We present a new method for 3D shape reconstruction from a single image, in which a deep neural network directly maps an image to a vector of network weights. The network \textcolor{black}{parametrized by} these weights represents a 3D shape by classifying every point in the volume as either within or outside the shape. The new representation has virtually unlimited capacity and resolution, and can have an arbitrary topology. Our experiments show that it leads to more accurate shape inference from a 2D projection than the existing methods, including voxel-, silhouette-, and mesh-based methods. The code is available at: https://github.com/gidilittwin/Deep-Meta
Queen Mary University of London（伦敦玛丽女王大学）；Fudan University（复旦大学）
Machine learning classifiers' capability is largely dependent on the scale of available training data and limited by the model overfitting in data-scarce learning tasks. To address this problem, this work proposes a novel framework of Meta Functional Learning (MFL) by meta-learning a generalisable functional model from data-rich tasks whilst simultaneously regularising knowledge transfer to data-scarce tasks. The MFL computes meta-knowledge on functional regularisation generalisable to different learning tasks by which functional training on limited labelled data promotes more discriminative f…
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a data structure that involves a deformable shape (roughly a finite dimensional sub manifold) together with a function defined on this shape taking value in another manifold. Indeed, if mathematical currents have already proved to be very efficient theoretically and numerically to mo…
A variety of deep functional maps have been proposed recently, from fully supervised to totally unsupervised, with a range of loss functions as well as different regularization terms. However, it is still not clear what are minimum ingredients of a deep functional map pipeline and whether such ingredients unify or generalize all recent work on deep functional maps. We show empirically minimum components for obtaining state of the art results with different loss functions, supervised as well as unsupervised. Furthermore, we propose a novel framework designed for both full-to-full as well as par…
We present a new technique named "Meta Deformation Network" for 3D shape matching via deformation, in which a deep neural network maps a reference shape onto the parameters of a second neural network whose task is to give the correspondence between a learned template and query shape via deformation. We categorize the second neural network as a meta-function, or a function generated by another function, as its parameters are dynamically given by the first network on a per-input basis. This leads to a straightforward overall architecture and faster execution speeds, without loss in the quality o…
Carnegie Mellon University（卡内基梅隆大学）；Boston University（波士顿大学）；George Mason University（乔治梅森大学）；University of Bristol（布里斯托大学）；Imperial College London（帝国理工学院）；UC Santa Barbara（加州大学圣巴巴拉分校）
We consider the problem of graph-matching on a network of 3D shapes with uncertainty quantification. We assume that the pairwise shape correspondences are efficiently represented as \emph{functional maps}, that match real-valued functions defined over pairs of shapes. By modeling functional maps between nearly isometric shapes as elements of the Lie group $SO(n)$, we employ \emph{synchronization} to enforce cycle consistency of the collection of functional maps over the graph, hereby enhancing the accuracy of the individual maps. We further introduce a tempered Bayesian probabilistic inference…
Tel Aviv University（特拉维夫大学）；Intel（英特尔）；USI Lugano（卢加诺大学）；Sapienza University of Rome（罗马大学）；Technion（以色列理工学院）
We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a …
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main idea is to first align rough approximations of the geometry and then add more and more details to refine the correspondence. We fuse classical shape registration with Functional Maps by embedding the input shapes into an intrinsic-extrinsic product space. Moreover, we disambiguate intrinsic symmetries by applying a surrogate based Markov chain Monte Carlo ini…
The Chinese University of Hong Kong（香港中文大学）；Chinese Academy of Sciences（中国科学院）
Model generalization capacity at domain shift (e.g., various imaging protocols and scanners) is crucial for deep learning methods in real-world clinical deployment. This paper tackles the challenging problem of domain generalization, i.e., learning a model from multi-domain source data such that it can directly generalize to an unseen target domain. We present a novel shape-aware meta-learning scheme to improve the model generalization in prostate MRI segmentation. Our learning scheme roots in the gradient-based meta-learning, by explicitly simulating domain shift with virtual meta-train and m…
