SIFT-like local feature descriptors are ubiquitously employed in computer vision applications such as content-based retrieval, video analysis, copy detection, object recognition, photo tourism, and 3D reconstruction. Feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations, in particular, affine and intensity scale transformations. However, real transformations that an image can undergo can only be approximately modeled in this way, and thus most descriptors are only approximately invariant in practice. Second, descriptors are usually high dimensional (e.g., SIFT is represented as a 128-dimensional vector). In large-scale retrieval and matching problems, this can pose challenges in storing and retrieving descriptor data. We map the descriptor vectors into the Hamming space in which the Hamming metric is used to compare the resulting representations. This way, we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples. We show extensive experimental validation, demonstrating the advantage of the proposed approach.

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 deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality.

Distance metric learning (DML) has been successfully applied to object classification, both in the standard regime of rich training data and in the few-shot scenario, where each category is represented by only a few examples. In this work, we propose a new method for DML that simultaneously learns the backbone network parameters, the embedding space, and the multi-modal distribution of each of the training categories in that space, in a single end-to-end training process. Our approach outperforms state-of-theart methods for DML-based object classification on a variety of standard fine-grained datasets. Furthermore, we demonstrate the effectiveness of our approach on the problem of few-shot object detection, by incorporating the proposed DML architecture as a classification head into a standard object detection model. We achieve the best results on the ImageNet-LOC dataset compared to strong baselines, when only a few training examples are available. We also offer the community a new episodic benchmark based on the ImageNet dataset for the few-shot object detection task. Code will be released upon acceptance of the paper.

The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly non-rigidly moving) 3D object from a single or multiple partial scans has received increasing attention in recent years. In this work, we propose a novel learningbased method for the completion of partial shapes. Unlike the majority of existing approaches, our method focuses on objects that can undergo non-rigid deformations. The core of our method is a variational autoencoder with graph convolutional operations that learns a latent space for complete realistic shapes. At inference, we optimize to find the representation in this latent space that best fits the generated shape to the known partial input. The completed shape exhibits a realistic appearance on the unknown part. We show promising results towards the completion of synthetic and real scans of human body and face meshes exhibiting different styles of articulation and partiality.

Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In recent years, significant attention has been devoted to descriptors obtained from the spectral decomposition of the Laplace-Beltrami operator associated with the shape. Notable examples in this family are the heat kernel signature (HKS) and the recently introduced wave kernel signature (WKS). The Laplacian-based descriptors achieve state-of-the-art performance in numerous shape analysis tasks; they are computationally efficient, isometry-invariant by construction, and can gracefully cope with a variety of transformations. In this paper, we formulate a generic family of parametric spectral descriptors. We argue that to be optimized for a specific task, the descriptor should take into account the statistics of the corpus of shapes to which it is applied (the "signal") and those of the class of transformations to which it is made insensitive (the "noise"). While such statistics are hard to model axiomatically, they can be learned from examples. Following the spirit of the Wiener filter in signal processing, we show a learning scheme for the construction of optimized spectral descriptors and relate it to Mahalanobis metric learning. The superiority of the proposed approach in generating correspondences is demonstrated on synthetic and scanned human figures. We also show that the learned descriptors are robust enough to be learned on synthetic data and transferred successfully to scanned shapes.