Related papers: Temporal Wasserstein non-negative matrix factoriza…

Two common problems in time series analysis are the decomposition of the data stream into disjoint segments that are each in some sense "homogeneous" - a problem known as Change Point Detection (CPD) - and the grouping of similar…

Identifying and segmenting moving objects from a moving monocular camera is difficult when there is unknown camera motion, different types of object motions and complex scene structures. To tackle these challenges, we take advantage of two…

Identifying independently moving objects is an essential task for dynamic scene understanding. However, traditional cameras used in dynamic scenes may suffer from motion blur or exposure artifacts due to their sampling principle. By…

In this article, we formulate topology optimization problems concerning the mass distribution as minimization problems for functionals on the Wasserstein space. We relax optimization problems regarding non-convex objective functions on the…

We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of…

In this paper, we establish a novel approach to proving existence of non-negative weak solutions for degenerate parabolic equations of fourth order, like the Cahn-Hilliard and certain thin film equations. The considered evolution equations…

Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or…

We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…

We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we…

Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class. Simply put, different objects move…

We propose to learn a probabilistic motion model from a sequence of images. Besides spatio-temporal registration, our method offers to predict motion from a limited number of frames, useful for temporal super-resolution. The model is based…

Event cameras provide rich signals that are suitable for motion estimation since they respond to changes in the scene. As any visual changes in the scene produce event data, it is paramount to classify the data into different motions (i.e.,…

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…

We present a novel approach for unsupervised activity segmentation which uses video frame clustering as a pretext task and simultaneously performs representation learning and online clustering. This is in contrast with prior works where…

Weakly supervised instance segmentation reduces the cost of annotations required to train models. However, existing approaches which rely only on image-level class labels predominantly suffer from errors due to (a) partial segmentation of…

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of…

In vivo calcium imaging through microscopes has enabled deep brain imaging of previously inaccessible neuronal populations within the brains of freely moving subjects. However, microendoscopic data suffer from high levels of background…

For safety-critical robotics applications such as autonomous driving, it is important to detect all required objects accurately in real-time. Motion segmentation offers a solution by identifying dynamic objects from the scene in a…

We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…

We introduce a novel semi-supervised video segmentation approach based on an efficient video representation, called as "super-trajectory". Each super-trajectory corresponds to a group of compact trajectories that exhibit consistent motion…