Deep Directional Statistics: Pose Estimation with Uncertainty Quantification

Modern deep learning systems successfully solve many perception tasks such as object pose estimation when the input image is of high quality. However, in challenging imaging conditions such as on low-resolution images or when the image is corrupted by imaging artifacts, current systems degrade considerably in accuracy. While a loss in performance is unavoidable, we would like our models to quantify their uncertainty in order to achieve robustness against images of varying quality. Probabilistic deep learning models combine the expressive power of deep learning with uncertainty quantification. In this paper, we propose a novel probabilistic deep learning model for the task of angular regression. Our model uses von Mises distributions to predict a distribution over object pose angle. Whereas a single von Mises distribution is making strong assumptions about the shape of the distribution, we extend the basic model to predict a mixture of von Mises distributions. We show how to learn a mixture model using a finite and infinite number of mixture components. Our model allows for likelihood-based training and efficient inference at test time. We demonstrate on a number of challenging pose estimation datasets that our model produces calibrated probability predictions and competitive or superior point estimates compared to the current state-of-the-art

Robust and Efficient Deep Visual Learning

The past decade was marked by significant progress in the field of artificial intelligence and statistical learning. However, the most impressive of modern models come in the form of computationally expensive black boxes, with the majority of them lacking the ability to reason about the confidence of their predictions robustly. Being capable of quantifying model uncertainty and recognizing failure scenarios is crucial when it comes to incorporating them into complex decision-making pipelines, e.g. autonomous driving or medical image analysis systems. It is also important to maintain a low computational cost of these models. In the present thesis, the aforementioned desired properties of robustness and efficiency of deep learning models are studied and developed in the three specific realms of computer vision. First, we investigate deep probabilistic models that allow uncertainty quantification, i.e. the models that "know what they do not know". Here, we propose a novel model for the task of angular regression that allows probabilistic object pose estimation from 2D images. We also showcase how the general deep density estimation paradigm can be adapted and utilized in two other real-world applications, ball trajectory prediction and brain imaging. Next, we turn to the field of 3D shape analysis and rendering. We propose a method for efficient encoding of 3D point clouds, the type of data that is hard to handle with conventional learning algorithms due to its unordered nature. We show that simple neural networks that use the developed encoding as input can match the performance of state-of-the-art methods on various point cloud processing tasks while using orders of magnitude less floating-point operations. Finally, we explore the emerging field of neural rendering and develop the framework that connects classic deformable 3D body models with modern image-to-image translation neural networks. This combination allows efficient photorealistic human avatar rendering in a controlled manner, with the possibility to control the camera flexibly and to change the body pose and shape appearance. The thesis concludes with the discussion of the presented methods, including current limitations and future research directions

ResFields: Residual Neural Fields for Spatiotemporal Signals

Neural fields, a category of neural networks trained to represent high-frequency signals, have gained significant attention in recent years due to their impressive performance in modeling complex 3D data, especially large neural signed distance (SDFs) or radiance fields (NeRFs) via a single multi-layer perceptron (MLP). However, despite the power and simplicity of representing signals with an MLP, these methods still face challenges when modeling large and complex temporal signals due to the limited capacity of MLPs. In this paper, we propose an effective approach to address this limitation by incorporating temporal residual layers into neural fields, dubbed ResFields, a novel class of networks specifically designed to effectively represent complex temporal signals. We conduct a comprehensive analysis of the properties of ResFields and propose a matrix factorization technique to reduce the number of trainable parameters and enhance generalization capabilities. Importantly, our formulation seamlessly integrates with existing techniques and consistently improves results across various challenging tasks: 2D video approximation, dynamic shape modeling via temporal SDFs, and dynamic NeRF reconstruction. Lastly, we demonstrate the practical utility of ResFields by showcasing its effectiveness in capturing dynamic 3D scenes from sparse sensory inputs of a lightweight capture system.Comment: Project page and code at https://markomih.github.io/ResFields

