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We learn to compute optical flow by combining a classical spatial-pyramid formulation with deep learning. This estimates large motions in a coarse-to-fine approach by warping one image of a pair at each pyramid level by the current flow…

We address unsupervised optical flow estimation for ego-centric motion. We argue that optical flow can be cast as a geometrical warping between two successive video frames and devise a deep architecture to estimate such transformation in…

In this paper, we consider the linearized translator equation $L_\phi u=f$, around entire convex translators $M=\textrm{graph}(\phi)\subset\mathbb{R}^4$, i.e. in the first dimension where the Bernstein property fails. Here, $L_\phi…

We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…

M\"obius transformations play an important role in both geometry and spherical image processing - they are the group of conformal automorphisms of 2D surfaces and the spherical equivalent of homographies. Here we present a novel,…

We construct a zeroth-order gradient estimator for a smooth function defined on the probability simplex. The proposed estimator queries the simplex only. We prove that projected gradient descent and the exponential weights algorithm, when…

Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient…

Let $\{P_{\theta}:\theta \in {\mathbb R}^d\}$ be a log-concave location family with $P_{\theta}(dx)=e^{-V(x-\theta)}dx,$ where $V:{\mathbb R}^d\mapsto {\mathbb R}$ is a known convex function and let $X_1,\dots, X_n$ be i.i.d. r.v. sampled…

Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…

Scene flow estimation is the task to predict the point-wise or pixel-wise 3D displacement vector between two consecutive frames of point clouds or images, which has important application in fields such as service robots and autonomous…

A model based on a convolutional neural network (CNN) is designed to reconstruct the three-dimensional turbulent flows beneath a free surface using surface measurements, including the surface elevation and surface velocity. Trained on…

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…

We construct a family of complete, properly embedded, annular translators $M$ such that $M$ lies in a slab and is invariant under reflections in the vertical coordinate planes. Each translator in the family is asymptotic as $z\to -\infty$…

We prove pinching estimates for dual flows provided the curvature function used in the inverse flow in de Sitter space is convex.

Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable…

The estimation of large and extreme image rotation plays a key role in multiple computer vision domains, where the rotated images are related by a limited or a non-overlapping field of view. Contemporary approaches apply convolutional…

We construct valuations on the space of finite-valued convex functions using integration of differential forms over the differential cycle associated to a convex function. We describe the kernel of this procedure and show that the…

Groundwater flow can have a significant impact on the thermal response of ground heat exchangers. The moving infinite line source model is thus widely used in practice as it considers both conductive and advective heat transfert processes.…

In this paper, we consider a fully nonlinear curvature flow of a convex hypersurface in the Euclidean n-space. This flow involves k-th elementary symmetric function for principal curvature radii and a function of support function. Under…

Despite the significant progress that has been made on estimating optical flow recently, most estimation methods, including classical and deep learning approaches, still have difficulty with multi-scale estimation, real-time computation,…