4,586 research outputs found
Extensions of independent component analysis for natural image data
An understanding of the statistical properties of natural images is useful for any kind of processing to be performed on them. Natural image statistics are, however, in many ways as complex as the world which they depict. Fortunately, the dominant low-level statistics of images are sufficient for many different image processing goals. A lot of research has been devoted to second order statistics of natural images over the years.
Independent component analysis is a statistical tool for analyzing higher than second order statistics of data sets. It attempts to describe the observed data as a linear combination of independent, latent sources. Despite its simplicity, it has provided valuable insights of many types of natural data. With natural image data, it gives a sparse basis useful for efficient description of the data. Connections between this description and early mammalian visual processing have been noticed.
The main focus of this work is to extend the known results of applying independent component analysis on natural images. We explore different imaging techniques, develop algorithms for overcomplete cases, and study the dependencies between the components by using a model that finds a topographic ordering for the components as well as by conditioning the statistics of a component on the activity of another. An overview is provided of the associated problem field, and it is discussed how these relatively small results may eventually be a part of a more complete solution to the problem of vision.reviewe
Deep Epitomic Convolutional Neural Networks
Deep convolutional neural networks have recently proven extremely competitive
in challenging image recognition tasks. This paper proposes the epitomic
convolution as a new building block for deep neural networks. An epitomic
convolution layer replaces a pair of consecutive convolution and max-pooling
layers found in standard deep convolutional neural networks. The main version
of the proposed model uses mini-epitomes in place of filters and computes
responses invariant to small translations by epitomic search instead of
max-pooling over image positions. The topographic version of the proposed model
uses large epitomes to learn filter maps organized in translational
topographies. We show that error back-propagation can successfully learn
multiple epitomic layers in a supervised fashion. The effectiveness of the
proposed method is assessed in image classification tasks on standard
benchmarks. Our experiments on Imagenet indicate improved recognition
performance compared to standard convolutional neural networks of similar
architecture. Our models pre-trained on Imagenet perform excellently on
Caltech-101. We also obtain competitive image classification results on the
small-image MNIST and CIFAR-10 datasets.Comment: 9 page
Tensor Analysis and Fusion of Multimodal Brain Images
Current high-throughput data acquisition technologies probe dynamical systems
with different imaging modalities, generating massive data sets at different
spatial and temporal resolutions posing challenging problems in multimodal data
fusion. A case in point is the attempt to parse out the brain structures and
networks that underpin human cognitive processes by analysis of different
neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the
multimodal, multi-scale nature of neuroimaging data is well reflected by a
multi-way (tensor) structure where the underlying processes can be summarized
by a relatively small number of components or "atoms". We introduce
Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network
notation in order to analyze these models. These diagrams not only clarify
matrix and tensor EEG and fMRI time/frequency analysis and inverse problems,
but also help understand multimodal fusion via Multiway Partial Least Squares
and Coupled Matrix-Tensor Factorization. We show here, for the first time, that
Granger causal analysis of brain networks is a tensor regression problem, thus
allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI
recordings shows the potential of the methods and suggests their use in other
scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE
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