Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D euclidean grid, resulting in a learnable parameterization that is unlimited in resolution. Unfortunately, these methods are often unsuitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Implicit Fields. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define DeepMesh - an end-to-end differentiable mesh representation that can vary its topology. We validate our theoretical insight through several applications: Single view 3D Reconstruction via Differentiable Rendering, Physically-Driven Shape Optimization, Full Scene 3D Reconstruction from Scans and End-to-End Training. In all cases our end-to-end differentiable parameterization gives us an edge over state-of-the-art algorithms.

Deep implicit surfaces excel at modeling generic shapes but do not always capture the regularities present in manufactured objects, which is something simple geometric primitives are particularly good at. In this paper, we propose a representation combining latent and explicit parameters that can be decoded into a set of deep implicit and geometric shapes that are consistent with each other. As a result, we can effectively model both complex and highly regular shapes that coexist in manufactured objects. This enables our approach to manipulate 3D shapes in an efficient and precise manner.

Deep neural networks have amply demonstrated their prowess but estimating the reliability of their predictions remains challenging. Deep Ensembles are widely considered as being one of the best methods for generating uncertainty estimates but are very expensive to train and evaluate.MC-Dropout is another popular alternative, which is less expensive, but also less reliable. Our central intuition is that there is a continuous spectrum of ensemble-like models of which MC-Dropout and Deep Ensembles are extreme examples. The first one uses effectively infinite number of highly correlated models while the second one relies on a finite number of independent models.To combine the benefits of both, we introduce Masksembles. Instead of randomly dropping parts of the network as in MC-dropout, Masksemble relies on a fixed number of binary masks, which are parameterized in a way that allows to change correlations between individual models. Namely, by controlling the overlap between the masks and their size one can choose the optimal configuration for the task at hand. This leads to a simple and easy to implement method with performance on par with Ensembles at a fraction of the cost. We experimentally validate Masksembles on two widely used datasets, CIFAR10 and ImageNet.

Geometric Deep Learning has recently made striking progress with the advent of continuous Deep Implicit Fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is not limited in resolution. Unfortunately, these methods are often not suitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Signed Distance Functions. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define MeshSDF, an end-to-end differentiable mesh representation which can vary its topology. We use two different applications to validate our theoretical insight: Single-View Reconstruction via Differentiable Rendering and Physically-Driven Shape Optimization. In both cases our differentiable parameterization gives us an edge over state-of-the-art algorithms.

People detection methods are highly sensitive to occlusions between pedestrians, which are extremely frequent in many situations where cameras have to be mounted at a limited height. The reduction of camera prices allows for the generalization of static multi-camera set-ups. Using joint visual information from multiple synchronized cameras gives the opportunity to improve detection performance. In this paper, we present a new large-scale and high-resolution dataset. It has been captured with seven static cameras in a public open area, and unscripted dense groups of pedestrians standing and walking. Together with the camera frames, we provide an accurate joint (extrinsic and intrinsic) calibration, as well as 7 series of 400 annotated frames for detection at a rate of 2 frames per second. This results in over 40 000 bounding boxes delimiting every person present in the area of interest, for a total of more than 300 individuals. We provide a series of benchmark results using baseline algorithms published over the recent months for multi-view detection with deep neural networks, and trajectory estimation using a non-Markovian model.

Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict oneself to shapes that can be parameterized using only few degrees of freedom. In this work, we introduce a new way to optimize complex shapes fast and accurately. To this end, we train Geodesic Convolutional Neural Networks to emulate a fluidynamics simulator. The key to making this approach practical is remeshing the original shape using a poly-cube map, which makes it possible to perform the computations on GPUs instead of CPUs. The neural net is then used to formulate an objective function that is differentiable with respect to the shape parameters, which can then be optimized using a gradient-based technique. This outperforms state-of-the-art methods by 5 to 20% for standard problems and, even more importantly, our approach applies to cases that previous methods cannot handle.

People detection in single 2D images has improved greatly in recent years. However, comparatively little of this progress has percolated into multi-camera multi-people tracking algorithms, whose performance still degrades severely when scenes become very crowded. In this work, we introduce a new architecture that combines Convolutional Neural Nets and Conditional Random Fields to explicitly model those ambiguities. One of its key ingredients are high-order CRF terms that model potential occlusions and give our approach its robustness even when many people are present. Our model is trained end-to-end and we show that it outperforms several state-of-the-art algorithms on challenging scenes.

Mean-field variational inference is one of the most popular approaches to inference in discrete random fields. Standard mean-field optimization is based on coordinate descent and in many situations can be impractical. Thus, in practice, various parallel techniques are used, which either rely on ad hoc smoothing with heuristically set parameters, or put strong constraints on the type of models. In this paper, we propose a novel proximal gradient-based approach to optimizing the variational objective. It is naturally parallelizable and easy to implement. We prove its convergence, and demonstrate that, in practice, it yields faster convergence and often finds better optima than more traditional mean-field optimization techniques. Moreover, our method is less sensitive to the choice of parameters.

We propose a new variational inference method based on the Kullback-Leibler (KL) proximal term. We make two contributions towards improving efficiency of variational inference. Firstly, we derive a KL proximal-point algorithm and show its equivalence to gradient descent with natural gradient in stochastic variational inference. Secondly, we use the proximal framework to derive efficient variational algorithms for non-conjugate models. We propose a splitting procedure to separate non-conjugate terms from conjugate ones. We then linearize the non-conjugate terms and show that the resulting subproblem admits a closed-form solution. Overall, our approach converts a non-conjugate model to subproblems that involve inference in well-known conjugate models. We apply our method to many models and derive generalizations for non-conjugate exponential family. Applications to real-world datasets show that our proposed algorithms are easy to implement, fast to converge, perform well, and reduce computations.