We propose a principled convolutional neural pyramid (CNP) framework for general low-level vision and image processing tasks. It is based on the essential finding that many applications require large receptive fields for structure understanding. But corresponding neural networks for regression either stack many layers or apply large kernels to achieve it, which is computationally very costly. Our pyramid structure can greatly enlarge the field while not sacrificing computation efficiency. Extra benefit includes adaptive network depth and progressive upsampling for quasi-realtime testing on VGA-size input. Our method profits a broad set of applications, such as depth RGB image restoration, completion, noise artifact removal, edge refinement, image filtering, image enhancement and colorization.
Another important topic is image deconvolution, which needs image priors, such as gradient distribution, to constrain the solution. Xu al @cite_51 demonstrated that simple CNNs can well approximate the inverse kernel and achieved decent results. As shown in Figure , large kernels for convolution require heavy computation.
@cite_51
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We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for dense networks. For a CNN, the equivalent kernel can be computed exactly and, unlike "deep kernels", has very few parameters: only the hyperparameters of the original CNN. Further, we show that this kernel has two properties that allow it to be computed efficiently; the cost of evaluating the kernel for a pair of images is similar to a single forward pass through the original CNN with only one filter per layer. The kernel equivalent to a 32-layer ResNet obtains 0.84 classification error on MNIST, a new record for GPs with a comparable number of parameters. Kernel normalization methods have been employed to improve robustness of optimization methods to reparametrization of convolution kernels, covariate shift, and to accelerate training of Convolutional Neural Networks (CNNs). However, our understanding of theoretical properties of these methods has lagged behind their success in applications. We develop a geometric framework to elucidate underlying mechanisms of a diverse range of kernel normalization methods. Our framework enables us to expound and identify geometry of space of normalized kernels. We analyze and delineate how state-of-the-art kernel normalization methods affect the geometry of search spaces of the stochastic gradient descent (SGD) algorithms in CNNs. Following our theoretical results, we propose a SGD algorithm with assurance of almost sure convergence of the methods to a solution at single minimum of classification loss of CNNs. Experimental results show that the proposed method achieves state-of-the-art performance for major image classification benchmarks with CNNs. Conventional deep convolutional neural networks (CNNs) apply convolution operators uniformly in space across all feature maps for hundreds of layers - this incurs a high computational cost for real time applications. For many problems such as object detection and semantic segmentation, we are able to obtain a low-cost computation mask, either from a priori problem knowledge, or from a low resolution segmentation network. We show that such computation masks can be used to reduce computation in the high resolution main network. Variants of sparse activation CNNs have previously been explored on small scale tasks, and showed no degradation in terms of object classification accuracy, but often measured gains in terms of theoretical FLOPs without realizing a practical speed-up when compared to highly optimized dense convolution implementations. In this work, we leverage the sparsity structure of computation masks and propose a novel tiling-based sparse convolution algorithm. We verified the effectiveness of our sparse CNN on LiDAR based 3D object detection, and we report significant wall-clock speed-ups compared to dense convolution, as well as improved detection accuracy. In recent years, state-of-the-art methods in computer vision have utilized increasingly deep convolutional neural network architectures (CNNs), with some of the most successful models employing hundreds or even thousands of layers. A variety of pathologies such as vanishing exploding gradients make training such deep networks challenging. While residual connections and batch normalization do enable training at these depths, it has remained unclear whether such specialized architecture designs are truly necessary to train deep CNNs. In this work, we demonstrate that it is possible to train vanilla CNNs with ten thousand layers or more simply by using an appropriate initialization scheme. We derive this initialization scheme theoretically by developing a mean field theory for signal propagation and by characterizing the conditions for dynamical isometry, the equilibration of singular values of the input-output Jacobian matrix. These conditions require that the convolution operator be an orthogonal transformation in the sense that it is norm-preserving. We present an algorithm for generating such random initial orthogonal convolution kernels and demonstrate empirically that they enable efficient training of extremely deep architectures.