Fast recursive ensemble convolution of haar-like features

International audienceHaar-like features are ubiquitous in computer vision, e.g. for Viola and Jones face detection or local descriptors such as Speeded-Up-Robust-Features. They are classically computed in one pass over integral image by reading the values at the feature corners. Here we present a new, general, parsing formalism for convolving them more efficiently. Our method is fully automatic and applicable to an arbitrary set of Haar-like features. The parser reduces the number of memory accesses which are the main computational bottleneck during convolution on modern computer architectures. It first splits the features into simpler kernels. Then it aligns and reuses them where applicable forming an ensemble of recursive convolution trees, which can be computed faster. This is illustrated with experiments, which show a significant speed-up over the classic approach

Operator-Valued Frames Associated with Measure Spaces

abstract: Since Duffin and Schaeffer's introduction of frames in 1952, the concept of a frame has received much attention in the mathematical community and has inspired several generalizations. The focus of this thesis is on the concept of an operator-valued frame (OVF) and a more general concept called herein an operator-valued frame associated with a measure space (MS-OVF), which is sometimes called a continuous g-frame. The first of two main topics explored in this thesis is the relationship between MS-OVFs and objects prominent in quantum information theory called positive operator-valued measures (POVMs). It has been observed that every MS-OVF gives rise to a POVM with invertible total variation in a natural way. The first main result of this thesis is a characterization of which POVMs arise in this way, a result obtained by extending certain existing Radon-Nikodym theorems for POVMs. The second main topic investigated in this thesis is the role of the theory of unitary representations of a Lie group G in the construction of OVFs for the L^2-space of a relatively compact subset of G. For G=R, Duffin and Schaeffer have given general conditions that ensure a sequence of (one-dimensional) representations of G, restricted to (-1/2,1/2), forms a frame for L^{2}(-1/2,1/2), and similar conditions exist for G=R^n. The second main result of this thesis expresses conditions related to Duffin and Schaeffer's for two more particular Lie groups: the Euclidean motion group on R^2 and the (2n+1)-dimensional Heisenberg group. This proceeds in two steps. First, for a Lie group admitting a uniform lattice and an appropriate relatively compact subset E of G, the Selberg Trace Formula is used to obtain a Parseval OVF for L^{2}(E) that is expressed in terms of irreducible representations of G. Second, for the two particular Lie groups an appropriate set E is found, and it is shown that for each of these groups, with suitably parametrized unitary duals, the Parseval OVF remains an OVF when perturbations are made to the parameters of the included representations.Dissertation/ThesisDoctoral Dissertation Mathematics 201

A Neutral Network Based Vehicle Classification System for Pervasive Smart Road Security

Pervasive smart computing environments make people get accustomed to convenient and secure services. The overall goal of this research is to classify vehicles along the I215 freeway in Salt Lake City, USA. This information will be used to predict future roadway needs and the expected life of a roadway. The classification of vehicles will be performed by a synthesis of multiple sets of features. All feature sets have not yet been determined; however, one such set will be the reduced wavelet transform of the image of a vehicle. In order to use such a feature, it is necessary that the image be normalized with respect to size, position, and so on. For example, a car in the right most lane in an image will appear smaller than one in the left most lane, because the right most lane is closest to the camera. Likewise, a vehicle’s size will vary depending on where in a lane its image is captured. In our case, the image capture area for each lane is approximately 100 feet of roadway. A goal of this paper is to normalize the image of a vehicle so that regardless of its lane or position in a lane, the features will be approximately the same. The wavelet transform itself will not be used directly for recognition. Instead, it will be input to a neural network and the output of the neural network will be one element of the feature set used for recognition

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book