A Closed-Form, Pairwise Solution to Local Non-Rigid Structure-from-Motion.

A recent trend in Non-Rigid Structure-from-Motion (NRSfM) is to express local, differential constraints between pairs of images, from which the surface normal at any point can be obtained by solving a system of polynomial equations. While this approach is more successful than its counterparts relying on global constraints, the resulting methods face two main problems: First, most of the equation systems they formulate are of high degree and must be solved using computationally expensive polynomial solvers. Some methods use polynomial reduction strategies to simplify the system, but this adds some phantom solutions. In any event, an additional mechanism is employed to pick the best solution, which adds to the computation without any guarantees on the reliability of the solution. Second, these methods formulate constraints between a pair of images. Even if there is enough motion between them, they may suffer from local degeneracies that make the resulting estimates unreliable without any warning mechanism. %Unfortunately, these systems are of high degree with up to five real solutions. Hence, a computationally expensive strategy is required to select a unique solution. Furthermore, they suffer from degeneracies that make the resulting estimates unreliable, without any mechanism to identify this situation. In this paper, we solve these problems for isometric/conformal NRSfM. We show that, under widely applicable assumptions, we can derive a new system of equations in terms of the surface normals, whose two solutions can be obtained in closed-form and can easily be disambiguated locally. Our formalism also allows us to assess how reliable the estimated local normals are and to discard them if they are not. Our experiments show that our reconstructions, obtained from two or more views, are significantly more accurate than those of state-of-the-art methods, while also being faster. %In this paper, we show that, under widely applicable assumptions, we can derive a new system of equations in terms of the surface normals, whose two solutions can be obtained in closed-form and can easily be disambiguated locally. Our formalism also allows us to assess how reliable the estimated local normals are and to discard them if they are not. Our experiments show that our reconstructions, obtained from two or more views, are significantly more accurate than those of state-of-the-art methods, while also being faster.

Rescheduling trains by crossover tracks to promote service quality of urban rail transit under partial blockages.

This study focuses on the rescheduling problem with disruptions that cause partial blockages in the urban rail transit (URT), contributing to extending the relative train rescheduling studies. The alternative driving measure (ADM), which could be regarded as one train rerouting measure, is used to skip the blocked section, and a mixed-integer nonlinear programming (MINLP) model is built based on it. Time-varying passenger flow as well as the turnaround process of rolling stocks is taken into consideration. To solve the model, a customized genetic algorithm is used to quickly generate high-quality solutions. Real-world data is studied and sensitivity analyses are taken to verify the feasibility and advantage of ADM. The results validate the proposed model and algorithm, as well as confirm that ADM shows significantly better performance than the practical operation measure in promoting passenger service quality of URT under partial blockage.

Generating High-Resolution 3D Faces and Bodies Using VQ-VAE-2 with PixelSNAIL Networks on 2D Representations.

Modeling and representing 3D shapes of the human body and face is a prominent field due to its applications in the healthcare, clothes, and movie industry. In our work, we tackled the problem of 3D face and body synthesis by reducing 3D meshes to 2D image representations. We show that the face can naturally be modeled on a 2D grid. At the same time, for more challenging 3D body geometries, we proposed a novel non-bijective 3D-2D conversion method representing the 3D body mesh as a plurality of rendered projections on the 2D grid. Then, we trained a state-of-the-art vector-quantized variational autoencoder (VQ-VAE-2) to learn a latent representation of 2D images and fit a PixelSNAIL autoregressive model to sample novel synthetic meshes. We evaluated our method versus a classical one based on principal component analysis (PCA) by sampling from the empirical cumulative distribution of the PCA scores. We used the empirical distributions of two commonly used metrics, specificity and diversity, to quantitatively demonstrate that the synthetic faces generated with our method are statistically closer to real faces when compared with the PCA ones. Our experiment on the 3D body geometry requires further research to match the test set statistics but shows promising results.