Continuous dynamical systems are cornerstones of many scientific and engineering disciplines. While machine learning offers powerful tools to model these systems from trajectory data, challenges arise when these trajectories are captured as images, resulting in pixel-level observations that are discrete in nature. Consequently, a naive application of a convolutional autoencoder can result in latent coordinates that are discontinuous in time. To resolve this, we propose continuity-preserving convolutional autoencoders (CpAEs) to learn continuous latent states and their corresponding continuous latent dynamical models from discrete image frames. We present a mathematical formulation for learning dynamics from image frames, which illustrates issues with previous approaches and motivates our methodology based on promoting the continuity of convolution filters, thereby preserving the continuity of the latent states. This approach enables CpAEs to produce latent states that evolve continuously with the underlying dynamics, leading to more accurate latent dynamical models. Extensive experiments across various scenarios demonstrate the effectiveness of CpAEs.

In the tasks of pose estimation and behavior analysis in computer vision, conventional models are often constrained by various factors or complex environments (such as multiple targets, small targets, occluded targets, etc.). To address this problem, this paper proposes a symmetric cascaded additive network (MulAG) to improve the accuracy of posture estimation and behavior analysis in complex environments. MulAG consists of two modules, MulA and MulG. The MulA module is designed based on a cascaded symmetric network structure and incorporates the addition operation. MulA extracts the posture spatial features of the target from a single frame image. And, the MulG module is designed based on three continuous GRUs (gated recurrent unit). Based on the MulA, MulG extracts the posture temporal features from the posture spatial features of the moving target and predicts the posture temporal features of the moving target. The paper firstly demonstrates the feasibility of addition operations in pose estimation tasks by comparing with MobileNet-v3 in ablation experiments. Secondly, on the HiEve and CrowdPose datasets, MulA achieves accuracy of 79.6% and 80.4%, respectively, outperforming the PTM model by 12.0% and 21.2%. And detection speed of MulA achieves the best value at 8.6ms, which is 1 times higher than HDGCN. The result demonstrates the effectiveness of MulA in multi-target pose estimation in complex scenes. Finally, on the HDMB-51 and UCF-101 datasets, MulAG achieves accuracy of 74.8% and 86.3%, respectively, outperforming HDGCN by 9.6% and 9.5%. Compared with SKP and GIST, the fps of MulAG (44.8s-1) is improved by 8.2% and 8.9%. These experiments highlight the generalizability and superiority of MulAG in behavior analysis and pose estimation tasks.

Capturing sufficient global context and rich spatial structure information is critical for dense prediction tasks. Convolutional Neural Network (CNN) is particularly adept at modeling fine-grained local features, while Transformer excels at modeling global context information. It is evident that CNN and Transformer exhibit complementary characteristics. Exploring the design of a network, that efficiently fuses these two models to leverage their strengths fully and achieve more accurate detection, represents a promising and worthwhile research topic. In this paper, we introduce a novel CNN-Transformer Iterative Fusion Network (CTIF-Net) for salient object detection. It efficiently combines CNN and Transformer to achieve superior performance by using a parallel dual encoder structure and a feature iterative fusion module. Firstly, CTIF-Net extracts features from the image using the CNN and the Transformer, respectively. Secondly, two feature convertors and a feature iterative fusion module are employed to combine and iteratively refine the two sets of features. The experimental results on multiple SOD datasets show that CTIF-Net outperforms 17 state-of-the-art methods, achieving higher performance in various mainstream evaluation metrics such as F-measure, S-measure, and MAE value. The code will be publicly available.

The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. However, deciphering the numerical integration in Neural ODE is still an open challenge, as many researches demonstrated that numerical integration significantly affects the performance of the model. In this paper, we propose the inverse modified differential equations (IMDE) to clarify the influence of numerical integration on training Neural ODE models. IMDE is determined by the learning task and the employed ODE solver. It is shown that training a Neural ODE model actually returns a close approximation of the IMDE, rather than the true ODE. With the help of IMDE, we deduce that (i) the discrepancy between the learned model and the true ODE is bounded by the sum of discretization error and learning loss; (ii) Neural ODE using non-symplectic numerical integration fail to learn conservation laws theoretically. Several experiments are performed to numerically verify our theoretical analysis.