Fig. 1. Given a pair of shapes, our method produces a point-wise map that is orientation-preserving as well as approximately continuous and bijective. Here we show the maps produced by different methods via texture transfer: BIM [Kim et al. 2011] has a large distortion on the face and the left hand; functional maps with ICP [Ovsjanikov et al. 2012] and PMF with the Gauss kernel [Vestner et al. 2017b] give a map that is flipped left to right; for PMF with the heat kernel [Vestner et al. 2017a], the orientation in the torso region is reversed; The map produced by our method preserves the orientation consistently and has lower overall error when compared to the ground-truth.We propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated directly in the functional (spectral) domain without using landmark or region correspondences and without relying on external symmetry information. This allows us to obtain functional maps that promote orientation preservation, even when using descriptors, that are invariant to orientation changes. We then show how higher quality, approximately continuous and bijective pointwise correspondences can be obtained from initial functional maps by introducing a novel refinement technique that aims to simultaneously improve the maps both in the spectral and spatial domains. This leads to a general pipeline for computing correspondences between shapes that results in high-quality maps, while admitting an efficient optimization scheme. We show through extensive evaluation that our approach improves upon state-of-the-art results on challenging isometric and non-isometric correspondence benchmarks according to both measures of continuity and coverage as well as producing semantically meaningful correspondences as measured by the distance to ground truth maps.

This paper proposes the application of bagging to obtain more robust and accurate predictions using Gaussian process regression models. The training data is re-sampled using the bootstrap method to form several training sets, from which multiple Gaussian process models are developed and combined through weighting to provide predictions. A number of weighting methods for model combination are discussed, including the simple averaging rule and the weighted averaging rules. We propose to weight the models by the inverse of their predictive variance, and thus the prediction uncertainty of the models is automatically accounted for. The bagging method for Gaussian process regression is successfully applied to the inferential estimation of quality variables in an industrial chemical plant.

Federated learning (FL) is a distributed deep learning method which enables multiple participants, such as mobile phones and IoT devices, to contribute a neural network model while their private training data remains in local devices. This distributed approach is promising in the edge computing system where have a large corpus of decentralized data and require high privacy. However, unlike the common training dataset, the data distribution of the edge computing system is imbalanced which will introduce biases in the model training and cause a decrease in accuracy of federated learning applications. In this paper, we demonstrate that the imbalanced distributed training data will cause accuracy degradation in FL. To counter this problem, we build a self-balancing federated learning framework call Astraea, which alleviates the imbalances by 1) Global data distribution based data augmentation, and 2) Mediator based multi-client rescheduling. The proposed framework relieves global imbalance by runtime data augmentation, and for averaging the local imbalance, it creates the mediator to reschedule the training of clients based on KullbackLeibler divergence (KLD) of their data distribution. Compared with FedAvg, the state-of-the-art FL algorithm, Astraea shows +5.59% and +5.89% improvement of top-1 accuracy on the imbalanced EMNIST and imbalanced CINIC-10 datasets, respectively. Meanwhile, the communication traffic of Astraea can be 92% lower than that of FedAvg.• We first find out that the global imbalanced training data will degrade the accuracy of CNN models trained by FL.• We propose a self-balancing federated learning framework, Astraea, along with two strategies to prevent the

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We propose a novel discrete solver for optimizing functional map‐based energies, including descriptor preservation and promoting structural properties such as area‐preservation, bijectivity and Laplacian commutativity among others. Unlike the commonly‐used continuous optimization methods, our approach enforces the functional map to be associated with a pointwise correspondence as a hard constraint, which provides a stronger link between optimized properties of functional and point‐to‐point maps. Under this hard constraint, our solver obtains functional maps with lower energy values compared to the standard continuous strategies. Perhaps more importantly, the recovered pointwise maps from our discrete solver preserve the optimized for functional properties and are thus of higher overall quality. We demonstrate the advantages of our discrete solver on a range of energies and shape categories, compared to existing techniques for promoting pointwise maps within the functional map framework. Finally, with this solver in hand, we introduce a novel Effective Functional Map Refinement (EFMR) method which achieves the state‐of‐the‐art accuracy on the SHREC'19 benchmark.

We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.155:2 • Melzi. et al the same or better quality at a fraction of the cost compared to the current top performing methods.(2) We demonstrate how higher-frequency information can be extracted from low-frequency spectral map representations. (3) We introduce a novel variational optimization problem and develop a theoretical justification of our method, shedding light on structural properties of functional maps. RELATED WORKShape matching is a very well-studied area of computer graphics. Below we review the methods most closely related to ours, concentrating on spectral techniques for finding correspondences between non-rigid shapes. We refer the interested readers to recent surveys including [Biasotti et al. 2016;Tam et al. 2013;Van Kaick et al. 2011] for a more in-depth treatment of the area.Point-based Spectral Methods. Early spectral methods for shape correspondence were based on directly optimizing pointwise maps between spectral shape embeddings based on either adjacency or Laplacian matrices of graphs and triangle meshes [Jain and Zhang 2006;Jain et al. 2007;Mateus et al. 2008;Ovsjanikov et al. 2010;Scott and Longuet-Higgins 1991;Umeyama 1988]. Such approaches suffer from the requirement of a good initialization, and rely on restricting assumptions about the type of transformation relating the shapes. An initialization algorithm with optimality guarantees, although limited to few tens of points, was introduced in [Maron et al. 2016] and later extended to deal with intrinsic symmetries in [Dym and Lipman 2017]. Spectral quantities (namely, sequences of Laplacian eigenfunctions) have also been used to define pointwise descriptors, and employed within variants of the quadratic assignment problem in Kimmel 2010, 2011]. These approaches have been recently generalized by spectral generalized multidimensional scaling [Aflalo et al. 2016], which explicitly formulates minimumdistortion shape correspondence in the spectral domain.

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In this paper, we propose a novel method, which we call CONSISTENT ZOOMOUT, for efficiently refining correspondences among deformable 3D shape collections, while promoting the resulting map consistency. Our formulation is closely related to a recent unidirectional spectral refinement framework, but naturally integrates map consistency constraints into the refinement. Beyond that, we show further that our formulation can be adapted to recover the underlying isometry among near-isometric shape collections with a theoretical guarantee, which is absent in the other spectral map synchronization frameworks. We demonstrate that our method improves the accuracy compared to the competing methods when synchronizing correspondences in both near-isometric and heterogeneous shape collections, but also significantly outperforms the baselines in terms of map consistency.