We consider the problem of 3D shape recovery from ultra-fast motion-blurred images. While 3D reconstruction from static images has been extensively studied, recovering geometry from extreme motion-blurred images remains challenging. Such scenarios frequently occur in both natural and industrial settings, such as fast-moving objects in sports (e.g., balls) or rotating machinery, where rapid motion distorts object appearance and makes traditional 3D reconstruction techniques like Multi-View Stereo (MVS) ineffective. In this paper, we propose a novel inverse rendering approach for shape recovery from ultra-fast motion-blurred images. While conventional rendering techniques typically synthesize blur by averaging across multiple frames, we identify a major computational bottleneck in the repeated computation of barycentric weights. To address this, we propose a fast barycentric coordinate solver, which significantly reduces computational overhead and achieves a speedup of up to$4.57 \times$, enabling efficient and photorealistic simulation of high-speed motion. Crucially, our method is fully differentiable, allowing gradients to propagate from rendered images to the underlying 3D shape, thereby facilitating shape recovery through inverse rendering. We validate our approach on two representative motion types: rapid translation and rotation. Experimental results demonstrate that our method enables efficient and realistic modeling of ultra-fast moving objects in the forward simulation. Moreover, it successfully recovers 3D shapes from 2D imagery of objects undergoing extreme translational and rotational motion, advancing the boundaries of vision-based 3D reconstruction.

We propose Probabilistic Inclusion Depth (PID) for the ensemble visualization of scalar fields. By introducing a probabilistic inclusion operator $\subset_{p}$, our method is a general data depth model supporting ensembles of fuzzy contours, such as soft masks from modern segmentation methods, and conventional ensembles of binary contours. We also advocate for extending contour extraction in scalar field ensembles to become a fuzzy decision by considering the probabilistic distribution of an isovalue to encode the sensitivity information. To reduce the complexity of the data depth computation, an efficient approximation using the mean probabilistic contour is devised. Furthermore, an order-of-magnitude reduction in computational time is achieved with an efficient parallel algorithm on the GPU. Our new method enables the computation of contour boxplots for ensembles of probabilistic masks, ensembles defined on various types of grids, and large 3D ensembles not studied by existing methods. The effectiveness of our method is evaluated through numerical comparisons with existing techniques on synthetic datasets, examples of real-world ensemble datasets, and expert feedback.