Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.Comment: to appear at ICCV 201

Design and implementation of photonic metamaterials

Los metamateriales son una nueva clase de materiales artificiales que pueden ser diseñados para poseer propiedades que serían difíciles o imposibles de encontrar en la naturaleza. Los metamateriales han posibilitado la aparición de un gran número de nuevos dispositivos fotónicos con asombrosas propiedades. Entre ellos, cabe destacar a los medios de índices negativos (NIMs) con los que es posible construir superlentes carentes del límite de resolución de las lentes convencionales, así como los dispositivos basados en óptica de transformación, una nueva teoría del electromagnetismo que permite conocer las propiedades que un medio debe tener para curvar o distorsionar el espacio electromagnético. Como consecuencia, ha sido posible crear dispositivos fascinantes, tales como capas de invisibilidad o agujeros negros ópticos. Debido a su importancia, en esta tesis nos hemos centrado en estas dos aplicaciones de los metamateriales. En el caso de los medios de índice negativo, hemos estudiado cómo éstos pueden ser construidos a partir de estructuras de transmisión extraordinaria. Como resultado principal, se ha diseñado y verificado experimentalmente un novedoso metamaterial de altas prestaciones que presenta una elevada figrua de mérito (sustancialmente mayor que las de trabajos previos)en el espectro visible. La estructura también presenta independencia de polarización y propiedades homogéneas para incidencia normal. Esta demostración corresponde al primer NIM experimental con bajas pérdidas en el régimen visible y también al primero formado por varias celdas unidad en la dirección de propagación, un paso imporante hacia NIMs homogéneos en esta banda. Este trabajo ha sido reconocido como uno de los últimos hitos en metamateriales ópticos tridimensionles. Además, otros autores han demostrado que las propiedades de esta estructura pueden ser empleadas para controlar la velocidad de propagación (subluminal y superluminal) de pulsos laser de femtosengudos o para conseguir cGarcía Meca, C. (2012). Design and implementation of photonic metamaterials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/16465Palanci

Mobile Map Browsers: Anticipated User Interaction for Data Pre-fetching

When browsing a graphical display of geospatial data on mobile devices, users typically change the displayed maps by panning, zooming in and out, or rotating the device. Limited storage space on mobile devices and slow wireless communications, however, impede the performance of these operations. To overcome the bottleneck that all map data to be displayed on the mobile device need to be downloaded on demand, this thesis investigates how anticipated user interactions affect intelligent pre-fetching so that an on-demand download session is extended incrementally. User interaction is defined as a set of map operations that each have corresponding effects on the spatial dataset required to generate the display. By anticipating user interaction based on past behavior and intuition on when waiting for data is acceptable, it is possible to device a set of strategies to better prepare the device with data for future use. Users that engage with interactive map displays for a variety of tasks, whether it be navigation, information browsing, or data collection, experience a dynamic display to accomplish their goal. With vehicular navigation, the display might update itself as a result of a GPS data stream reflecting movement through space. This movement is not random, especially as is the case of moving vehicles and, therefore, this thesis suggests that mobile map data could be pre-fetched in order to improve usability. Pre-fetching memory-demanding spatial data can benefit usability in several ways, but in particular it can (1) reduce latency when downloading data over wireless connections and (2) better prepare a device for situations where wireless internet connectivity is weak or intermittent. This thesis investigates mobile map caching and devises an algorithm for pre-fetching data on behalf of the application user. Two primary models are compared: isotropic (direction-independent) and anisotropic (direction-dependent) pre-fetching. A prefetching simulation is parameterized with many trajectories that vary in complexity (a metric of direction change within the trajectory) and it is shown that, although anisotropic pre-fetching typically results in a better pre-fetching accuracy, it is not ideal for all scenarios. This thesis suggests a combination of models to accommodate the significant variation in moving object trajectories. In addition, other methods for pre-fetching spatial data are proposed for future research

