SHREC'22 Track: Sketch-Based 3D Shape Retrieval in the Wild

Sketch-based 3D shape retrieval (SBSR) is an important yet challenging task, which has drawn more and more attention in recent years. Existing approaches address the problem in a restricted setting, without appropriately simulating real application scenarios. To mimic the realistic setting, in this track, we adopt large-scale sketches drawn by amateurs of different levels of drawing skills, as well as a variety of 3D shapes including not only CAD models but also models scanned from real objects. We define two SBSR tasks and construct two benchmarks consisting of more than 46,000 CAD models, 1,700 realistic models, and 145,000 sketches in total. Four teams participated in this track and submitted 15 runs for the two tasks, evaluated by 7 commonly-adopted metrics. We hope that, the benchmarks, the comparative results, and the open-sourced evaluation code will foster future research in this direction among the 3D object retrieval community.

G-VAE, a Geometric Convolutional VAE for ProteinStructure Generation

Analyzing the structure of proteins is a key part of understanding their functions and thus their role in biology at the molecular level. In addition, design new proteins in a methodical way is a major engineering challenge. In this work, we introduce a joint geometric-neural networks approach for comparing, deforming and generating 3D protein structures. Viewing protein structures as 3D open curves, we adopt the Square Root Velocity Function (SRVF) representation and leverage its suitable geometric properties along with Deep Residual Networks (ResNets) for a joint registration and comparison. Our ResNets handle better large protein deformations while being more computationally efficient. On top of the mathematical framework, we further design a Geometric Variational Auto-Encoder (G-VAE), that once trained, maps original, previously unseen structures, into a low-dimensional (latent) hyper-sphere. Motivated by the spherical structure of the pre-shape space, we naturally adopt the von Mises-Fisher (vMF) distribution to model our hidden variables. We test the effectiveness of our models by generating novel protein structures and predicting completions of corrupted protein structures. Experimental results show that our method is able to generate plausible structures, different from the structures in the training data.

Residual Networks as Flows of Velocity Fields for Diffeomorphic Time Series Alignment

Non-linear (large) time warping is a challenging source of nuisance in time-series analysis. In this paper, we propose a novel diffeomorphic temporal transformer network for both pairwise and joint time-series alignment. Our ResNet-TW (Deep Residual Network for Time Warping) tackles the alignment problem by compositing a flow of incremental diffeomorphic mappings. Governed by the flow equation, our Residual Network (ResNet) builds smooth, fluid and regular flows of velocity fields and consequently generates smooth and invertible transformations (i.e. diffeomorphic warping functions). Inspired by the elegant Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, the final transformation is built by the flow of time-dependent vector fields which are none other than the building blocks of our Residual Network. The latter is naturally viewed as an Eulerian discretization schema of the flow equation (an ODE). Once trained, our ResNet-TW aligns unseen data by a single inexpensive forward pass. As we show in experiments on both univariate (84 datasets from UCR archive) and multivariate time-series (MSR Action-3D, Florence-3D and MSR Daily Activity), ResNet-TW achieves competitive performance in joint alignment and classification.

Magnifying Subtle Facial Motions for Effective 4D Expression Recognition

In this paper, an effective pipeline to automatic 4D Facial Expression Recognition (4D FER) is proposed. It combines two growing but disparate ideas in Computer Vision -- computing the spatial facial deformations using tools from Riemannian geometry and magnifying them using temporal filtering. The flow of 3D faces is first analyzed to capture the spatial deformations based on the recently-developed Riemannian approach, where registration and comparison of neighboring 3D faces are led jointly. Then, the obtained temporal evolution of these deformations are fed into a magnification method in order to amplify the facial activities over the time. The latter, main contribution of this paper, allows revealing subtle (hidden) deformations which enhance the emotion classification performance. We evaluated our approach on BU-4DFE dataset, the state-of-art 94.18% average performance and an improvement that exceeds 10% in classification accuracy, after magnifying extracted geometric features (deformations), are achieved.

ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks

In deformable registration, the geometric framework - large deformation diffeomorphic metric mapping or LDDMM, in short - has inspired numerous techniques for comparing, deforming, averaging and analyzing shapes or images. Grounded in flows, which are akin to the equations of motion used in fluid dynamics, LDDMM algorithms solve the flow equation in the space of plausible deformations, i.e. diffeomorphisms. In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Euler's discretization scheme. The central idea is to represent time-dependent velocity fields as fully connected ReLU neural networks (building blocks) and derive optimal weights by minimizing a regularized loss function. Computing minimizing paths between deformations, thus between shapes, turns to find optimal network parameters by back-propagating over the intermediate building blocks. Geometrically, at each time step, ResNet-LDDMM searches for an optimal partition of the space into multiple polytopes, and then computes optimal velocity vectors as affine transformations on each of these polytopes. As a result, different parts of the shape, even if they are close (such as two fingers of a hand), can be made to belong to different polytopes, and therefore be moved in different directions without costing too much energy. Importantly, we show how diffeomorphic transformations, or more precisely bilipshitz transformations, are predicted by our algorithm. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations. We thus provide essential foundations for more advanced shape variability analysis under a novel joint geometric-neural networks Riemannian-like framework, i.e. ResNet-LDDMM.

Sparse Coding of Shape Trajectories for Facial Expression and Action Recognition

The detection and tracking of human landmarks in video streams has gained in reliability partly due to the availability of affordable RGB-D sensors. The analysis of such time-varying geometric data is playing an important role in the automatic human behavior understanding. However, suitable shape representations as well as their temporal evolution, termed trajectories, often lie to nonlinear manifolds. This puts an additional constraint (i.e., nonlinearity) in using conventional Machine Learning techniques. As a solution, this paper accommodates the well-known Sparse Coding and Dictionary Learning approach to study time-varying shapes on the Kendall shape spaces of 2D and 3D landmarks. We illustrate effective coding of 3D skeletal sequences for action recognition and 2D facial landmark sequences for macro- and micro-expression recognition. To overcome the inherent nonlinearity of the shape spaces, intrinsic and extrinsic solutions were explored. As main results, shape trajectories give rise to more discriminative time-series with suitable computational properties, including sparsity and vector space structure. Extensive experiments conducted on commonly-used datasets demonstrate the competitiveness of the proposed approaches with respect to state-of-the-art.

A Novel Geometric Framework on Gram Matrix Trajectories for Human Behavior Understanding

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the benefit to bring naturally a second desirable quantity when comparing shapes, the spatial covariance, in addition to the conventional affine-shape representation. We derived then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the underlying manifold. Specifically, our approach involves three steps: (1) landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of fixed-rank to build time-parameterized trajectories; (2) a temporal warping is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; (3) finally, a pairwise proximity function SVM is used to classify them, incorporating the (dis-)similarity measure into the kernel function. We show that such representation and metric achieve competitive results in applications as action recognition and emotion recognition from 3D skeletal data, and facial expression recognition from videos. Experiments have been conducted on several publicly available up-to-date benchmarks.

A Novel Space-Time Representation on the Positive Semidefinite Con for Facial Expression Recognition

In this paper, we study the problem of facial expression recognition using a novel space-time geometric representation. We describe the temporal evolution of facial landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the advantage to bring naturally a second desirable quantity when comparing shapes -- the spatial covariance -- in addition to the conventional affine-shape representation. We derive then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the manifold. Specifically, our approach involves three steps: 1) facial landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of rank 2, to build time-parameterized trajectories; 2) a temporal alignment is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; 3) finally, pairwise proximity function SVM (ppfSVM) is used to classify them, incorporating the latter (dis-)similarity measure into the kernel function. We show the effectiveness of the proposed approach on four publicly available benchmarks (CK+, MMI, Oulu-CASIA, and AFEW). The results of the proposed approach are comparable to or better than the state-of-the-art methods when involving only facial landmarks.