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Novel-view synthesis (NVS) can be tackled through different approaches, depending on the general setting: a single source image to a short video sequence, exact or noisy camera pose information, 3D-based information such as point clouds etc. The most challenging scenario, the one where we stand in this work, only considers a unique source image to generate a novel one from another viewpoint. However, in such a tricky situation, the latest learning-based solutions often struggle to integrate the camera viewpoint transformation. Indeed, the extrinsic information is often passed as-is, through a low-dimensional vector. It might even occur that such a camera pose, when parametrized as Euler angles, is quantized through a one-hot representation. This vanilla encoding choice prevents the learnt architecture from inferring novel views on a continuous basis (from a camera pose perspective). We claim it exists an elegant way to better encode relative camera pose, by leveraging 3D-related concepts such as the epipolar constraint. We, therefore, introduce an innovative method that encodes the viewpoint transformation as a 2D feature image. Such a camera encoding strategy gives meaningful insights to the network regarding how the camera has moved in space between the two views. By encoding the camera pose information as a finite number of coloured epipolar lines, we demonstrate through our experiments that our strategy outperforms vanilla encoding., Comment: Accepted at BMVC 2022 - 21 pages

Image-based 3D reconstruction has increasingly stunning results over the past few years with the latest improvements in computer vision and graphics. Geometry and topology are two fundamental concepts when dealing with 3D mesh structures. But the latest often remains a side issue in the 3D mesh-based reconstruction literature. Indeed, performing per-vertex elementary displacements over a 3D sphere mesh only impacts its geometry and leaves the topological structure unchanged and fixed. Whereas few attempts propose to update the geometry and the topology, all need to lean on costly 3D ground-truth to determine the faces/edges to prune. We present in this work a method that aims to refine the topology of any 3D mesh through a face-pruning strategy that extensively relies upon 2D alpha masks and camera pose information. Our solution leverages a differentiable renderer that renders each face as a 2D soft map. Its pixel intensity reflects the probability of being covered during the rendering process by such a face. Based on the 2D soft-masks available, our method is thus able to quickly highlight all the incorrectly rendered faces for a given viewpoint. Because our module is agnostic to the network that produces the 3D mesh, it can be easily plugged into any self-supervised image-based (either synthetic or natural) 3D reconstruction pipeline to get complex meshes with a non-spherical topology., Comment: 11 pages ; published at ISVC,Oral - 2022

Let b $\ge$ 2 be an integer and let s b (n) denote the sum of the digits of the representation of an integer n in base b. For sufficiently large N , one has Card{n $\le$ N : |s 3 (n) -- s 2 (n)| $\le$ 0.1457205 log n} \textgreater{} N 0.970359. The proof only uses the separate (or marginal) distributions of the values of s 2 (n) and s 3 (n).

For degrees $3$ to $6$, we first give numerical results on polynomials which take many prime values on an interval of consecutive values of the variable. In particular, we have improved Ruby's record for the "$n$ out of $n$" case, for $n\ =\ 58$, by using a polynomial of degree $6$. In the theoretical part of this paper, we describe a heuristic probabilistic model in the "$n$ out of $n$" case: exactly $n$ (different) prime values on an interval of $n$ consecutive values of the variable. We find that the heuristic value of the probability of the event "$n$ out of $n$" for a generic polynomial is equal to the product of two factors: an arithmetic factor related to global conditions of non-divisibility, and a size factor determined by the position of the polynomial in a "well-shaped" domain of the space of coefficients. This leads to a heuristic estimate for the number of "$n$ out of $n$" polynomials in a given "well-shaped" domain. Finally, results of extended numerical experiments show a satisfactory agreement with the heuristic values given by the model., Comment: in French

The coking process is composed of two main stages: drying process and pyrolysis of coal. A heat and mass transfer model was developed to simulate the drying process of coal. The mechanisms of heat and mass transfer described in the model are: conduction through the coal cake; conduction and convection through the gas in pores; generation, flux and condensation of water vapor. The model has been implemented in finite element software. It requires basic data on the coke oven charge properties and oven dimensions as input. These input data were obtained by experiments or from the literature. The proposed model includes condensation and evaporation allowing us to reproduce the temperature plateau observed experimentally.

A first encounter with $A(\lambda) := \int_0^{+\infty}\{\lambda t\}\{t\}t^{-2}dt.$ This text contains the detailed calculations leading to the results of our paper "Etude de l'autocorrelation multiplicative de la fonction "partie fractionnaire"", to appear in the Ramanujan Journal., Comment: 45 pages, 1 figure