Randomized hybrid linear modeling by local best-fit flats

The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method for hybrid linear modeling based on selecting a set of local best fit flats that minimize a global l1 error measure. The size of the local neighborhoods is determined automatically by the Jones' l2 beta numbers; it is proven under certain geometric conditions that good local neighborhoods exist and are found by our method. We also demonstrate how to use this algorithm for fast determination of the number of affine subspaces. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the algorithm on synthetic and real hybrid linear data.Comment: To appear in the proceedings of CVPR 201

Auxiliary Guided Autoregressive Variational Autoencoders

Generative modeling of high-dimensional data is a key problem in machine learning. Successful approaches include latent variable models and autoregressive models. The complementary strengths of these approaches, to model global and local image statistics respectively, suggest hybrid models that encode global image structure into latent variables while autoregressively modeling low level detail. Previous approaches to such hybrid models restrict the capacity of the autoregressive decoder to prevent degenerate models that ignore the latent variables and only rely on autoregressive modeling. Our contribution is a training procedure relying on an auxiliary loss function that controls which information is captured by the latent variables and what is left to the autoregressive decoder. Our approach can leverage arbitrarily powerful autoregressive decoders, achieves state-of-the art quantitative performance among models with latent variables, and generates qualitatively convincing samples.Comment: Published as a conference paper at ECML-PKDD 201

Full Resolution Image Compression with Recurrent Neural Networks

This paper presents a set of full-resolution lossy image compression methods based on neural networks. Each of the architectures we describe can provide variable compression rates during deployment without requiring retraining of the network: each network need only be trained once. All of our architectures consist of a recurrent neural network (RNN)-based encoder and decoder, a binarizer, and a neural network for entropy coding. We compare RNN types (LSTM, associative LSTM) and introduce a new hybrid of GRU and ResNet. We also study "one-shot" versus additive reconstruction architectures and introduce a new scaled-additive framework. We compare to previous work, showing improvements of 4.3%-8.8% AUC (area under the rate-distortion curve), depending on the perceptual metric used. As far as we know, this is the first neural network architecture that is able to outperform JPEG at image compression across most bitrates on the rate-distortion curve on the Kodak dataset images, with and without the aid of entropy coding.Comment: Updated with content for CVPR and removed supplemental material to an external link for size limitation

Geometric Prior Based Deep Human Point Cloud Geometry Compression

The emergence of digital avatars has raised an exponential increase in the demand for human point clouds with realistic and intricate details. The compression of such data becomes challenging with overwhelming data amounts comprising millions of points. Herein, we leverage the human geometric prior in geometry redundancy removal of point clouds, greatly promoting the compression performance. More specifically, the prior provides topological constraints as geometry initialization, allowing adaptive adjustments with a compact parameter set that could be represented with only a few bits. Therefore, we can envisage high-resolution human point clouds as a combination of geometric priors and structural deviations. The priors could first be derived with an aligned point cloud, and subsequently the difference of features is compressed into a compact latent code. The proposed framework can operate in a play-and-plug fashion with existing learning based point cloud compression methods. Extensive experimental results show that our approach significantly improves the compression performance without deteriorating the quality, demonstrating its promise in a variety of applications

Wavelets and Imaging Informatics: A Review of the Literature

AbstractModern medicine is a field that has been revolutionized by the emergence of computer and imaging technology. It is increasingly difficult, however, to manage the ever-growing enormous amount of medical imaging information available in digital formats. Numerous techniques have been developed to make the imaging information more easily accessible and to perform analysis automatically. Among these techniques, wavelet transforms have proven prominently useful not only for biomedical imaging but also for signal and image processing in general. Wavelet transforms decompose a signal into frequency bands, the width of which are determined by a dyadic scheme. This particular way of dividing frequency bands matches the statistical properties of most images very well. During the past decade, there has been active research in applying wavelets to various aspects of imaging informatics, including compression, enhancements, analysis, classification, and retrieval. This review represents a survey of the most significant practical and theoretical advances in the field of wavelet-based imaging informatics

Kernel Spectral Curvature Clustering (KSCC)

Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches exist for modeling data by mixtures of affine subspaces (which is often referred to as hybrid linear modeling). We translate some important instances of multi-manifold modeling to hybrid linear modeling in embedded spaces, without explicitly performing the embedding but applying the kernel trick. The resulting algorithm, Kernel Spectral Curvature Clustering, uses kernels at two levels - both as an implicit embedding method to linearize nonflat manifolds and as a principled method to convert a multiway affinity problem into a spectral clustering one. We demonstrate the effectiveness of the method by comparing it with other state-of-the-art methods on both synthetic data and a real-world problem of segmenting multiple motions from two perspective camera views.Comment: accepted to 2009 ICCV Workshop on Dynamical Visio