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Image interpolation, or image morphing, refers to a visual transition between two (or more) input images. For such a transition to look visually appealing, its desirable properties are (i) to be smooth; (ii) to apply the minimal required change in the image; and (iii) to seem real, avoiding unnatural artifacts in each image in the transition. To obtain a smooth and straightforward transition, one may adopt the well-known Wasserstein Barycenter Problem (WBP). While this approach guarantees minimal changes under the Wasserstein metric, the resulting images might seem unnatural. In this work, we propose a novel approach for image morphing that possesses all three desired properties. To this end, we define a constrained variant of the WBP that enforces the intermediate images to satisfy an image prior. We describe an algorithm that solves this problem and demonstrate it using the sparse prior and generative adversarial networks.
In this thesis, we consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides in two scenarios: (I) the measures are given and we need to compute their Wasserstein barycenter, and (ii) the me
In this work we introduce the concept of Bures-Wasserstein barycenter $Q_*$, that is essentially a Frechet mean of some distribution $mathbb{P}$ supported on a subspace of positive semi-definite Hermitian operators $mathbb{H}_{+}(d)$. We allow a bary
This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables the computa
We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. Based on the weak regularity lemma from the theory of graphons, we l
This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [106] and introduce a new metric, called the Wasserstein distance between merg