Metamaterial-Enabled Transformation Optics

<p>Transformation Optics is a design methodology that uses the form invariance of Maxwell's equations to distort electromagnetic fields. This distortion is imposed on a region of space by mimicking a curvilinear coordinate system with prescribed magnetoelectric material parameters. By simply specifying the correct coordinate transformation, researchers have created such exotic devices as invisibility cloaks, ``perfect'' lenses, and illusion devices.</p><p>Unfortunately, these devices typically require correspondingly exotic material parameters that do not occur in Nature. Researchers have therefore turned to complex artificial media known as metamaterials to approximate the desired responses. However, the metamaterial design process is complex, and there are limitations on the responses that they achieve.</p><p>In this dissertation, we explore both the applicability and limitations of metamaterials in Transformation Optics design. We begin in Chapter 2 by investigating the freedoms available to use in the transformation optics design process itself. We show that quasi-conformal mappings may be used to alleviate some of the complexity of material design in both two- and three-dimensional design. We then go on in Chapter 3 to apply this method to the design of a transformation-optics modified optic. We show that even a highly-approximate implementation of such a lens would retain many of the key performance feautures that we would expect from a full material prescription.</p><p>However, the approximations made in the design of our lens may not be valid in other areas of transformation optical design. For instance, the high-frequency approximations of our lens design ignore the effects of impedance mismatch, and the approximation is not valid when the material parameters vary on the order of a wavelength. Therefore, in Chapter 4 we use other freedoms available to us to design a full-parameter cloak of invisibility. By tailoring the electromagnetic environment of our cloak, we are able to achieve three distinct material responses with a singe metamaterial unit cell. We show the power of our design by experimentally demonstrating a cloak of ten wavelengths in diameter at microwave frequencies.</p><p>In addition to these specific examples, we seek a general method to simulate transformation optics devices containing metamaterial inclusions. In Chapter 5, we examine the discrete-approximation, and we apply it to the design of an electromagnetic cloak. We show that the point-dipole description of metamaterial elements allows us to correct for some aberrations that appear when the limits of homogenization are violated.</p><p>Finally, we examine so-called ``complementary metamaterials'' and their utility in transformation optics devices. Complementary metamaterials exchange the void and metallized regions of conventional metamaterial elements, and thereby offer a dual response to the electromagnetic field. This duality is attractive because it provides a straightforward method of creating broadband, highly-anisotropic magnetics. We analyze these elements and show that they may be incorporated into our discrete-dipole model. However, we show that the unique characteristics of complementary elements limit their functionality when used as effective materials.</p>Dissertatio

Screened poisson hyperfields for shape coding

We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the effect of the screening parameter is a change of measure of the underlying metric space. Screening also indicates a conditioned random walker biased by the choice of measure. A continuum of shape fields is created by varying the screening parameter or, equivalently, the bias of the random walker. In addition to creating a regional encoding of the diffusion with a different bias, we further break down the influence of boundary interactions by considering a number of independent random walks, each emanating from a certain boundary point, whose superposition yields the screened Poisson field. Probing the screened Poisson equation from these two complementary perspectives leads to a high-dimensional hyperfield: a rich characterization of the shape that encodes global, local, interior, and boundary interactions. To extract particular shape information as needed in a compact way from the hyperfield, we apply various decompositions either to unveil parts of a shape or parts of a boundary or to create consistent mappings. The latter technique involves lower-dimensional embeddings, which we call screened Poisson encoding maps (SPEM). The expressive power of the SPEM is demonstrated via illustrative experiments as well as a quantitative shape retrieval experiment over a public benchmark database on which the SPEM method shows a high-ranking performance among the existing state-of-the-art shape retrieval methods

Disentangling Geometric Deformation Spaces in Generative Latent Shape Models

A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior generative model of geometric disentanglement for 3D shapes, wherein the space of object geometry is factorized into rigid orientation, non-rigid pose, and intrinsic shape. The resulting model can be trained from raw 3D shapes, without correspondences, labels, or even rigid alignment, using a combination of classical spectral geometry and probabilistic disentanglement of a structured latent representation space. Our improvements include more sophisticated handling of rotational invariance and the use of a diffeomorphic flow network to bridge latent and spectral space. The geometric structuring of the latent space imparts an interpretable characterization of the deformation space of an object. Furthermore, it enables tasks like pose transfer and pose-aware retrieval without requiring supervision. We evaluate our model on its generative modelling, representation learning, and disentanglement performance, showing improved rotation invariance and intrinsic-extrinsic factorization quality over the prior model.Comment: 22 page

DarSIA: An Open-Source Python Toolbox for Two-Scale Image Processing of Dynamics in Porous Media

Understanding porous media flow is inherently a multi-scale challenge, where at the core lies the aggregation of pore-level processes to a continuum, or Darcy-scale, description. This challenge is directly mirrored in image processing, where pore-scale grains and interfaces may be clearly visible in the image, yet continuous Darcy-scale parameters may be what are desirable to quantify. Classical image processing is poorly adapted to this setting, as most techniques do not explicitly utilize the fact that the image contains explicit physical processes. Here, we extend classical image processing concepts to what we define as “physical images” of porous materials and processes within them. This is realized through the development of a new open-source image analysis toolbox specifically adapted to time-series of images of porous materials.publishedVersio

The INCF Digital Atlasing Program: Report on Digital Atlasing Standards in the Rodent Brain

The goal of the INCF Digital Atlasing Program is to provide the vision and direction necessary to make the rapidly growing collection of multidimensional data of the rodent brain (images, gene expression, etc.) widely accessible and usable to the international research community. This Digital Brain Atlasing Standards Task Force was formed in May 2008 to investigate the state of rodent brain digital atlasing, and formulate standards, guidelines, and policy recommendations.&#xd;&#xa;&#xd;&#xa;Our first objective has been the preparation of a detailed document that includes the vision and specific description of an infrastructure, systems and methods capable of serving the scientific goals of the community, as well as practical issues for achieving&#xd;&#xa;the goals. This report builds on the 1st INCF Workshop on Mouse and Rat Brain Digital Atlasing Systems (Boline et al., 2007, _Nature Preceedings_, doi:10.1038/npre.2007.1046.1) and includes a more detailed analysis of both the current state and desired state of digital atlasing along with specific recommendations for achieving these goals