A Closest Point Proposal for MCMC-based Probabilistic Surface Registration

We propose to view non-rigid surface registration as a probabilistic inference problem. Given a target surface, we estimate the posterior distribution of surface registrations. We demonstrate how the posterior distribution can be used to build shape models that generalize better and show how to visualize the uncertainty in the established correspondence. Furthermore, in a reconstruction task, we show how to estimate the posterior distribution of missing data without assuming a fixed point-to-point correspondence. We introduce the closest-point proposal for the Metropolis-Hastings algorithm. Our proposal overcomes the limitation of slow convergence compared to a random-walk strategy. As the algorithm decouples inference from modeling the posterior using a propose-and-verify scheme, we show how to choose different distance measures for the likelihood model. All presented results are fully reproducible using publicly available data and our open-source implementation of the registration framework

SUM: Sequential Scene Understanding and Manipulation

In order to perform autonomous sequential manipulation tasks, perception in cluttered scenes remains a critical challenge for robots. In this paper, we propose a probabilistic approach for robust sequential scene estimation and manipulation - Sequential Scene Understanding and Manipulation(SUM). SUM considers uncertainty due to discriminative object detection and recognition in the generative estimation of the most likely object poses maintained over time to achieve a robust estimation of the scene under heavy occlusions and unstructured environment. Our method utilizes candidates from discriminative object detector and recognizer to guide the generative process of sampling scene hypothesis, and each scene hypotheses is evaluated against the observations. Also SUM maintains beliefs of scene hypothesis over robot physical actions for better estimation and against noisy detections. We conduct extensive experiments to show that our approach is able to perform robust estimation and manipulation

Improved fMRI-based Pain Prediction using Bayesian Group-wise Functional Registration

In recent years, neuroimaging has undergone a paradigm shift, moving away from the traditional brain mapping approach toward developing integrated, multivariate brain models that can predict categories of mental events. However, large interindividual differences in brain anatomy and functional localization after standard anatomical alignment remain a major limitation in performing this analysis, as it leads to feature misalignment across subjects in subsequent predictive models

Generative shape and image analysis by combining Gaussian processes and MCMC sampling

Fully automatic analysis of faces is important for automatic access control, human computer interaction or for automatically evaluate surveillance videos. For humans it is easy to look at and interpret faces. Assigning attributes, moods or even intentions to the depicted person seem to happen without any difficulty. In contrast computers struggle even for simple questions and still fail to answer more demanding questions like: "Are these two persons looking at each other?" The interpretation of an image depicting a face is facilitated using a generative model for faces. Modeling the variability between persons, illumination, view angle or occlusions lead to a rich abstract representation. The model state encodes comprehensive information reducing the effort needed to solve a wide variety of tasks. However, to use a generative model, first the model needs to be built and secondly the model has to be adapted to a particular image. There exist many highly tuned algorithms for either of these steps. Most algorithms require more or less user input. These algorithms often lack robustness, full automation or wide applicability to different objects or data modalities. Our main contribution in this PhD-thesis is the presentation of a general, probabilistic framework to build and adapt generative models. Using the framework, we exploit information probabilistically in the domain it originates from, independent of the problem domain. The framework combines Gaussian processes and Data-Driven MCMC sampling. The generative models are built using the Gaussian process formulation. To adapt a model we use the Metropolis Hastings algorithm based on a propose-and-verify strategy. The framework consists of different well separated parts. Model building is separated from the adaptation. The adaptation is further separated into update proposals and a verification layer. This allows to adapt, exchange, remove or integrate individual parts without changes to other parts. The framework is presented in the context of facial data analysis. We introduce a new kernel exploiting the symmetry of faces and augment a learned generative model with additional flexibility. We show how a generative model is rigidly aligned, non-rigidly registered or adapted to 2d images with the same basic algorithm. We exploit information from 2d images to constrain 3d registration. We integrate directed proposal into sampling shifting the algorithm towards stochastic optimization. We show how to handle missing data by adapting the used likelihood model. We integrate a discriminative appearance model into the image likelihood model to handle occlusions. We demonstrate the wide applicability of our framework by solving also medical image analysis problems reusing the parts introduced for faces

