Eigendecomposition-free Training of Deep Networks with Zero Eigenvalue-based Losses

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be solved by finding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix representing a linear system. Incorporating this in deep learning frameworks would allow us to explicitly encode known notions of geometry, instead of having the network implicitly learn them from data. However, performing eigendecomposition within a network requires the ability to differentiate this operation. Unfortunately, while theoretically doable, this introduces numerical instability in the optimization process in practice. In this paper, we introduce an eigendecomposition-free approach to training a deep network whose loss depends on the eigenvector corresponding to a zero eigenvalue of a matrix predicted by the network. We demonstrate on several tasks, including keypoint matching and 3D pose estimation, that our approach is much more robust than explicit differentiation of the eigendecomposition, It has better convergence properties and yields state-of-the-art results on both tasks.Comment: 25 page

ACNe: Attentive Context Normalization for Robust Permutation-Equivariant Learning

Many problems in computer vision require dealing with sparse, unordered data in the form of point clouds. Permutation-equivariant networks have become a popular solution-they operate on individual data points with simple perceptrons and extract contextual information with global pooling. This can be achieved with a simple normalization of the feature maps, a global operation that is unaffected by the order. In this paper, we propose Attentive Context Normalization (ACN), a simple yet effective technique to build permutation-equivariant networks robust to outliers. Specifically, we show how to normalize the feature maps with weights that are estimated within the network, excluding outliers from this normalization. We use this mechanism to leverage two types of attention: local and global-by combining them, our method is able to find the essential data points in high-dimensional space to solve a given task. We demonstrate through extensive experiments that our approach, which we call Attentive Context Networks (ACNe), provides a significant leap in performance compared to the state-of-the-art on camera pose estimation, robust fitting, and point cloud classification under noise and outliers. Source code: https://github.com/vcg-uvic/acne.Comment: CVPR 202

Quantum Statistics-Inspired Neural Attention

Sequence-to-sequence (encoder-decoder) models with attention constitute a cornerstone of deep learning research, as they have enabled unprecedented sequential data modeling capabilities. This effectiveness largely stems from the capacity of these models to infer salient temporal dynamics over long horizons; these are encoded into the obtained neural attention (NA) distributions. However, existing NA formulations essentially constitute point-wise selection mechanisms over the observed source sequences; that is, attention weights computation relies on the assumption that each source sequence element is independent of the rest. Unfortunately, although convenient, this assumption fails to account for higher-order dependencies which might be prevalent in real-world data. This paper addresses these limitations by leveraging Quantum-Statistical modeling arguments. Specifically, our work broadens the notion of NA, by attempting to account for the case that the NA model becomes inherently incapable of discerning between individual source elements; this is assumed to be the case due to higher-order temporal dynamics. On the contrary, we postulate that in some cases selection may be feasible only at the level of pairs of source sequence elements. To this end, we cast NA into inference of an attention density matrix (ADM) approximation. We derive effective training and inference algorithms, and evaluate our approach in the context of a machine translation (MT) application. We perform experiments with challenging benchmark datasets. As we show, our approach yields favorable outcomes in terms of several evaluation metrics.Comment: Submitted to The 23rd Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD 2019

3DRegNet: A Deep Neural Network for 3D Point Registration

We present 3DRegNet, a novel deep learning architecture for the registration of 3D scans. Given a set of 3D point correspondences, we build a deep neural network to address the following two challenges: (i) classification of the point correspondences into inliers/outliers, and (ii) regression of the motion parameters that align the scans into a common reference frame. With regard to regression, we present two alternative approaches: (i) a Deep Neural Network (DNN) registration and (ii) a Procrustes approach using SVD to estimate the transformation. Our correspondence-based approach achieves a higher speedup compared to competing baselines. We further propose the use of a refinement network, which consists of a smaller 3DRegNet as a refinement to improve the accuracy of the registration. Extensive experiments on two challenging datasets demonstrate that we outperform other methods and achieve state-of-the-art results. The code is available.Comment: 15 pages, 8 figures, 6 table

Learning 3D-3D Correspondences for One-shot Partial-to-partial Registration

While 3D-3D registration is traditionally tacked by optimization-based methods, recent work has shown that learning-based techniques could achieve faster and more robust results. In this context, however, only PRNet can handle the partial-to-partial registration scenario. Unfortunately, this is achieved at the cost of relying on an iterative procedure, with a complex network architecture. Here, we show that learning-based partial-to-partial registration can be achieved in a one-shot manner, jointly reducing network complexity and increasing registration accuracy. To this end, we propose an Optimal Transport layer able to account for occluded points thanks to the use of outlier bins. The resulting OPRNet framework outperforms the state of the art on standard benchmarks, demonstrating better robustness and generalization ability than existing techniques.Comment: 11 page

