We introduce the first learning-based method for recovering shapes from Laplacian spectra. Our model consists of a cycle-consistent module that maps between learned latent vectors of an auto-encoder and sequences of eigenvalues. This module provides an efficient and effective linkage between Laplacian spectrum and geometry. Our data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Our learning model applies without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, mesh superresolution, shape exploration, style transfer, spectrum estimation from point clouds, segmentation transfer and pointto-point matching.

We introduce a new method for non‐rigid registration of 3D human shapes. Our proposed pipeline builds upon a given parametric model of the human, and makes use of the functional map representation for encoding and inferring shape maps throughout the registration process. This combination endows our method with robustness to a large variety of nuisances observed in practical settings, including non‐isometric transformations, downsampling, topological noise and occlusions; further, the pipeline can be applied invariably across different shape representations (e.g. meshes and point clouds), and in the presence of (even dramatic) missing parts such as those arising in real‐world depth sensing applications. We showcase our method on a selection of challenging tasks, demonstrating results in line with, or even surpassing, state‐of‐the‐art methods in the respective areas.

Luminescence (nano)thermometry is a remote sensing technique that relies on the temperature dependency of the luminescence features (e.g., bandshape, peak energy or intensity, and excited state lifetimes and risetimes) of a phosphor to measure temperature. This technique provides precise thermal readouts with superior spatial resolution in short acquisition times. Although luminescence thermometry is just starting to become a more mature subject, it exhibits enormous potential in several areas, e.g., optoelectronics, photonics, micro‐ and nanofluidics, and nanomedicine. This work reviews the latest trends in the field, including the establishment of a comprehensive theoretical background and standardized practices. The reliability, repeatability, and reproducibility of the technique are also discussed, along with the use of multiparametric analysis and artificial‐intelligence algorithms to enhance thermal readouts. In addition, examples are provided to underscore the challenges that luminescence thermometry faces, alongside the need for a continuous search and design of new materials, experimental techniques, and analysis procedures to improve the competitiveness, accessibility, and popularity of the technology

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We introduce a novel learning-based method to recover shapes from their Laplacian spectra, based on establishing and exploring connections in a learned latent space. The core of our approach consists in a cycle-consistent module that maps between a learned latent space and sequences of eigenvalues. This module provides an efficient and effective link between the shape geometry, encoded in a latent vector, and its Laplacian spectrum. Our proposed data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Moreover, these latent space connections enable novel applications for both analyzing and controlling the spectral properties of deformable shapes, especially in the context of a shape collection. Our learning model and the associated analysis apply without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), nature of the latent space (generated by an auto-encoder or a parametric model), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, latent space exploration and analysis, mesh super-resolution, shape exploration, style transfer, spectrum estimation for point clouds, segmentation transfer and non-rigid shape matching.