We propose a novel construction for extracting a central or limit shape in a shape collection, connected via a functional map network. Our approach is based on enriching the latent space induced by a functional map network with an additional natural metric structure. We call this shape‐like dual object the limit shape and show that its construction avoids many of the biases introduced by selecting a fixed base shape or template. We also show that shape differences between real shapes and the limit shape can be computed and characterize the unique properties of each shape in a collection – leading to a compact and rich shape representation. We demonstrate the utility of this representation in a range of shape analysis tasks, including improving functional maps in difficult situations through the mediation of limit shapes, understanding and visualizing the variability within and across different shape classes, and several others. In this way, our analysis sheds light on the missing geometric structure in previously used latent functional spaces, demonstrates how these can be addressed and finally enables a compact and meaningful shape representation useful in a variety of practical applications.
We present a novel neural network architecture, termed Decomposer-Composer, for semantic structure-aware 3D shape modeling. Our method utilizes an auto-encoderbased pipeline, and produces a novel factorized shape latent space, where the semantic structure of the shape collection translates into a data-dependent sub-space factorization, and where shape composition and decomposition become simple linear operations on the embedding coordinates. We further propose to model shape assembly using an explicit learned part deformation module, which utilizes a 3D spatial transformer network to perform an innetwork volumetric grid deformation, and which allows us to train the whole system end-to-end. The resulting network allows us to perform part-level shape manipulation, unattainable by existing approaches. Our extensive ablation study, comparison to baseline methods and qualitative analysis demonstrate the improved performance of the proposed method.
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-oblivious operators, such as the classical Laplacian. Coupled with this novel operator, our reconstruction network achieves very high reconstruction accuracy, even in the presence of incomplete information about a shape, given a soft or functional map expressed in a reduced basis. Finally, we demonstrate that the multiplicative functional algebra enjoyed by these operators can be used to synthesize entirely new unseen shapes, in the context of shape interpolation and shape analogy applications.
Scaling up the vocabulary and complexity of current visual understanding systems is necessary in order to bridge the gap between human and machine visual intelligence. However, a crucial impediment to this end lies in the difficulty of generalizing to data distributions that come from real-world scenarios. Typically such distributions follow Zipf's law which states that only a small portion of the collected object classes will have abundant examples (head); while most classes will contain just a few (tail). In this paper, we propose to study a novel task concerning the generalization of visual relationships that are on the distribution's tail, i.e. we investigate how to help AI systems to better recognize rare relationships like < S:dog, P:riding, O:horse >, where the subject S, predicate P, and/or the object O come from the tail of the corresponding distributions. To achieve this goal, we first introduce two large-scale visual-relationship detection benchmarks built upon the widely used Visual Genome and GQA datasets. We also propose an intuitive evaluation protocol that gives credit to classifiers who prefer concepts that are semantically close to the ground truth class according to wordNet-or word2vec-induced metrics. Finally, we introduce a visiolinguistic version of a Hubless loss which we show experimentally that it consistently encourages classifiers to be more predictive of the tail classes while still being accurate on head classes. Our code and models are available on http://bit.ly/LTVRR.
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