Efficient Belief Propagation for Perception and Manipulation in Clutter

Autonomous service robots are required to perform tasks in common human indoor environments. To achieve goals associated with these tasks, the robot should continually perceive, reason its environment, and plan to manipulate objects, which we term as goal-directed manipulation. Perception remains the most challenging aspect of all stages, as common indoor environments typically pose problems in recognizing objects under inherent occlusions with physical interactions among themselves. Despite recent progress in the field of robot perception, accommodating perceptual uncertainty due to partial observations remains challenging and needs to be addressed to achieve the desired autonomy. In this dissertation, we address the problem of perception under uncertainty for robot manipulation in cluttered environments using generative inference methods. Specifically, we aim to enable robots to perceive partially observable environments by maintaining an approximate probability distribution as a belief over possible scene hypotheses. This belief representation captures uncertainty resulting from inter-object occlusions and physical interactions, which are inherently present in clutterred indoor environments. The research efforts presented in this thesis are towards developing appropriate state representations and inference techniques to generate and maintain such belief over contextually plausible scene states. We focus on providing the following features to generative inference while addressing the challenges due to occlusions: 1) generating and maintaining plausible scene hypotheses, 2) reducing the inference search space that typically grows exponentially with respect to the number of objects in a scene, 3) preserving scene hypotheses over continual observations. To generate and maintain plausible scene hypotheses, we propose physics informed scene estimation methods that combine a Newtonian physics engine within a particle based generative inference framework. The proposed variants of our method with and without a Monte Carlo step showed promising results on generating and maintaining plausible hypotheses under complete occlusions. We show that estimating such scenarios would not be possible by the commonly adopted 3D registration methods without the notion of a physical context that our method provides. To scale up the context informed inference to accommodate a larger number of objects, we describe a factorization of scene state into object and object-parts to perform collaborative particle-based inference. This resulted in the Pull Message Passing for Nonparametric Belief Propagation (PMPNBP) algorithm that caters to the demands of the high-dimensional multimodal nature of cluttered scenes while being computationally tractable. We demonstrate that PMPNBP is orders of magnitude faster than the state-of-the-art Nonparametric Belief Propagation method. Additionally, we show that PMPNBP successfully estimates poses of articulated objects under various simulated occlusion scenarios. To extend our PMPNBP algorithm for tracking object states over continuous observations, we explore ways to propose and preserve hypotheses effectively over time. This resulted in an augmentation-selection method, where hypotheses are drawn from various proposals followed by the selection of a subset using PMPNBP that explained the current state of the objects. We discuss and analyze our augmentation-selection method with its counterparts in belief propagation literature. Furthermore, we develop an inference pipeline for pose estimation and tracking of articulated objects in clutter. In this pipeline, the message passing module with the augmentation-selection method is informed by segmentation heatmaps from a trained neural network. In our experiments, we show that our proposed pipeline can effectively maintain belief and track articulated objects over a sequence of observations under occlusion.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163159/1/kdesingh_1.pd

Approximating Intersections and Differences Between Linear Statistical Shape Models Using Markov Chain Monte Carlo

To date, the comparison of Statistical Shape Models (SSMs) is often solely performance-based, carried out by means of simplistic metrics such as compactness, generalization, or specificity. Any similarities or differences between the actual shape spaces can neither be visualized nor quantified. In this paper, we present a new method to qualitatively compare two linear SSMs in dense correspondence by computing approximate intersection spaces and set-theoretic differences between the (hyper-ellipsoidal) allowable shape domains spanned by the models. To this end, we approximate the distribution of shapes lying in the intersection space using Markov chain Monte Carlo and subsequently apply Principal Component Analysis (PCA) to the posterior samples, eventually yielding a new SSM of the intersection space. We estimate differences between linear SSMs in a similar manner; here, however, the resulting spaces are no longer convex and we do not apply PCA but instead use the posterior samples for visualization. We showcase the proposed algorithm qualitatively by computing and analyzing intersection spaces and differences between publicly available face models, focusing on gender-specific male and female as well as identity and expression models. Our quantitative evaluation based on SSMs built from synthetic and real-world data sets provides detailed evidence that the introduced method is able to recover ground-truth intersection spaces and differences accurately.Comment: Accepted to WACV'2

A Probabilistic Treatment To Point Cloud Matching And Motion Estimation

Probabilistic and efficient motion estimation is paramount in many robotic applications, including state estimation and position tracking. Iterative closest point (ICP) is a popular algorithm that provides ego-motion estimates for mobile robots by matching point cloud pairs. Estimating motion efficiently using ICP is challenging due to the large size of point clouds. Further, sensor noise and environmental uncertainties result in uncertain motion and state estimates. Probabilistic inference is a principled approach to quantify uncertainty but is computationally expensive and thus challenging to use in complex real-time robotics tasks. In this thesis, we address these challenges by leveraging recent advances in optimization and probabilistic inference and present four core contributions. First is SGD-ICP, which employs stochastic gradient descent (SGD) to align two point clouds efficiently. The second is Bayesian-ICP, which combines SGD-ICP with stochastic gradient Langevin dynamics to obtain distributions over transformations efficiently. We also propose an adaptive motion model that employs Bayesian-ICP to produce environment-aware proposal distributions for state estimation. The third is Stein-ICP, a probabilistic ICP technique that exploits GPU parallelism for speed gains. Stein-ICP exploits the Stein variational gradient descent framework to provide non-parametric estimates of the transformation and can model complex multi-modal distributions. The fourth contribution is Stein particle filter, capable of filtering non-Gaussian, high-dimensional dynamical systems. This method can be seen as a deterministic flow of particles from an initial to the desired state. This transport of particles is embedded in a reproducing kernel Hilbert space where particles interact with each other through a repulsive force that brings diversity among the particles