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Accurate camera pose estimation is a fundamental requirement for numerous applications, such as autonomous driving, mobile robotics, and augmented reality. In this work, we address the problem of estimating the global 6 DoF camera pose from a single RGB image in a given environment. Previous works consider every part of the image valuable for localization. However, many image regions such as the sky, occlusions, and repetitive non-distinguishable patterns cannot be utilized for localization. In addition to adding unnecessary computation efforts, extracting and matching features from such regions produce many wrong matches which in turn degrades the localization accuracy and efficiency. Our work addresses this particular issue and shows by exploiting an interesting concept of sparse 3D models that we can exploit discriminatory environment parts and avoid useless image regions for the sake of a single image localization. Interestingly, through avoiding selecting keypoints from non-reliable image regions such as trees, bushes, cars, pedestrians, and occlusions, our work acts naturally as an outlier filter. This makes our system highly efficient in that minimal set of correspondences is needed and highly accurate as the number of outliers is low. Our work exceeds state-ofthe-art methods on outdoor Cambridge Landmarks dataset. With only relying on single image at inference, it outweighs in terms of accuracy methods that exploit pose priors and/or reference 3D models while being much faster. By choosing as little as 100 correspondences, it surpasses similar methods that localize from thousands of correspondences, while being more efficient. In particular, it achieves, compared to these methods, an improvement of localization by 33% on OldHospital scene. Furthermore, It outstands direct pose regressors even those that learn from sequence of images

Geometric matching is a challenging computer vision task that involves finding correspondences between two views of a 3D scene. Dense geometric matching, i.e., finding every matching pixel, is an appealing approach due to, among other things, the capacity for sub-pixel accuracy and low-texture robustness. While previous results have shown that sparse and semi-sparse methods are better suited than dense approaches for geometry estimation, we propose a novel dense method that outperforms them. We accomplish this by formulating dense global matching as a probabilistic regression task using deep kernels, in contrast to typical correlation volume processing. Furthermore, we show that replacing local correlation with warped feature stacking in the refinement stage further boosts performance. Finally, we observe that a systematic attenuation of the model confidence improves geometry estimation results. Our full approach, $\textbf{D}$eep $\textbf{K}$ernelized Dense Geometric $\textbf{M}$atching, sets a new state-of-the-art on the competitive HPatches, YFCC100m, MegaDepth-1500, and ScanNet-1500 geometry estimation benchmarks. We provide code for all our experiments, instructions for downloading datasets, and pretrained models, at //github.com/Parskatt/dkm

Estimating the accurate depth from a single image is challenging since it is inherently ambiguous and ill-posed. While recent works design increasingly complicated and powerful networks to directly regress the depth map, we take the path of CRFs optimization. Due to the expensive computation, CRFs are usually performed between neighborhoods rather than the whole graph. To leverage the potential of fully-connected CRFs, we split the input into windows and perform the FC-CRFs optimization within each window, which reduces the computation complexity and makes FC-CRFs feasible. To better capture the relationships between nodes in the graph, we exploit the multi-head attention mechanism to compute a multi-head potential function, which is fed to the networks to output an optimized depth map. Then we build a bottom-up-top-down structure, where this neural window FC-CRFs module serves as the decoder, and a vision transformer serves as the encoder. The experiments demonstrate that our method significantly improves the performance across all metrics on both the KITTI and NYUv2 datasets, compared to previous methods. Furthermore, the proposed method can be directly applied to panorama images and outperforms all previous panorama methods on the MatterPort3D dataset. Project page: //weihaosky.github.io/newcrfs.

In deep learning, fine-grained N:M sparsity reduces the data footprint and bandwidth of a General Matrix multiply (GEMM) by x2, and doubles throughput by skipping computation of zero values. So far, it was only used to prune weights. We examine how this method can be used also for activations and their gradients (i.e., "neural gradients"). To this end, we first establish a tensor-level optimality criteria. Previous works aimed to minimize the mean-square-error (MSE) of each pruned block. We show that while minimization of the MSE works fine for pruning the activations, it catastrophically fails for the neural gradients. Instead, we show that optimal pruning of the neural gradients requires an unbiased minimum-variance pruning mask. We design such specialized masks, and find that in most cases, 1:2 sparsity is sufficient for training, and 2:4 sparsity is usually enough when this is not the case. Further, we suggest combining several such methods together in order to potentially speed up training even more. A reference implementation is supplied in //github.com/brianchmiel/Act-and-Grad-structured-sparsity.

We introduce canonical weight normalization for convolutional neural networks. Inspired by the canonical tensor decomposition, we express the weight tensors in so-called canonical networks as scaled sums of outer vector products. In particular, we train network weights in the decomposed form, where scale weights are optimized separately for each mode. Additionally, similarly to weight normalization, we include a global scaling parameter. We study the initialization of the canonical form by running the power method and by drawing randomly from Gaussian or uniform distributions. Our results indicate that we can replace the power method with cheaper initializations drawn from standard distributions. The canonical re-parametrization leads to competitive normalization performance on the MNIST, CIFAR10, and SVHN data sets. Moreover, the formulation simplifies network compression. Once training has converged, the canonical form allows convenient model-compression by truncating the parameter sums.

Convolutional neural networks (CNN) are the dominant deep neural network (DNN) architecture for computer vision. Recently, Transformer and multi-layer perceptron (MLP)-based models, such as Vision Transformer and MLP-Mixer, started to lead new trends as they showed promising results in the ImageNet classification task. In this paper, we conduct empirical studies on these DNN structures and try to understand their respective pros and cons. To ensure a fair comparison, we first develop a unified framework called SPACH which adopts separate modules for spatial and channel processing. Our experiments under the SPACH framework reveal that all structures can achieve competitive performance at a moderate scale. However, they demonstrate distinctive behaviors when the network size scales up. Based on our findings, we propose two hybrid models using convolution and Transformer modules. The resulting Hybrid-MS-S+ model achieves 83.9% top-1 accuracy with 63M parameters and 12.3G FLOPS. It is already on par with the SOTA models with sophisticated designs. The code and models will be made publicly available.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.

Deep neural networks have achieved remarkable success in computer vision tasks. Existing neural networks mainly operate in the spatial domain with fixed input sizes. For practical applications, images are usually large and have to be downsampled to the predetermined input size of neural networks. Even though the downsampling operations reduce computation and the required communication bandwidth, it removes both redundant and salient information obliviously, which results in accuracy degradation. Inspired by digital signal processing theories, we analyze the spectral bias from the frequency perspective and propose a learning-based frequency selection method to identify the trivial frequency components which can be removed without accuracy loss. The proposed method of learning in the frequency domain leverages identical structures of the well-known neural networks, such as ResNet-50, MobileNetV2, and Mask R-CNN, while accepting the frequency-domain information as the input. Experiment results show that learning in the frequency domain with static channel selection can achieve higher accuracy than the conventional spatial downsampling approach and meanwhile further reduce the input data size. Specifically for ImageNet classification with the same input size, the proposed method achieves 1.41% and 0.66% top-1 accuracy improvements on ResNet-50 and MobileNetV2, respectively. Even with half input size, the proposed method still improves the top-1 accuracy on ResNet-50 by 1%. In addition, we observe a 0.8% average precision improvement on Mask R-CNN for instance segmentation on the COCO dataset.

Graph Neural Networks (GNNs) for representation learning of graphs broadly follow a neighborhood aggregation framework, where the representation vector of a node is computed by recursively aggregating and transforming feature vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs in capturing different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.