Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a number of problems but only recently have found their way into generative image models. We here introduce a recurrent image model based on multi-dimensional long short-term memory units which are particularly suited for image modeling due to their spatial structure. Our model scales to images of arbitrary size and its likelihood is computationally tractable. We find that it outperforms the state of the art in quantitative comparisons on several image datasets and produces promising results when used for texture synthesis and inpainting.
@cite_5 used one-dimensional LSTMs to generate images in a sequential manner (DRAW). Because the model was defined over Bernoulli variables, normalized RGB values had to be treated as probabilities, making a direct comparison with other image models difficult. In contrast to our model, the presence of stochastic latent variables in DRAW means that its likelihood cannot be evaluated but has to be approximated.
@cite_5
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We introduce convolutional DRAW, a homogeneous deep generative model achieving state-of-the-art performance in latent variable image modeling. The algorithm naturally stratifies information into higher and lower level details, creating abstract features and as such addressing one of the fundamentally desired properties of representation learning. Furthermore, the hierarchical ordering of its latents creates the opportunity to selectively store global information about an image, yielding a high quality 'conceptual compression' framework. Probabilistic models of natural images are usually evaluated by measuring performance on rather indirect tasks, such as denoising and inpainting. A more direct way to evaluate a generative model is to draw samples from it and to check whether statistical properties of the samples match the statistics of natural images. This method is seldom used with high-resolution images, because current models produce samples that are very different from natural images, as assessed by even simple visual inspection. We investigate the reasons for this failure and we show that by augmenting existing models so that there are two sets of latent variables, one set modelling pixel intensities and the other set modelling image-specific pixel covariances, we are able to generate high-resolution images that look much more realistic than before. The overall model can be interpreted as a gated MRF where both pair-wise dependencies and mean intensities of pixels are modulated by the states of latent variables. Finally, we confirm that if we disallow weight-sharing between receptive fields that overlap each other, the gated MRF learns more efficient internal representations, as demonstrated in several recognition tasks. Patch-based low-rank models have shown effective in exploiting spatial redundancy of natural images especially for the application of image denoising. However, two-dimensional low-rank model can not fully exploit the spatio-temporal correlation in larger data sets such as multispectral images and 3D MRIs. In this work, we propose a novel low-rank tensor approximation framework with Laplacian Scale Mixture (LSM) modeling for multi-frame image denoising. First, similar 3D patches are grouped to form a tensor of d-order and high-order Singular Value Decomposition (HOSVD) is applied to the grouped tensor. Then the task of multiframe image denoising is formulated as a Maximum A Posterior (MAP) estimation problem with the LSM prior for tensor coefficients. Both unknown sparse coefficients and hidden LSM parameters can be efficiently estimated by the method of alternating optimization. Specifically, we have derived closed-form solutions for both subproblems. Experimental results on spectral and dynamic MRI images show that the proposed algorithm can better preserve the sharpness of important image structures and outperform several existing state-of-the-art multiframe denoising methods (e.g., BM4D and tensor dictionary learning). In this paper we present the Latent Regression Forest (LRF), a novel framework for real-time, 3D hand pose estimation from a single depth image. In contrast to prior forest-based methods, which take dense pixels as input, classify them independently and then estimate joint positions afterwards, our method can be considered as a structured coarse-to-fine search, starting from the centre of mass of a point cloud until locating all the skelet al joints. The searching process is guided by a learnt Latent Tree Model which reflects the hierarchical topology of the hand. Our main contributions can be summarised as follows: (i) Learning the topology of the hand in an unsupervised, data-driven manner. (ii) A new forest-based, discriminative framework for structured search in images, as well as an error regression step to avoid error accumulation. (iii) A new multi-view hand pose dataset containing 180K annotated images from 10 different subjects. Our experiments show that the LRF out-performs state-of-the-art methods in both accuracy and efficiency.