Search

Portrait viewpoint and illumination editing is an important problem with several applications in VR/AR, movies, and photography. Comprehensive knowledge of geometry and illumination is critical for obtaining photorealistic results. Current methods are unable to explicitly model in 3D while handling both viewpoint and illumination editing from a single image. In this paper, we propose VoRF, a novel approach that can take even a single portrait image as input and relight human heads under novel illuminations that can be viewed from arbitrary viewpoints. VoRF represents a human head as a continuous volumetric field and learns a prior model of human heads using a coordinate-based MLP with individual latent spaces for identity and illumination. The prior model is learned in an auto-decoder manner over a diverse class of head shapes and appearances, allowing VoRF to generalize to novel test identities from a single input image. Additionally, VoRF has a reflectance MLP that uses the intermediate features of the prior model for rendering One-Light-at-A-Time (OLAT) images under novel views. We synthesize novel illuminations by combining these OLAT images with target environment maps. Qualitative and quantitative evaluations demonstrate the effectiveness of VoRF for relighting and novel view synthesis, even when applied to unseen subjects under uncontrolled illumination. This work is an extension of Rao et al. (VoRF: Volumetric Relightable Faces 2022). We provide extensive evaluation and ablative studies of our model and also provide an application, where any face can be relighted using textual input. [ABSTRACT FROM AUTHOR]

We provide a new forbidden criterion for the realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six. [ABSTRACT FROM AUTHOR]

We study the classical result by Bruijn and Erdős regarding the bound on the number of lines determined by a n-point configuration in the plane, and in the light of the recently proven Tropical Sylvester-Gallai theorem, come up with a tropical version of the above-mentioned result. In this work, we introduce stable tropical lines, which help in answering questions pertaining to incidence geometry in the tropical plane. Projective duality in the tropical plane helps in translating the question for stable lines to stable intersections that have been previously studied in depth. Invoking duality between Newton subdivisions and line arrangements, we are able to classify stable intersections with shapes of cells in subdivisions, and this ultimately helps us in coming up with a bound. In this process, we also encounter various unique properties of linear Newton subdivisions which are dual to tropical line arrangements. [ABSTRACT FROM AUTHOR]

Given a lattice polygon P with g interior lattice points, we can associate to P two moduli spaces: the moduli space of algebraic curves that are non-degenerate with respect to P and the moduli space of tropical curves of genus g with Newton polygon P. We completely classify the possible dimensions such a moduli space can have in the tropical case. For non-hyperelliptic polygons, the dimension must be between g and 2 g + 1 and can take on any integer value in this range, with exceptions only in the cases of genus 3, 4, and 7. We provide a similar result for hyperelliptic polygons, for which the range of dimensions is from g to 2 g - 1 . In the case of non-hyperelliptic polygons, our results also hold for the moduli space of algebraic curves that are non-degenerate with respect to P. [ABSTRACT FROM AUTHOR]

Tropical curves in R 2 correspond to metric planar graphs but not all planar graphs arise in this way. We describe several new classes of graphs which cannot occur. For instance, this yields a full combinatorial characterization of the tropically planar graphs of genus at most five. [ABSTRACT FROM AUTHOR]