Perception is often described as a predictive process based on an optimal inference with respect to a generative model. We study here the principled construction of a generative model specifically crafted to probe motion perception. In that context, we first provide an axiomatic, biologically-driven derivation of the model. This model synthesizes random dynamic textures which are defined by stationary Gaussian distributions obtained by the random aggregation of warped patterns. Importantly, we show that this model can equivalently be described as a stochastic partial differential equation. Using this characterization of motion in images, it allows us to recast motion-energy models into a principled Bayesian inference framework. Finally, we apply these textures in order to psychophysically probe speed perception in humans. In this framework, while the likelihood is derived from the generative model, the prior is estimated from the observed results and accounts for the perceptual bias in a principled fashion.

Significant progress has been made for speech-driven 3D face animation, but most works focus on learning the motion of mesh/geometry, ignoring the impact of dynamic texture. In this work, we reveal that dynamic texture plays a key role in rendering high-fidelity talking avatars, and introduce a high-resolution 4D dataset \textbf{TexTalk4D}, consisting of 100 minutes of audio-synced scan-level meshes with detailed 8K dynamic textures from 100 subjects. Based on the dataset, we explore the inherent correlation between motion and texture, and propose a diffusion-based framework \textbf{TexTalker} to simultaneously generate facial motions and dynamic textures from speech. Furthermore, we propose a novel pivot-based style injection strategy to capture the complicity of different texture and motion styles, which allows disentangled control. TexTalker, as the first method to generate audio-synced facial motion with dynamic texture, not only outperforms the prior arts in synthesising facial motions, but also produces realistic textures that are consistent with the underlying facial movements. Project page: https://xuanchenli.github.io/TexTalk/.

We propose a method to reproduce dynamic appearance textures with space-stationary but time-varying visual statistics. While most previous work decomposes dynamic textures into static appearance and motion, we focus on dynamic appearance that results not from motion but variations of fundamental properties, such as rusting, decaying, melting, and weathering. To this end, we adopt the neural ordinary differential equation (ODE) to learn the underlying dynamics of appearance from a target exemplar. We simulate the ODE in two phases. At the "warm-up" phase, the ODE diffuses a random noise to an initial state. We then constrain the further evolution of this ODE to replicate the evolution of visual feature statistics in the exemplar during the generation phase. The particular innovation of this work is the neural ODE achieving both denoising and evolution for dynamics synthesis, with a proposed temporal training scheme. We study both relightable (BRDF) and non-relightable (RGB) appearance models. For both we introduce new pilot datasets, allowing, for the first time, to study such phenomena: For RGB we provide 22 dynamic textures acquired from free online sources; For BRDFs, we further acquire a dataset of 21 flash-lit videos of time-varying materials, enabled by a simple-to-construct setup. Our experiments show that our method consistently yields realistic and coherent results, whereas prior works falter under pronounced temporal appearance variations. A user study confirms our approach is preferred to previous work for such exemplars.

The main challenge of dynamic texture synthesis lies in how to maintain spatial and temporal consistency in synthesized videos. The major drawback of existing dynamic texture synthesis models comes from poor treatment of the long-range texture correlation and motion information. To address this problem, we incorporate a new loss term, called the Shifted Gram loss, to capture the structural and long-range correlation of the reference texture video. Furthermore, we introduce a frame sampling strategy to exploit long-period motion across multiple frames. With these two new techniques, the application scope of existing texture synthesis models can be extended. That is, they can synthesize not only homogeneous but also structured dynamic texture patterns. Thorough experimental results are provided to demonstrate that our proposed dynamic texture synthesis model offers state-of-the-art visual performance.

Perception is often described as a predictive process based on an optimal inference with respect to a generative model. We study here the principled construction of a generative model specifically crafted to probe motion perception. In that context, we first provide an axiomatic, biologically-driven derivation of the model. This model synthesizes random dynamic textures which are defined by stationary Gaussian distributions obtained by the random aggregation of warped patterns. Importantly, we show that this model can equivalently be described as a stochastic partial differential equation.