Real Time Trajectory Prediction Using Deep Conditional Generative Models

Data driven methods for time series forecasting that quantify uncertainty open new important possibilities for robot tasks with hard real time constraints, allowing the robot system to make decisions that trade off between reaction time and accuracy in the predictions. Despite the recent advances in deep learning, it is still challenging to make long term accurate predictions with the low latency required by real time robotic systems. In this paper, we propose a deep conditional generative model for trajectory prediction that is learned from a data set of collected trajectories. Our method uses encoder and decoder deep networks that maps complete or partial trajectories to a Gaussian distributed latent space and back, allowing for fast inference of the future values of a trajectory given previous observations. The encoder and decoder networks are trained using stochastic gradient variational Bayes. In the experiments, we show that our model provides more accurate long term predictions with a lower latency that popular models for trajectory forecasting like recurrent neural networks or physical models based on differential equations. Finally, we test our proposed approach in a robot table tennis scenario to evaluate the performance of the proposed method in a robotic task with hard real time constraints

Антиплоская осесимметричная деформация несжимаемого тела в условиях ползучести

Flow of incompressible medium under varying gradient of pressure is considered. It is assumed that medium exhibits nonlinear elastic and creep behavior. The theory of large strains based on transport equations for the tensors of reversible and irreversible deformations is used for problem formulation. Analytical and numerical methods are applied to solve the problemРассматривается течение несжимаемой среды в цилиндрической трубе под действием изменяю- щегося перепада давления. Материал проявляет нелинейные упругие и вязкие свойства. Матема- тическая модель строится с использованием теории больших деформаций, основанной на диффе- ренциальных уравнениях переноса для обратимых и необратимых деформаций. Решение ищется с помощью аналитических и численных методо

Антиплоская деформация упрочняющейся упруговязкопластической среды

Deforming of hardening elastoviscoplastic medium under the action of variable pressure gradient is con- sidered in this paper. The displacement vector of material points has only vertical component. Mathe- matical model is based on the theory of large elastoplastic deformations. Differential transport equations of tensors of reversible and irreversible deformations are formulated. Irreversible deformations are split up into plastic and creep deformations. The solution is obtained with the use of analytical and numerical methods. The influence of hardening and viscosity parameters on medium deformation is analyzed.В работе рассмотрена деформация упрочняющейся упруговязкопластической среды под действием изменяющегося перепада давления. Вектор перемещений точек среды имеет только вертикальную компоненту. Математическая модель основана на теории больших упругопластических деформаций, в рамках которой сформулированы дифференциальные уравнения переноса тензоров обратимых и необратимых деформаций. При этом необратимые деформации включают в себя деформации ползучести и пластические деформации. Решение задачи получено с использованием аналитических и численных методов. Проанализировано влияние параметров упрочнения и вязкости на деформирование сред

Антиплоская деформация упрочняющейся упруговязкопластической среды

Deforming of hardening elastoviscoplastic medium under the action of variable pressure gradient is con- sidered in this paper. The displacement vector of material points has only vertical component. Mathe- matical model is based on the theory of large elastoplastic deformations. Differential transport equations of tensors of reversible and irreversible deformations are formulated. Irreversible deformations are split up into plastic and creep deformations. The solution is obtained with the use of analytical and numerical methods. The influence of hardening and viscosity parameters on medium deformation is analyzed.В работе рассмотрена деформация упрочняющейся упруговязкопластической среды под действием изменяющегося перепада давления. Вектор перемещений точек среды имеет только вертикальную компоненту. Математическая модель основана на теории больших упругопластических деформаций, в рамках которой сформулированы дифференциальные уравнения переноса тензоров обратимых и необратимых деформаций. При этом необратимые деформации включают в себя деформации ползучести и пластические деформации. Решение задачи получено с использованием аналитических и численных методов. Проанализировано влияние параметров упрочнения и вязкости на деформирование сред