Stanford University（斯坦福大学）；University of California San Diego（加州大学圣迭戈分校）
Various 3D semantic attributes such as segmentation masks, geometric features, keypoints, and materials can be encoded as per-point probe functions on 3D geometries. Given a collection of related 3D shapes, we consider how to jointly analyze such probe functions over different shapes, and how to discover common latent structures using a neural network --- even in the absence of any correspondence information. Our network is trained on point cloud representations of shape geometry and associated semantic functions on that point cloud. These functions express a shared semantic understanding of t…
Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape matching and image segmentation, to exploration of large shape collections. Despite the numerous advantages of such representation, however, the problem of converting a given functional map back to a point-to-point map has received a surprisingly limited interest. In this paper we analyze the general problem of point-wise map recovery from arbitrary functiona…
University of Nottingham（诺丁汉大学）；Shenzhen University（深圳大学）；Wuhan University of Technology（武汉理工大学）；University of Leicester（莱斯特大学）
In this paper, we propose a novel retinal layer boundary model for segmentation of optical coherence tomography (OCT) images. The retinal layer boundary model consists of 9 open parametric contours representing the 9 retinal layers in OCT images. An intensity-based Mumford-Shah (MS) variational functional is first defined to evolve the retinal layer boundary model to segment the 9 layers simultaneously. By making use of the normals of open parametric contours, we construct equal sized adjacent narrowbands that are divided by each contour. Regional information in each narrowband can thus be int…
State-of-the-art fully intrinsic networks for non-rigid shape matching often struggle to disambiguate the symmetries of the shapes leading to unstable correspondence predictions. Meanwhile, recent advances in the functional map framework allow to enforce orientation preservation using a functional representation for tangent vector field transfer, through so-called complex functional maps. Using this representation, we propose a new deep learning approach to learn orientation-aware features in a fully unsupervised setting. Our architecture is built on top of DiffusionNet, making it robust to di…
Institute of Mathematics & Statistics（数学与统计研究所）；Mazaryk University（马萨里克大学）；Olin Business School（奥林商学院）；Washington University in St. Louis（圣路易斯华盛顿大学）；School of Mathematics & Statistics（数学与统计学院）；The University of Glasgow（格拉斯哥大学）
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a systematic and consistent description of each surface shape. Three innovative forms of analysis are then introduced. The first uses surface integration to address issues of registration, principal component analysis and the measurement of asymmetry, all in functional form. Computational issues are handled through discrete approximations to integrals, based in thi…
École normale supérieure de Cachan（卡尚高等师范学院）；Université Montpellier II（蒙彼利埃第二大学）；University of Copenhagen（哥本哈根大学）
This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on varying geometrical supports. Analysing variability of fshapes' ensembles require the modelling and quantification of joint variations in geometry and signal, which have been treated separately in previous approaches. Instead, building on the ideas of shape spaces for purely geometrical objects, we propose the extended concept of fshape bundles and define Ri…
This paper proposes a learning-based framework for reconstructing 3D shapes from functional operators, compactly encoded as small-sized matrices. To this end we introduce a novel neural architecture, called OperatorNet, which takes as input a set of linear operators representing a shape and produces its 3D embedding. We demonstrate that this approach significantly outperforms previous purely geometric methods for the same problem. Furthermore, we introduce a novel functional operator, which encodes the extrinsic or pose-dependent shape information, and thus complements purely intrinsic pose-ob…
In this work, we present a novel non-rigid shape matching framework based on multi-resolution functional maps with spectral attention. Existing functional map learning methods all rely on the critical choice of the spectral resolution hyperparameter, which can severely affect the overall accuracy or lead to overfitting, if not chosen carefully. In this paper, we show that spectral resolution tuning can be alleviated by introducing spectral attention. Our framework is applicable in both supervised and unsupervised settings, and we show that it is possible to train the network so that it can ada…
