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This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the piecewise polynomials of degrees $m\ (m\geq1)$ and $m-1$ respectively to approximate the velocity and pressure inside the elements, and piecewise polynomials of degree $m$ to approximate their numerical traces on the interfaces of elements. In the fully discrete method, the backward Euler difference scheme is used to approximate the time derivative. The methods are shown to yield globally divergence-free velocity approximation. Optimal a priori error estimates in the energy norm and $L^2$ norm are established. A convergent linearized iterative algorithm is designed for solving the fully discrete system. Numerical experiments are provided to verify the theoretical results., Comment: 34 pages, 68 figures. arXiv admin note: text overlap with arXiv:2401.15470

We present a method for generating video sequences with coherent motion between a pair of input key frames. We adapt a pretrained large-scale image-to-video diffusion model (originally trained to generate videos moving forward in time from a single input image) for key frame interpolation, i.e., to produce a video in between two input frames. We accomplish this adaptation through a lightweight fine-tuning technique that produces a version of the model that instead predicts videos moving backwards in time from a single input image. This model (along with the original forward-moving model) is subsequently used in a dual-directional diffusion sampling process that combines the overlapping model estimates starting from each of the two keyframes. Our experiments show that our method outperforms both existing diffusion-based methods and traditional frame interpolation techniques., Comment: project page: https://svd-keyframe-interpolation.github.io/

A jump cut offers an abrupt, sometimes unwanted change in the viewing experience. We present a novel framework for smoothing these jump cuts, in the context of talking head videos. We leverage the appearance of the subject from the other source frames in the video, fusing it with a mid-level representation driven by DensePose keypoints and face landmarks. To achieve motion, we interpolate the keypoints and landmarks between the end frames around the cut. We then use an image translation network from the keypoints and source frames, to synthesize pixels. Because keypoints can contain errors, we propose a cross-modal attention scheme to select and pick the most appropriate source amongst multiple options for each key point. By leveraging this mid-level representation, our method can achieve stronger results than a strong video interpolation baseline. We demonstrate our method on various jump cuts in the talking head videos, such as cutting filler words, pauses, and even random cuts. Our experiments show that we can achieve seamless transitions, even in the challenging cases where the talking head rotates or moves drastically in the jump cut., Comment: Correct typos in the caption of Figure 1; Change the project website address. Project page: https://jeanne-wang.github.io/jumpcutsmoothing/

We present a method that uses a text-to-image model to generate consistent content across multiple image scales, enabling extreme semantic zooms into a scene, e.g., ranging from a wide-angle landscape view of a forest to a macro shot of an insect sitting on one of the tree branches. We achieve this through a joint multi-scale diffusion sampling approach that encourages consistency across different scales while preserving the integrity of each individual sampling process. Since each generated scale is guided by a different text prompt, our method enables deeper levels of zoom than traditional super-resolution methods that may struggle to create new contextual structure at vastly different scales. We compare our method qualitatively with alternative techniques in image super-resolution and outpainting, and show that our method is most effective at generating consistent multi-scale content., Comment: Project page: https://powers-of-10.github.io/

We propose a sparse end-to-end multi-person pose regression framework, termed QueryPose, which can directly predict multi-person keypoint sequences from the input image. The existing end-to-end methods rely on dense representations to preserve the spatial detail and structure for precise keypoint localization. However, the dense paradigm introduces complex and redundant post-processes during inference. In our framework, each human instance is encoded by several learnable spatial-aware part-level queries associated with an instance-level query. First, we propose the Spatial Part Embedding Generation Module (SPEGM) that considers the local spatial attention mechanism to generate several spatial-sensitive part embeddings, which contain spatial details and structural information for enhancing the part-level queries. Second, we introduce the Selective Iteration Module (SIM) to adaptively update the sparse part-level queries via the generated spatial-sensitive part embeddings stage-by-stage. Based on the two proposed modules, the part-level queries are able to fully encode the spatial details and structural information for precise keypoint regression. With the bipartite matching, QueryPose avoids the hand-designed post-processes and surpasses the existing dense end-to-end methods with 73.6 AP on MS COCO mini-val set and 72.7 AP on CrowdPose test set. Code is available at https://github.com/buptxyb666/QueryPose., Comment: Published on NeurIPS 2022

Multi-person pose estimation generally follows top-down and bottom-up paradigms. Both of them use an extra stage ($\boldsymbol{e.g.,}$ human detection in top-down paradigm or grouping process in bottom-up paradigm) to build the relationship between the human instance and corresponding keypoints, thus leading to the high computation cost and redundant two-stage pipeline. To address the above issue, we propose to represent the human parts as adaptive points and introduce a fine-grained body representation method. The novel body representation is able to sufficiently encode the diverse pose information and effectively model the relationship between the human instance and corresponding keypoints in a single-forward pass. With the proposed body representation, we further deliver a compact single-stage multi-person pose regression network, termed as AdaptivePose. During inference, our proposed network only needs a single-step decode operation to form the multi-person pose without complex post-processes and refinements. We employ AdaptivePose for both 2D/3D multi-person pose estimation tasks to verify the effectiveness of AdaptivePose. Without any bells and whistles, we achieve the most competitive performance on MS COCO and CrowdPose in terms of accuracy and speed. Furthermore, the outstanding performance on MuCo-3DHP and MuPoTS-3D further demonstrates the effectiveness and generalizability on 3D scenes. Code is available at https://github.com/buptxyb666/AdaptivePose., Comment: Submit to IEEE TCSVT; 11 pages. arXiv admin note: text overlap with arXiv:2112.13635