The key idea of variational auto-encoders (VAEs) resembles that of traditional auto-encoder models in which spatial information is supposed to be explicitly encoded in the latent space. However, the latent variables in VAEs are vectors, which can be interpreted as multiple feature maps of size 1x1. Such representations can only convey spatial information implicitly when coupled with powerful decoders. In this work, we propose spatial VAEs that use feature maps of larger size as latent variables to explicitly capture spatial information. This is achieved by allowing the latent variables to be sampled from matrix-variate normal (MVN) distributions whose parameters are computed from the encoder network. To increase dependencies among locations on latent feature maps and reduce the number of parameters, we further propose spatial VAEs via low-rank MVN distributions. Experimental results show that the proposed spatial VAEs outperform original VAEs in capturing rich structural and spatial information.
In computer vision tasks, structural information usually means spatial information of images. There are two main strategies to preserve spatial information in AE for image tasks. One is to apply very powerful decoders, like conditional pixel convolutional neural networks (PixelCNNs) @cite_5 @cite_23 @cite_25 @cite_10 , that generate output images pixel-by-pixel. In this way, the decoders can recover spatial information in the form of dependencies among pixels. However, pixel-by-pixel generation is very slow, resulting in major speed problems in practice. The other method is to let the latent representations explicitly contain spatial information and apply decoders that can make use of such information. To apply this strategy for image tasks, usually the latent representations are feature maps of size between the size of a pixel ( @math ) and that of the input image, while the decoders are deconvolutional neural networks (DCNNs) @cite_20 . Since most computer vision tasks only require high-level spatial information like relative locations of objects instead of detailed relationships among pixels, preserving only rough spatial information is enough, and this strategy is proved effective and efficient.
@cite_23 @cite_5 @cite_10 @cite_25 @cite_20
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One of the long-standing tasks in computer vision is to use a single 2-D view of an object in order to produce its 3-D shape. Recovering the lost dimension in this process has been the goal of classic shape-from-X methods, but often the assumptions made in those works are quite limiting to be useful for general 3-D objects. This problem has been recently addressed with deep learning methods containing a 2-D (convolution) encoder followed by a 3-D (deconvolution) decoder. These methods have been reasonably successful, but memory and run time constraints impose a strong limitation in terms of the resolution of the reconstructed 3-D shapes. In particular, state-of-the-art methods are able to reconstruct 3-D shapes represented by volumes of at most 323 voxels using state-of-the-art desktop computers. In this work, we present a scalable 2-D single view to 3-D volume reconstruction deep learning method, where the 3-D (deconvolution) decoder is replaced by a simple inverse discrete cosine transform (IDCT) decoder. Our simpler architecture has an order of magnitude faster inference when reconstructing 3-D volumes compared to the convolution-deconvolutional model, an exponentially smaller memory complexity while training and testing, and a sub-linear run-time training complexity with respect to the output volume size. We show on benchmark datasets that our method can produce high-resolution reconstructions with state of the art accuracy. In this paper, we propose a novel method for image inpainting based on a Deep Convolutional Generative Adversarial Network (DCGAN). We define a loss function consisting of two parts: (1) a contextual loss that preserves similarity between the input corrupted image and the recovered image, and (2) a perceptual loss that ensures a perceptually realistic output image. Given a corrupted image with missing values, we use back-propagation on this loss to map the corrupted image to a smaller latent space. The mapped vector is then passed through the generative model to predict the missing content. The proposed framework is evaluated on the CelebA and SVHN datasets for two challenging inpainting tasks with random 80 corruption and large blocky corruption. Experiments show that our method can successfully predict semantic information in the missing region and achieve pixel-level photorealism, which is impossible by almost all existing methods. Semantic labeling (or pixel-level land-cover classification) in ultrahigh-resolution imagery (<10 cm) requires statistical models able to learn high-level concepts from spatial data, with large appearance variations. Convolutional neural networks (CNNs) achieve this goal by learning discriminatively a hierarchy of representations of increasing abstraction. In this paper, we present a CNN-based system relying on a downsample-then-upsample architecture. Specifically, it first learns a rough spatial map of high-level representations by means of convolutions and then learns to upsample them back to the original resolution by deconvolutions. By doing so, the CNN learns to densely label every pixel at the original resolution of the image. This results in many advantages, including: 1) the state-of-the-art numerical accuracy; 2) the improved geometric accuracy of predictions; and 3) high efficiency at inference time. We test the proposed system on the Vaihingen and Potsdam subdecimeter resolution data sets, involving the semantic labeling of aerial images of 9- and 5-cm resolution, respectively. These data sets are composed by many large and fully annotated tiles, allowing an unbiased evaluation of models making use of spatial information. We do so by comparing two standard CNN architectures with the proposed one: standard patch classification, prediction of local label patches by employing only convolutions, and full patch labeling by employing deconvolutions. All the systems compare favorably or outperform a state-of-the-art baseline relying on superpixels and powerful appearance descriptors. The proposed full patch labeling CNN outperforms these models by a large margin, also showing a very appealing inference time. Supervised training of a convolutional network for object classification should make explicit any information related to the class of objects and disregard any auxiliary information associated with the capture of the image or the variation within the object class. Does this happen in practice? Although this seems to pertain to the very final layers in the network, if we look at earlier layers we find that this is not the case. In fact, strong spatial information is implicit. This paper addresses this, in particular, exploiting the image representation at the first fully connected layer, i.e. the global image descriptor which has been recently shown to be most effective in a range of visual recognition tasks. We empirically demonstrate evidences for the finding in the contexts of four different tasks: 2d landmark detection, 2d object keypoints prediction, estimation of the RGB values of input image, and recovery of semantic label of each pixel. We base our investigation on a simple framework with ridge rigression commonly across these tasks, and show results which all support our insight. Such spatial information can be used for computing correspondence of landmarks to a good accuracy, but should potentially be useful for improving the training of the convolutional nets for classification purposes.