Generative dynamic texture models (GDTMs) are widely used for dynamic texture (DT) segmentation in the video sequences. GDTMs represent DTs as a set of linear dynamical systems (LDSs). A major limitation of these models concerns the automatic selection of a proper number of DTs. Dirichlet process mixture (DPM) models which have appeared recently as the cornerstone of the non-parametric Bayesian statistics, is an optimistic candidate toward resolving this issue. Under this motivation to resolve the aforementioned drawback, we propose a novel non-parametric fully Bayesian approach for DT segmentation, formulated on the basis of a joint DPM and GDTM construction. This interaction causes the algorithm to overcome the problem of automatic segmentation properly. We derive the Variational Bayesian Expectation-Maximization (VBEM) inference for the proposed model. Moreover, in the E-step of inference, we apply Rauch-Tung-Striebel smoother (RTSS) algorithm on Variational Bayesian LDSs. Ultimately, experiments on different video sequences are performed. Experiment results indicate that the proposed algorithm outperforms the previous methods in efficiency and accuracy noticeably.

This paper studies the dynamic generator model for spatial-temporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a non-linear transformation of a latent state vector, where the non-linear transformation is parametrized by a top-down neural network. The sequence of latent state vectors follows a non-linear auto-regressive model, where the state vector of the next frame is a non-linear transformation of the state vector of the current frame as well as an independent noise vector that provides randomness in the transition. The non-linear transformation of this transition model can be parametrized by a feedforward neural network. We show that this model can be learned by an alternating back-propagation through time algorithm that iteratively samples the noise vectors and updates the parameters in the transition model and the generator model. We show that our training method can learn realistic models for dynamic textures and action patterns.

Video sequences contain rich dynamic patterns, such as dynamic texture patterns that exhibit stationarity in the temporal domain, and action patterns that are non-stationary in either spatial or temporal domain. We show that a spatial-temporal generative ConvNet can be used to model and synthesize dynamic patterns. The model defines a probability distribution on the video sequence, and the log probability is defined by a spatial-temporal ConvNet that consists of multiple layers of spatial-temporal filters to capture spatial-temporal patterns of different scales. The model can be learned from the training video sequences by an "analysis by synthesis" learning algorithm that iterates the following two steps. Step 1 synthesizes video sequences from the currently learned model. Step 2 then updates the model parameters based on the difference between the synthesized video sequences and the observed training sequences. We show that the learning algorithm can synthesize realistic dynamic patterns.

Stability is a desirable characteristic for linear dynamical systems, but it is often ignored by algorithms that learn these systems from data. We propose a novel method for learning stable linear dynamical systems: we formulate an approximation of the problem as a convex program, start with a solution to a relaxed version of the program, and incrementally add constraints to improve stability. Rather than continuing to generate constraints until we reach a feasible solution, we test stability at each step; because the convex program is only an approximation of the desired problem, this early stopping rule can yield a higher-quality solution. We apply our algorithm to the task of learning dynamic textures from image sequences as well as to modeling biosurveillance drug-sales data. The constraint generation approach leads to noticeable improvement in the quality of simulated sequences. We compare our method to those of Lacy and Bernstein [1, 2], with positive results in terms of accuracy, quality of simulated sequences, and efficiency.

Stability is a desirable characteristic for linear dynamical systems, but it is often ignored by algorithms that learn these systems from data. We propose a novel method for learning stable linear dynamical systems: we formulate an approximation of the problem as a convex program, start with a solution to a relaxed version of the program, and incrementally add constraints to improve stability. Rather than continuing to generate constraints until we reach a feasible solution, we test stability at each step; because the convex program is only an approximation of the desired problem, this early stopping rule can yield a higher-quality solution. We apply our algorithm to the task of learning dynamic textures from image sequences as well as to modeling biosurveillance drug-sales data. The constraint generation approach leads to noticeable improvement in the quality of simulated sequences. We compare our method to those of Lacy and Bernstein [1, 2], with positive results in terms of accuracy, quality of simulated sequences, and efficiency.