相关论文: Temporal Wasserstein non-negative matrix factoriza…

We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced for which these equations are gradient flows. This metric…

The goal of this paper is to discover, segment, and track independently moving objects in complex visual scenes. Previous approaches have explored the use of optical flow for motion segmentation, leading to imperfect predictions due to…

Weakly supervised instance segmentation has gained popularity because it reduces high annotation cost of pixel-level masks required for model training. Recent approaches for weakly supervised instance segmentation detect and segment objects…

Real time outdoor navigation in highly dynamic environments is an crucial problem. The recent literature on real time static SLAM don't scale up to dynamic outdoor environments. Most of these methods assume moving objects as outliers or…

We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…

In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein…

Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…

The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…

We propose a variational model with diffeomorphic optimal transportation for joint image reconstruction and motion estimation. The proposed model is a production of assembling the Wasserstein distance with the Benamou--Brenier formula in…

Human beings have the ability to continuously analyze a video and immediately extract the motion components. We want to adopt this paradigm to provide a coherent and stable motion segmentation over the video sequence. In this perspective,…

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…

We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…

A major challenge for video semantic segmentation is the lack of labeled data. In most benchmark datasets, only one frame of a video clip is annotated, which makes most supervised methods fail to utilize information from the rest of the…

In this dissertation, I present my work towards exploring temporal information for better video understanding. Specifically, I have worked on two problems: action recognition and semantic segmentation. For action recognition, I have…

We construct an efficient primal-dual forward-backward (PDFB) splitting method for computing a class of minimizing movement schemes with nonlinear mobility transport distances, and apply it to computing Wasserstein-like gradient flows. This…

The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit sphere of the optimal transport displacements from its 1D…

We propose a continuous optimization method for solving dense 3D scene flow problems from stereo imagery. As in recent work, we represent the dynamic 3D scene as a collection of rigidly moving planar segments. The scene flow problem then…

An optical flow gradient algorithm was applied to spontaneously forming net- works of neurons and glia in culture imaged by fluorescence optical microscopy in order to map functional calcium signaling with single pixel resolution. Optical…

Moving Object Segmentation is a challenging task for jittery/wobbly videos. For jittery videos, the non-smooth camera motion makes discrimination between foreground objects and background layers hard to solve. While most recent works for…