Scribble-Supervised Semantic Segmentation by Random Walk on Neural Representation and Self-Supervision on Neural Eigenspace

Scribble-supervised semantic segmentation has gained much attention recently for its promising performance without high-quality annotations. Many approaches have been proposed. Typically, they handle this problem to either introduce a well-labeled dataset from another related task, turn to iterative refinement and post-processing with the graphical model, or manipulate the scribble label. This work aims to achieve semantic segmentation supervised by scribble label directly without auxiliary information and other intermediate manipulation. Specifically, we impose diffusion on neural representation by random walk and consistency on neural eigenspace by self-supervision, which forces the neural network to produce dense and consistent predictions over the whole dataset. The random walk embedded in the network will compute a probabilistic transition matrix, with which the neural representation diffused to be uniform. Moreover, given the probabilistic transition matrix, we apply the self-supervision on its eigenspace for consistency in the image's main parts. In addition to comparing the common scribble dataset, we also conduct experiments on the modified datasets that randomly shrink and even drop the scribbles on image objects. The results demonstrate the superiority of the proposed method and are even comparable to some full-label supervised ones. The code and datasets are available at https://github.com/panzhiyi/RW-SS

DeepFit: 3D Surface Fitting via Neural Network Weighted Least Squares

We propose a surface fitting method for unstructured 3D point clouds. This method, called DeepFit, incorporates a neural network to learn point-wise weights for weighted least squares polynomial surface fitting. The learned weights act as a soft selection for the neighborhood of surface points thus avoiding the scale selection required of previous methods. To train the network we propose a novel surface consistency loss that improves point weight estimation. The method enables extracting normal vectors and other geometrical properties, such as principal curvatures, the latter were not presented as ground truth during training. We achieve state-of-the-art results on a benchmark normal and curvature estimation dataset, demonstrate robustness to noise, outliers and density variations, and show its application on noise removal.Comment: arXiv admin note: text overlap with arXiv:1812.0070

Single-Stage 6D Object Pose Estimation

Most recent 6D pose estimation frameworks first rely on a deep network to establish correspondences between 3D object keypoints and 2D image locations and then use a variant of a RANSAC-based Perspective-n-Point (PnP) algorithm. This two-stage process, however, is suboptimal: First, it is not end-to-end trainable. Second, training the deep network relies on a surrogate loss that does not directly reflect the final 6D pose estimation task. In this work, we introduce a deep architecture that directly regresses 6D poses from correspondences. It takes as input a group of candidate correspondences for each 3D keypoint and accounts for the fact that the order of the correspondences within each group is irrelevant, while the order of the groups, that is, of the 3D keypoints, is fixed. Our architecture is generic and can thus be exploited in conjunction with existing correspondence-extraction networks so as to yield single-stage 6D pose estimation frameworks. Our experiments demonstrate that these single-stage frameworks consistently outperform their two-stage counterparts in terms of both accuracy and speed.Comment: CVPR 202

Learning 2D-3D Correspondences To Solve The Blind Perspective-n-Point Problem

Conventional absolute camera pose via a Perspective-n-Point (PnP) solver often assumes that the correspondences between 2D image pixels and 3D points are given. When the correspondences between 2D and 3D points are not known a priori, the task becomes the much more challenging blind PnP problem. This paper proposes a deep CNN model which simultaneously solves for both the 6-DoF absolute camera pose and 2D--3D correspondences. Our model comprises three neural modules connected in sequence. First, a two-stream PointNet-inspired network is applied directly to both the 2D image keypoints and the 3D scene points in order to extract discriminative point-wise features harnessing both local and contextual information. Second, a global feature matching module is employed to estimate a matchability matrix among all 2D--3D pairs. Third, the obtained matchability matrix is fed into a classification module to disambiguate inlier matches. The entire network is trained end-to-end, followed by a robust model fitting (P3P-RANSAC) at test time only to recover the 6-DoF camera pose. Extensive tests on both real and simulated data have shown that our method substantially outperforms existing approaches, and is capable of processing thousands of points a second with the state-of-the-art accuracy.Comment: A blind-PnP solve

Beyond Cartesian Representations for Local Descriptors

The dominant approach for learning local patch descriptors relies on small image regions whose scale must be properly estimated a priori by a keypoint detector. In other words, if two patches are not in correspondence, their descriptors will not match. A strategy often used to alleviate this problem is to "pool" the pixel-wise features over log-polar regions, rather than regularly spaced ones. By contrast, we propose to extract the "support region" directly with a log-polar sampling scheme. We show that this provides us with a better representation by simultaneously oversampling the immediate neighbourhood of the point and undersampling regions far away from it. We demonstrate that this representation is particularly amenable to learning descriptors with deep networks. Our models can match descriptors across a much wider range of scales than was possible before, and also leverage much larger support regions without suffering from occlusions. We report state-of-the-art results on three different datasets