We present direct featureless methods for estimating the eight parameters of an "exact" projective (homographic) coordinate transformation to register pairs of images, together with the application of seamlessly combining a plurality of images of the same scene, resulting in a single image (or new image sequence) of greater resolution or spatial extent. The approach is "exact" for two cases of static scenes: 1) images taken from the same location of an arbitrary three-dimensional (3-D) scene, with a camera that is free to pan, tilt, rotate about its optical axis, and zoom, or 2) images of a flat scene taken from arbitrary locations. The featureless projective approach generalizes interframe camera motion estimation methods that have previously used an affine model (which lacks the degrees of freedom to "exactly" characterize such phenomena as camera pan and tilt) and/or which have relied upon finding points of correspondence between the image frames. The featureless projective approach...

Given a unitary operator A representing a physical quantity of interest, we employ concepts from group representation theory to define two natural signal energy densities for A. The first is invariant to A and proves useful when the effect of A is to be ignored; the second is covariant to A and measures the “A ” content of signals. We also consider joint densities for multiple operators and, in the process, provide an alternative interpretation of Cohen’s general construction for joint distributions of arbitrary variables.

We are entering a pivotal era in which we will become inextricably intertwined with computational technology that will become part of our everyday lives in a much more immediate and intimate way than in the past. The recent explosion of interest in so-called "wearable computers" is indicative of this general trend. The purpose of this paper is to provide an historical account of my wearable computer effort, from the 1970s (WearComp0) to present (WearComp7), with emphasis on a particular variation whose origins were in imaging applications. This application, known as `personal imaging', originated as a computerized photographer's assistant which I developed for what many regarded as an obscure photographic technique. However, it later evolved into a more diverse apparatus and methodology, combining machine vision and computer graphics, in a wearable tetherless apparatus, useful in day-to-day living. Personal imaging, at the intersection of art, science, and technology, has given rise t...

Perspective projections in the space-frequency plane are analyzed, and it is shown that under certain conditions they can be approximately modeled in terms of the fractional Fourier transform. The region of validity of the approximation is examined. Numerical examples are presented. © 2000 Optical Society of America [S0740-3232(00)00612-8] OCIS codes: 100.0100, 150.0150.

This paper considers the problem of detecting nonstationary phenomena, and chirps in particular, from very noisy data. Chirps are waveforms of the very general form A(t) exp(iλ ϕ(t)), where λ is a (large) base frequency, the phase ϕ(t) is time-varying and the amplitude A(t) is slowly varying. Given a set of noisy measurements, we would like to test whether there is signal or whether the data is just noise. One particular application of note in conjunction with this problem is the detection of gravitational waves predicted by Einstein’s Theory of General Relativity. We introduce detection strategies which are very sensitive and more flexible than existing feature detectors. The idea is to use structured algorithms which exploit information in the so-called chirplet graph to chain chirplets together adaptively as to form chirps with polygonal instantaneous frequency. We then search for the path in the graph which provides the best trade-off between complexity and goodness of fit. Underlying our methodology is the idea that while the signal may be extremely weak so that none of the individual empirical coefficients is statistically significant, one can still reliably detect by combining several coefficients into a

We introduce a modied Matching Pursuit algorithm, called Fast Ridge Pursuit, to approximate N-dimensional signals with M Gaussian chirps at a computational cost O(MN) instead of the expected O(MN 2 log N). At each iteration of the pursuit, the best Gabor atom is rst selected, then its scale and chirp rate are locally optimized so as to get a good chirp atom. A ridge theorem of the Gaussian chirp dictionary is proved, from which an estimate of the locally optimal scale and chirp is built. The procedure is restricted to a sub-dictionary of local maxima of the Gaussian Gabor dictionary, so as to accelerate further the pursuit. The eciency and speed of the method is demonstrated on a sound signal. EDICS : 2-TIFR 1 Introduction There has been a considerable interest last decade in developing analysis techniques to decompose nonstationary signals into elementary components, called atoms, that characterize their salient features. As many signals display both oscillatory phenomena, whic...

An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed. The analytic signal is first locally represented as a modulated oscillation, its demodulate is Taylor-expanded everywhere, and this expansion is given a novel representation in terms of the Bell polynomials. Time-domain moments of the demodulated signal are then seen to interact with frequency-domain derivatives of the wavelet, inducing an hierarchy of departures of the analytic wavelet transform from the analytic signal. Assumptions regarding the joint properties of the signal and wavelet then permit considerable simplification of the expressions for the time- and scale-varying form of these deviations. Using this result one may quantify the time-varying bias associated with signal estimation via wavelet ridge analysis for both amplitude and phase definitions of the ridges. An improved estimator which eliminates the lowest-order bias contribution is proposed. Index Terms Complex wavelet, Hilbert transform, wavelet ridge analysis, amplitude and frequency modulated signals. I.

A European consortium has been working since September 2004 on all video-based technical aspects of threedimensional television. The group has structured its technical activities under five technical committees focusing on capturing 3D live scenes, converting the captured scenes to an abstract 3D representations, transmitting the 3D visual information, displaying the 3D video, and processing of signals for the conversion of the abstract 3D video to signals needed to drive the display. The display of 3D video signals by holographic means is highly desirable. Synthesis of high-resolution computer generated holograms with high spatial frequency content, using fast algorithms, is crucial. Fresnel approximation with its fast implementations, fast superposition of zonelens terms, look-up tables using pre-computed holoprimitives are reported in the literature. Phase-retrieval methods are also under investigation. Successful solutions to this problem will benefit from proper utilization and adaptation of signal processing tools like waveletes, fresnelets, chirplets, and atomic decompositions and various optimization algorithms like matching pursuit or simulated annealing.

Chirped wavelets are utilized to detect dispersed signals in the joint time/scale domain. Specifically, pulses that become dispersed by transmission through the ionosphere and are received by satellites as nonlinear chirps are investigated. Since the dispersion greatly lowers the signal-to-noise ratios, it is difficult to isolate the signals in the time domain. Satellite data are examined with discrete wavelet expansions. Detection is accomplished via a template matching threshold scheme. Quantitative experimental results demonstrate that the chirped wavelet detection scheme is successful in detecting the transionospheric pulses at very low signal-to-noise ratios. 1. Introduction Time/frequency methods can be useful tools for detecting signals that cannot be easily isolated in either time or frequency. Our interest lies primarily with the satellite-based detection of impulse signals, which are dispersed as they travel through the ionosphere, and appear as nonlinear chirps at the rece...

Humanistic computing is proposed as a new signal processing framework in which the processing apparatus is inextricably intertwined with the natural capabilities of our human body and mind. Rather than trying to emulate human intelligence, humanistic computing recognizes that the human brain is perhaps the best neural network of its kind, and that there are many new signal processing applications (within the domain of personal technologies) that can make use of this excellent but often overlooked processor. The emphasis of this paper is on personal imaging applications of humanistic computing, to take a first step toward an intelligent wearable camera system that can allow us to effortlessly capture our day-to-day experiences, help us remember and see better, provide us with personal safety through crime reduction, and facilitate new forms of communication through collective connected humanistic computing. The author’s wearable signal processing hardware, which began as a cumbersome backpackbased photographic apparatus of the 1970’s and evolved into a clothing-based apparatus in the early 1980’s, currently provides the computational power of a UNIX workstation concealed within ordinary-looking eyeglasses and clothing. Thus it may be worn continuously during all facets of ordinary day-to-day living, so that, through long-term adaptation, it begins to function as a true extension of the mind and body.