Shape-from-Template dans Flatland

International audienceLe Shape-from-template (SfT) consiste en la reconstruction d'un objet déformable observé sur une image grâce à sa forme de référence. Le 2DSfT est le cas usuel du SfT où la forme de référence est une surface plongée dans un espace 3D et l'image une projection 2D. Nous présentons le 1DSfT, un nouveau cas du SfT où la forme de référence est une courbe plongée dans un espace 2D et l'image une projection 1D. Nous nous concentrons sur les déformations isométriques, pour lesquelles le 2DSfT est un problème bien posé. À travers une étude théorique du 1DSfT avec projection perspective, nous montrons que ce cas est lié au 2DSfT, mais qu'il possède des propriétés différentes : (i) le 1DSfT ne possède pas de solution à la fois exacte et locale et (ii) le 1DSfT ne possède pas de solution unique, mais un nombre fini d'au moins deux solutions. Ensuite, nous proposons deux méthodes d'initialisation convexes: une solution locale et analytique basée sur la linéarité infinitésimale et une solution globale basée sur l'inextensibilité. Nous montrons comment le raffinement non-convexe peut être implémenté et comment l'isométrie peut être contrainte avec une nouvelle paramétrisation basée sur l'angle. Enfin, notre méthode est testée sur des données simulées et réelles

Placental Flattening via Volumetric Parameterization

We present a volumetric mesh-based algorithm for flattening the placenta to a canonical template to enable effective visualization of local anatomy and function. Monitoring placental function in vivo promises to support pregnancy assessment and to improve care outcomes. We aim to alleviate visualization and interpretation challenges presented by the shape of the placenta when it is attached to the curved uterine wall. To do so, we flatten the volumetric mesh that captures placental shape to resemble the well-studied ex vivo shape. We formulate our method as a map from the in vivo shape to a flattened template that minimizes the symmetric Dirichlet energy to control distortion throughout the volume. Local injectivity is enforced via constrained line search during gradient descent. We evaluate the proposed method on 28 placenta shapes extracted from MRI images in a clinical study of placental function. We achieve sub-voxel accuracy in mapping the boundary of the placenta to the template while successfully controlling distortion throughout the volume. We illustrate how the resulting mapping of the placenta enhances visualization of placental anatomy and function. Our code is freely available at https://github.com/mabulnaga/placenta-flattening .Comment: MICCAI 201

Low-Resolution Spectrum of the Diffuse Galactic Light and 3.3 um PAH emission with AKARI InfraRed Camera

We first obtained the spectrum of the diffuse Galactic light (DGL) at general interstellar space in 1.8-5.3 um wavelength region with the low-resolution prism spectroscopy mode of the AKARI Infra-Red Camera (IRC) NIR channel. The 3.3 um PAH band is detected in the DGL spectrum at Galactic latitude |b| < 15 deg, and its correlations with the Galactic dust and gas are confirmed. The correlation between the 3.3 um PAH band and the thermal emission from the Galactic dust is expressed not by a simple linear correlation but by a relation with extinction. Using this correlation, the spectral shape of DGL at optically thin region (5 deg < |b| < 15 deg) was derived as a template spectrum. Assuming that the spectral shape of this template spectrum is uniform at any position, DGL spectrum can be estimated by scaling this template spectrum using the correlation between the 3.3 um PAH band and the thermal emission from the Galactic dust.Comment: 7 pages, 5 figures, accepted by Publications of the Astronomical Society of Japan (PASJ

A Study of the Direct-Fitting Method for Measurement of Galaxy Velocity Dispersions

We have measured the central stellar velocity dispersions of 33 nearby spiral and elliptical galaxies, using a straightforward template-fitting algorithm operating in the pixel domain. The spectra, obtained with the Double Spectrograph at Palomar Observatory, cover both the Ca triplet and the Mg b region, and we present a comparison of the velocity dispersion measurements from these two spectral regions. Model fits to the Ca triplet region generally yield good results with little sensitivity to the choice of template star. In contrast, the Mg b region is more sensitive to template mismatch and to details of the fitting procedure such as the order of a polynomial used to match the continuum shape of the template to the object. As a consequence of the correlation of the [Mg/Fe] ratio with velocity dispersion, it is difficult to obtain a satisfactory model fit to the Mg b lines and the surrounding Fe blends simultaneously, particularly for giant elliptical galaxies with large velocity dispersions. We demonstrate that if the metallicities of the galaxy and template star are not well matched, then direct template-fitting results are improved if the Mg b lines themselves are excluded from the fit and the velocity dispersion is determined from the surrounding weaker lines.Comment: 14 pages. To appear in A

Template-Cut: A Pattern-Based Segmentation Paradigm

We present a scale-invariant, template-based segmentation paradigm that sets up a graph and performs a graph cut to separate an object from the background. Typically graph-based schemes distribute the nodes of the graph uniformly and equidistantly on the image, and use a regularizer to bias the cut towards a particular shape. The strategy of uniform and equidistant nodes does not allow the cut to prefer more complex structures, especially when areas of the object are indistinguishable from the background. We propose a solution by introducing the concept of a "template shape" of the target object in which the nodes are sampled non-uniformly and non-equidistantly on the image. We evaluate it on 2D-images where the object's textures and backgrounds are similar, and large areas of the object have the same gray level appearance as the background. We also evaluate it in 3D on 60 brain tumor datasets for neurosurgical planning purposes.Comment: 8 pages, 6 figures, 3 tables, 6 equations, 51 reference

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application

A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows

The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude, circulation, etc.) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and is able to reproduce known physical scaling laws when processing a set of voriticity fields that evolve over time

DeformNet: Free-Form Deformation Network for 3D Shape Reconstruction from a Single Image

3D reconstruction from a single image is a key problem in multiple applications ranging from robotic manipulation to augmented reality. Prior methods have tackled this problem through generative models which predict 3D reconstructions as voxels or point clouds. However, these methods can be computationally expensive and miss fine details. We introduce a new differentiable layer for 3D data deformation and use it in DeformNet to learn a model for 3D reconstruction-through-deformation. DeformNet takes an image input, searches the nearest shape template from a database, and deforms the template to match the query image. We evaluate our approach on the ShapeNet dataset and show that - (a) the Free-Form Deformation layer is a powerful new building block for Deep Learning models that manipulate 3D data (b) DeformNet uses this FFD layer combined with shape retrieval for smooth and detail-preserving 3D reconstruction of qualitatively plausible point clouds with respect to a single query image (c) compared to other state-of-the-art 3D reconstruction methods, DeformNet quantitatively matches or outperforms their benchmarks by significant margins. For more information, visit: https://deformnet-site.github.io/DeformNet-website/ .Comment: 11 pages, 9 figures, NIP