Related papers: Wassersplines for Neural Vector Field--Controlled …
Generating smooth animations from a limited number of sequential observations has a number of applications in vision. For example, it can be used to increase number of frames per second, or generating a new trajectory only based on first…
Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…
We present HyperFLINT (Hypernetwork-based FLow estimation and temporal INTerpolation), a novel deep learning-based approach for estimating flow fields, temporally interpolating scalar fields, and facilitating parameter space exploration in…
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
Various machine learning tasks, from generative modeling to domain adaptation, revolve around the concept of dataset transformation and manipulation. While various methods exist for transforming unlabeled datasets, principled methods to do…
We deal with the task of sampling from an unnormalized Boltzmann density $\rho_D$ by learning a Boltzmann curve given by energies $f_t$ starting in a simple density $\rho_Z$. First, we examine conditions under which Fisher-Rao flows are…
A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…
We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
This work presents a supervised learning based approach to the computer vision problem of frame interpolation. The presented technique could also be used in the cartoon animations since drawing each individual frame consumes a noticeable…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
Humans can intuitively decompose an image into a sequence of strokes to create a painting, yet existing methods for generating drawing processes are limited to specific data types and often rely on expensive human-annotated datasets. We…
In this paper, we present an advanced approach to solving the inverse rig problem in blendshape animation, using high-quality corrective blendshapes. Our algorithm introduces novel enhancements in three key areas: ensuring high data…
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of…
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement…
This paper introduces a novel deep learning framework for image animation. Given an input image with a target object and a driving video sequence depicting a moving object, our framework generates a video in which the target object is…
This paper investigates a time discrete variational model for splines in Wasserstein spaces to interpolate probability measures. Cubic splines in Euclidean space are known to minimize the integrated squared acceleration subject to a set of…
Exploiting image patches instead of whole images have proved to be a powerful approach to tackle various problems in image processing. Recently, Wasserstein patch priors (WPP), which are based on the comparison of the patch distributions of…
We propose a novel framework to produce cartoon videos by fetching the color information from two input keyframes while following the animated motion guided by a user sketch. The key idea of the proposed approach is to estimate the dense…