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

Nonlinear Hebbian learning as a unifying principle in receptive field formation

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely Nonlinear Hebbian Learning. When Nonlinear Hebbian Learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities

Digital Image Processing

This book presents several recent advances that are related or fall under the umbrella of 'digital image processing', with the purpose of providing an insight into the possibilities offered by digital image processing algorithms in various fields. The presented mathematical algorithms are accompanied by graphical representations and illustrative examples for an enhanced readability. The chapters are written in a manner that allows even a reader with basic experience and knowledge in the digital image processing field to properly understand the presented algorithms. Concurrently, the structure of the information in this book is such that fellow scientists will be able to use it to push the development of the presented subjects even further

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning

Dimensionality reduction and sparse representations in computer vision

The proliferation of camera equipped devices, such as netbooks, smartphones and game stations, has led to a significant increase in the production of visual content. This visual information could be used for understanding the environment and offering a natural interface between the users and their surroundings. However, the massive amounts of data and the high computational cost associated with them, encumbers the transfer of sophisticated vision algorithms to real life systems, especially ones that exhibit resource limitations such as restrictions in available memory, processing power and bandwidth. One approach for tackling these issues is to generate compact and descriptive representations of image data by exploiting inherent redundancies. We propose the investigation of dimensionality reduction and sparse representations in order to accomplish this task. In dimensionality reduction, the aim is to reduce the dimensions of the space where image data reside in order to allow resource constrained systems to handle them and, ideally, provide a more insightful description. This goal is achieved by exploiting the inherent redundancies that many classes of images, such as faces under different illumination conditions and objects from different viewpoints, exhibit. We explore the description of natural images by low dimensional non-linear models called image manifolds and investigate the performance of computer vision tasks such as recognition and classification using these low dimensional models. In addition to dimensionality reduction, we study a novel approach in representing images as a sparse linear combination of dictionary examples. We investigate how sparse image representations can be used for a variety of tasks including low level image modeling and higher level semantic information extraction. Using tools from dimensionality reduction and sparse representation, we propose the application of these methods in three hierarchical image layers, namely low-level features, mid-level structures and high-level attributes. Low level features are image descriptors that can be extracted directly from the raw image pixels and include pixel intensities, histograms, and gradients. In the first part of this work, we explore how various techniques in dimensionality reduction, ranging from traditional image compression to the recently proposed Random Projections method, affect the performance of computer vision algorithms such as face detection and face recognition. In addition, we discuss a method that is able to increase the spatial resolution of a single image, without using any training examples, according to the sparse representations framework. In the second part, we explore mid-level structures, including image manifolds and sparse models, produced by abstracting information from low-level features and offer compact modeling of high dimensional data. We propose novel techniques for generating more descriptive image representations and investigate their application in face recognition and object tracking. In the third part of this work, we propose the investigation of a novel framework for representing the semantic contents of images. This framework employs high level semantic attributes that aim to bridge the gap between the visual information of an image and its textual description by utilizing low level features and mid level structures. This innovative paradigm offers revolutionary possibilities including recognizing the category of an object from purely textual information without providing any explicit visual example