Many high dimensional vector distances tend to a constant. This is typically considered a negative "contrast-loss" phenomenon that hinders clustering and other machine learning techniques. We reinterpret "contrast-loss" as a blessing. Re-deriving "contrast-loss" using the law of large numbers, we show it results in a distribution's instances concentrating on a thin "hyper-shell". The hollow center means apparently chaotically overlapping distributions are actually intrinsically separable. We use this to develop distribution-clustering, an elegant algorithm for grouping of data points by their (unknown) underlying distribution. Distribution-clustering, creates notably clean clusters from raw unlabeled data, estimates the number of clusters for itself and is inherently robust to "outliers" which form their own clusters. This enables trawling for patterns in unorganized data and may be the key to enabling machine intelligence.
While we do not agree with Aggarwal al's @cite_37 interpretation of contrast-loss'', we are inspired by their attempts to develop a general intuition about the behavior of algorithms in high-dimensional space. This motivates us to analyze the problem from both intuitive and mathematical perspectives. We hope it contributes to the general understanding of high dimensional space.
@cite_37
2462462929 2523714292 2963470893 2479644247
In this paper, we propose a non-local structured prior for volumetric multi-view 3D reconstruction. Towards this goal, we present a novel Markov random field model based on ray potentials in which assumptions about large 3D surface patches such as planarity or Manhattan world constraints can be efficiently encoded as probabilistic priors. We further derive an inference algorithm that reasons jointly about voxels, pixels and image segments, and estimates marginal distributions of appearance, occupancy, depth, normals and planarity. Key to tractable inference is a novel hybrid representation that spans both voxel and pixel space and that integrates non-local information from 2D image segmentations in a principled way. We compare our non-local prior to commonly employed local smoothness assumptions and a variety of state-of-the-art volumetric reconstruction baselines on challenging outdoor scenes with textureless and reflective surfaces. Our experiments indicate that regularizing over larger distances has the potential to resolve ambiguities where local regularizers fail. Despite the breakthroughs in accuracy and speed of single image super-resolution using faster and deeper convolutional neural networks, one central problem remains largely unsolved: how do we recover the finer texture details when we super-resolve at large upscaling factors? The behavior of optimization-based super-resolution methods is principally driven by the choice of the objective function. Recent work has largely focused on minimizing the mean squared reconstruction error. The resulting estimates have high peak signal-to-noise ratios, but they are often lacking high-frequency details and are perceptually unsatisfying in the sense that they fail to match the fidelity expected at the higher resolution. In this paper, we present SRGAN, a generative adversarial network (GAN) for image super-resolution (SR). To our knowledge, it is the first framework capable of inferring photo-realistic natural images for 4x upscaling factors. To achieve this, we propose a perceptual loss function which consists of an adversarial loss and a content loss. The adversarial loss pushes our solution to the natural image manifold using a discriminator network that is trained to differentiate between the super-resolved images and original photo-realistic images. In addition, we use a content loss motivated by perceptual similarity instead of similarity in pixel space. Our deep residual network is able to recover photo-realistic textures from heavily downsampled images on public benchmarks. An extensive mean-opinion-score (MOS) test shows hugely significant gains in perceptual quality using SRGAN. The MOS scores obtained with SRGAN are closer to those of the original high-resolution images than to those obtained with any state-of-the-art method. Despite the breakthroughs in accuracy and speed of single image super-resolution using faster and deeper convolutional neural networks, one central problem remains largely unsolved: how do we recover the finer texture details when we super-resolve at large upscaling factors? The behavior of optimization-based super-resolution methods is principally driven by the choice of the objective function. Recent work has largely focused on minimizing the mean squared reconstruction error. The resulting estimates have high peak signal-to-noise ratios, but they are often lacking high-frequency details and are perceptually unsatisfying in the sense that they fail to match the fidelity expected at the higher resolution. In this paper, we present SRGAN, a generative adversarial network (GAN) for image super-resolution (SR). To our knowledge, it is the first framework capable of inferring photo-realistic natural images for 4x upscaling factors. To achieve this, we propose a perceptual loss function which consists of an adversarial loss and a content loss. The adversarial loss pushes our solution to the natural image manifold using a discriminator network that is trained to differentiate between the super-resolved images and original photo-realistic images. In addition, we use a content loss motivated by perceptual similarity instead of similarity in pixel space. Our deep residual network is able to recover photo-realistic textures from heavily downsampled images on public benchmarks. An extensive mean-opinion-score (MOS) test shows hugely significant gains in perceptual quality using SRGAN. The MOS scores obtained with SRGAN are closer to those of the original high-resolution images than to those obtained with any state-of-the-art method. 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.