spatio-temporal data. Our work extends the previously reported theoretical work on the global coordination model to temporal analysis of continuous, multi-dimensional data. We have developed algorithms for time-varying data analysis and used them in full-scale, real-world applications. The applications demonstrated in this thesis include tracking, synthesis, recognitions and retrieval of dynamic objects based on their shape, appearance and motion. The proposed approach in this thesis has advantages over existing approaches to analyzing complex spatio-temporal data. Experiments show that the new modeling features of our approach improve the performance of existing approaches in many applications. In object tracking, our approach is the first one to track nonlinear appearance variations by using low-dimensional representation of the appearance change in globally-coordinated linear subspaces. In dynamic texture synthesis, we are able to model non-stationary dynamic textures, which cannot be handled by any of the existing approaches. In human motion synthesis, we show that realistic synthesis can be performed without using specific transition points, or key frames

Hierarchical Object Parsing from Structured Noisy Point Clouds

Object parsing and segmentation from point clouds are challenging tasks because the relevant data is available only as thin structures along object boundaries or other features, and is corrupted by large amounts of noise. To handle this kind of data, flexible shape models are desired that can accurately follow the object boundaries. Popular models such as Active Shape and Active Appearance models lack the necessary flexibility for this task, while recent approaches such as the Recursive Compositional Models make model simplifications in order to obtain computational guarantees. This paper investigates a hierarchical Bayesian model of shape and appearance in a generative setting. The input data is explained by an object parsing layer, which is a deformation of a hidden PCA shape model with Gaussian prior. The paper also introduces a novel efficient inference algorithm that uses informed data-driven proposals to initialize local searches for the hidden variables. Applied to the problem of object parsing from structured point clouds such as edge detection images, the proposed approach obtains state of the art parsing errors on two standard datasets without using any intensity information.Comment: 13 pages, 16 figure

Deep Normalizing Flows for State Estimation

Safe and reliable state estimation techniques are a critical component of next-generation robotic systems. Agents in such systems must be able to reason about the intentions and trajectories of other agents for safe and efficient motion planning. However, classical state estimation techniques such as Gaussian filters often lack the expressive power to represent complex underlying distributions, especially if the system dynamics are highly nonlinear or if the interaction outcomes are multi-modal. In this work, we use normalizing flows to learn an expressive representation of the belief over an agent's true state. Furthermore, we improve upon existing architectures for normalizing flows by using more expressive deep neural network architectures to parameterize the flow. We evaluate our method on two robotic state estimation tasks and show that our approach outperforms both classical and modern deep learning-based state estimation baselines.Comment: Accepted to FUSION 202