Recovering 4D world from monocular video is a crucial yet challenging task. Conventional methods usually rely on the assumptions of multi-view videos, known camera parameters, or static scenes. In this paper, we relax all these constraints and tackle a highly ambitious but practical task: With only one monocular video without camera parameters, we aim to recover the dynamic 3D world alongside the camera poses. To solve this, we introduce GFlow, a new framework that utilizes only 2D priors (depth and optical flow) to lift a video to a 4D scene, as a flow of 3D Gaussians through space and time. GFlow starts by segmenting the video into still and moving parts, then alternates between optimizing camera poses and the dynamics of the 3D Gaussian points. This method ensures consistency among adjacent points and smooth transitions between frames. Since dynamic scenes always continually introduce new visual content, we present prior-driven initialization and pixel-wise densification strategy for Gaussian points to integrate new content. By combining all those techniques, GFlow transcends the boundaries of 4D recovery from causal videos; it naturally enables tracking of points and segmentation of moving objects across frames. Additionally, GFlow estimates the camera poses for each frame, enabling novel view synthesis by changing camera pose. This capability facilitates extensive scene-level or object-level editing, highlighting GFlow's versatility and effectiveness.

Prediction of abdominal aortic aneurysm (AAA) growth is of essential importance for the early treatment and surgical intervention of AAA. Capturing key features of vascular growth, such as blood flow and intraluminal thrombus (ILT) accumulation play a crucial role in uncovering the intricated mechanism of vascular adaptation, which can ultimately enhance AAA growth prediction capabilities. However, local correlations between hemodynamic metrics, biological and morphological characteristics, and AAA growth rates present high inter-patient variability that results in that the temporal-spatial biochemical and mechanical processes are still not fully understood. Hence, this study aims to integrate the physics-based knowledge with deep learning with a patch-based convolutional neural network (CNN) approach by incorporating important multiphysical features relating to its pathogenesis for validating its impact on AAA growth prediction. For this task, we observe that the unstructured multiphysical features cannot be directly employed in the kernel-based CNN. To tackle this issue, we propose a parameterization of features to leverage the spatio-temporal relations between multiphysical features. The proposed architecture was tested on different combinations of four features including radius, intraluminal thrombus thickness, time-average wall shear stress, and growth rate from 54 patients with 5-fold cross-validation with two metrics, a root mean squared error (RMSE) and relative error (RE). We conduct extensive experiments on AAA patients, the results show the effect of leveraging multiphysical features and demonstrate the superiority of the presented architecture to previous state-of-the-art methods in AAA growth prediction.

Translating recent advances in abdominal aortic aneurysm (AAA) growth and remodeling (G&R) knowledge into a predictive, patient-specific clinical treatment tool requires a major paradigm shift in computational modeling. The objectives of this study are to develop a prediction framework that first calibrates the physical AAA G&R model using patient-specific serial computed tomography (CT) scan images, predicts the expansion of an AAA in the future, and quantifies the associated uncertainty in the prediction. We adopt a Bayesian calibration method to calibrate parameters in the G&R computational model and predict the magnitude of AAA expansion. The proposed Bayesian approach can take different sources of uncertainty; therefore, it is well suited to achieve our aims in predicting the AAA expansion process as well as in computing the propagated uncertainty. We demonstrate how to achieve the proposed aims by solving the formulated Bayesian calibration problems for cases with the synthetic G&R model output data and real medical patient-specific CT data. We compare and discuss the performance of predictions and computation time under different sampling cases of the model output data and patient data, both of which are simulated by the G&R computation. Furthermore, we apply our Bayesian calibration to real patient-specific serial CT data and validate our prediction. The accuracy and efficiency of the proposed method is promising, which appeals to computational and medical communities.