The Missing Data Encoder: Cross-Channel Image Completion\\with Hide-And-Seek Adversarial Network

Image completion is the problem of generating whole images from fragments only. It encompasses inpainting (generating a patch given its surrounding), reverse inpainting/extrapolation (generating the periphery given the central patch) as well as colorization (generating one or several channels given other ones). In this paper, we employ a deep network to perform image completion, with adversarial training as well as perceptual and completion losses, and call it the ``missing data encoder'' (MDE). We consider several configurations based on how the seed fragments are chosen. We show that training MDE for ``random extrapolation and colorization'' (MDE-REC), i.e. using random channel-independent fragments, allows a better capture of the image semantics and geometry. MDE training makes use of a novel ``hide-and-seek'' adversarial loss, where the discriminator seeks the original non-masked regions, while the generator tries to hide them. We validate our models both qualitatively and quantitatively on several datasets, showing their interest for image completion, unsupervised representation learning as well as face occlusion handling

Shape optimization for quadratic functionals and states with random right-hand sides

In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation where the state function depends linearly on a random input parameter. This framework covers important objectives such as tracking-type functionals for elliptic second order partial differential equations and the compliance in linear elasticity. We show that the robust objective and its gradient are completely and explicitly determined by low-order moments of the random input. We then derive a cheap, deterministic algorithm to minimize this objective and present model cases in structural optimization

The plasmonic resonances of a bowtie antenna

Metallic bowtie-shaped nanostructures are very interesting objects in optics, due to their capability of localizing and enhancing electromagnetic fields in the vicinity of their central neck. In this article, we investigate the electrostatic plasmonic resonances of two-dimensional bowtie-shaped domains by looking at the spectrum of their Poincar\'e variational operator. In particular, we show that the latter only consists of essential spectrum and fills the whole interval $[0,1]$. This behavior is very different from what occurs in the counterpart situation of a bowtie domain with only close-to-touching wings, a case where the essential spectrum of the Poincar\'e variational operator is reduced to an interval strictly contained in $[0,1]$. We provide an explanation for this difference by showing that the spectrum of the Poincar\'e variational operator of bowtie-shaped domains with close-to-touching wings has eigenvalues which densify and eventually fill the remaining intervals as the distance between the two wings tends to zero

MultIOD: Rehearsal-free Multihead Incremental Object Detector

Class-Incremental learning (CIL) is the ability of artificial agents to accommodate new classes as they appear in a stream. It is particularly interesting in evolving environments where agents have limited access to memory and computational resources. The main challenge of class-incremental learning is catastrophic forgetting, the inability of neural networks to retain past knowledge when learning a new one. Unfortunately, most existing class-incremental object detectors are applied to two-stage algorithms such as Faster-RCNN and rely on rehearsal memory to retain past knowledge. We believe that the current benchmarks are not realistic, and more effort should be dedicated to anchor-free and rehearsal-free object detection. In this context, we propose MultIOD, a class-incremental object detector based on CenterNet. Our main contributions are: (1) we propose a multihead feature pyramid and multihead detection architecture to efficiently separate class representations, (2) we employ transfer learning between classes learned initially and those learned incrementally to tackle catastrophic forgetting, and (3) we use a class-wise non-max-suppression as a post-processing technique to remove redundant boxes. Without bells and whistles, our method outperforms a range of state-of-the-art methods on two Pascal VOC datasets.Comment: Under review at the WACV 2024 conferenc

A consistent approximation of the total perimeter functional for topology optimization algorithms

This article revolves around the total perimeter functional, one particular version of the perimeter of a shape O contained in a fixed computational domain D measuring the total area of its boundary ¿O, as opposed to its relative perimeter, which only takes into account the regions of ¿O strictly inside D. We construct and analyze approximate versions of the total perimeter which make sense for general “density functions” u, as generalized characteristic functions of shapes. Their use in the context of density-based topology optimization is particularly convenient insofar as they do not involve the gradient of the optimized function u. Two different constructions are proposed: while the first one involves the convolution of the function u with a smooth mollifier, the second one is based on the resolution of an elliptic boundary-value problem featuring Robin boundary conditions. The “consistency” of these approximations with the original notion of total perimeter is appraised from various points of view. At first, we prove the pointwise convergence of our approximate functionals, then the convergence of their derivatives, as the level of smoothing tends to 0, when the considered density function u is the characteristic function of a “regular enough” shape O ¿ D. Then, we focus on the G-convergence of the second type of approximate total perimeter functional, that based on elliptic regularization. Several numerical examples are eventually presented in two and three space dimensions to validate our theoretical findings and demonstrate the efficiency of the proposed functionals in the context of structural optimization.This work is partly supported by the project ANR-18-CE40-0013 SHAPO, financed by the French Agence Nationale de la Recherche (ANR). S.A. benefitted from the support of the chair "Modeling advanced polymers for innovative material solutions" led by the École Polytechnique and the Fondation de l'École Polytechnique, and sponsored by Arkema.Postprint (published version