Masked object registration in the Fourier domain

Registration is one of the most common tasks of image analysis and computer vision applications. The requirements of most registration algorithms include large capture range and fast computation so that the algorithms are robust to different scenarios and can be computed in a reasonable amount of time. For these purposes, registration in the Fourier domain using normalized cross-correlation is well suited and has been extensively studied in the literature. Another common requirement is masking, which is necessary for applications where certain regions of the image that would adversely affect the registration result should be ignored. To address these requirements, we have derived a mathematical model that describes an exact form for embedding the masking step fully into the Fourier domain so that all steps of translation registration can be computed efficiently using Fast Fourier Transforms. We provide algorithms and implementation details that demonstrate the correctness of our derivations. We also demonstrate how this masked FFT registration approach can be applied to improve the Fourier-Mellin algorithm that calculates translation, rotation, and scale in the Fourier domain. We demonstrate the computational efficiency, advantages, and correctness of our algorithm on a number of images from real-world applications. Our framework enables fast, global, parameter-free registration of images with masked regions.     

Multiplicative filtering in the fractional Fourier domain

In this article, we investigate the multiplicative filtering in the fractional Fourier transform (FRFT) domain based on the generalized convolution theorem which states that the convolution of two signals in time domain results in simple multiplication of their FRFTs in the FRFT domain. In order to efficiently implement multiplicative filtering, we express the generalized convolution structure by the conventional convolution operation. Utilizing the generalized convolution structure, we convert the multiplicative filtering in the FRFT domain easily to the time domain. Based on the model of multiplicative filtering in the FRFT domain, a practical method is proposed to achieve the multiplicative filtering through convolution in the time domain. This method can be realized by classical Fast Fourier transform (FFT) and has the same capability compared with the method achieved in the FRFT domain. As convolution can be performed by FFT, this method is more useful from practical engineering perspective.     

Motion estimation in the 3-D Gabor domain.

Motion estimation methods can be broadly classified as being spatiotemporal or frequency domain in nature. The Gabor representation is an analysis framework providing localized frequency information. When applied to image sequences, the 3-D Gabor representation displays spatiotemporal/spatiotemporal-frequency (st/stf) information, enabling the application of robust frequency domain methods with adjustable spatiotemporal resolution. In this work, the 3-D Gabor representation is applied to motion analysis. We demonstrate that piecewise uniform translational motion can be estimated by using a uniform translation motion model in the st/stf domain. The resulting motion estimation method exhibits both good spatiotemporal resolution and substantial noise resistance compared to existing spatiotemporal methods. To form the basis of this model, we derive the signature of the translational motion in the 3-D Gabor domain. Finally, to obtain higher spatiotemporal resolution for more complex motions, a dense motion field estimation method is developed to find a motion estimate for every pixel in the sequence.     

Bearing estimation in the bispectrum domain

A new array processing method is presented for bearing estimation based on the cross bispectrum of the array output data. The method is based on the asymptotic distribution of cross-bispectrum estimates and uses maximum likelihood theory. It is demonstrated that, when the noise additive sources are spatially correlated Gaussian with unknown cross-spectral matrix (CSM), the cross-bispectrum method provides better bearing estimates than the stochastic maximum likelihood method with known CSM. Analytical studies and simulations are given to document the performance of the new method     

The errors in FFT estimation of the Fourier transform

The problem of determining the error in approximating the Fourier transform by the discrete Fourier transform is studied. Exact formulas for the relative error are established for classes of functions, called canonical-k (k⩾0), and asymptotic error formulas are established for a much wider class of functions, called order-k. The formulas are dependent only on the class and not on the function in the class whose Fourier transform is being approximated, and this facilitates the application of the results     

Formulation of the Fourier transform in the spectral domain technique

A way to formulate the transform in spectral domain technique is presented.     

Maximum likelihood blind channel estimation in the presence ofDoppler shifts

Transmitter/receiver motion in mobile radio channels may cause frequency shifts in each received path due to Doppler effects. Most blind equalization methods, however, assume time-invariant channels and may not be applicable to fading channels with severe Doppler spread. We address the problem of simultaneously estimating the Doppler shift and channel parameters in a blind setup. Both deterministic and stochastic maximum likelihood methods are developed and iterative solutions proposed. The stochastic maximum likelihood solution is based on the modified version of the Baum-Welch (1970) algorithm, which originated in the study of hidden Markov models. The proposed methods are well suited for short data records appearing in TDMA systems. Identifiability and performance analysis issues are discussed, and Cramer-Rao bounds are derived. In addition, some illustrative simulations are presented     

Fourier domain techniques for digital angiography of the heart

Digital angiography is widely considered simply as a method in which images taken at different times are subtracted from each other. This paper presents some techniques which are performed in the frequency domain after the application of the Fourier transform. Nonselective bypass angiograms and intravenous ventriculograms are taken as examples to show that simple procedures utilizing these techniques exhibit the advantages of improved signal-to-noise ratio in the subtraction images, reduction of motion artifacts, easy application of phase-synchronous subtraction, integration, and quantitative visualization of blood propagation. It is furthermore shown that the storage of the angiographic image sequence as Fourier coefficients leads to data compression and convenient data access in an image database.     

Adaptive Fourier estimation of time-varying evoked potentials

An estimation procedure for dealing with time-varying evoked potentials is presented here. The evoked response is modeled as a dynamic Fourier series and the Fourier coefficients are estimated adaptively by the least mean square algorithm. Approximate expressions have been developed for the estimation error and time constant of adaptation. A procedure for optimizing the estimator performance is also presented. The effectiveness of the estimator in dealing with simulated as well as actual evoked responses is demonstrated.     

Sampling random signals in a fractional Fourier domain

In this paper, we consider the sampling and reconstruction schemes for random signals in the fractional Fourier domain. We define the bandlimited random signal in the fractional Fourier domain, and then propose the uniform sampling and multi-channel sampling theorems for the bandlimited random signal in the fractional Fourier domain by analyzing statistical properties of the input and the output signals for the fractional Fourier filters. Our formulation and results are general and include derivative sampling and periodic nonuniform sampling in the fractional Fourier domain for random signals as special cases.     

Subspace-based estimation of time delays and Doppler shifts

This paper considers the problem of estimating the time delays and Doppler shifts of a known waveform received via several distinct paths by an array of antennas. The general maximum likelihood estimator is presented, and is shown to require a 2d-dimensional nonlinear minimization, where d is the number of received signal reflections. Two alternative solutions based on signal and noise subspace fitting are proposed, requiring only a d-dimensional minimization. In particular, we show how to decouple the required search into a two-step procedure, where the delays are estimated and the Dopplers solved for explicitly. Initial conditions for the time delay search can be obtained by applying generalizations of the MUSIC and ESPRIT algorithms, which are also outlined in the paper. Simulation examples are included to illustrate the algorithms' performance relative to the Cramer-Rao bound     

On the estimation of radar polarization orientation shifts inducedby terrain slopes

In recent studies, D. L. Schuler et al. (2000) applied polarimetric imaging radar-derived orientation angles to measure topography, and J. S. Lee et al. (2000) used orientation angles for polarimetric SAR data compensation, to ensure accurate estimation of geophysical parameters in rugged terrain areas. To support these applications, it is important to accurately estimate shifts in orientation angles induced by the azimuth slope variations. However, in many cases, inconsistency in the estimation of orientation angle shifts was encountered in several areas, introducing noisy and erroneous results. The present authors develop a unified analysis of estimation algorithms based on the circular polarization covariance matrix. The concept of reflection symmetry is used to explain the soundness of the circular polarization method and to show problems associated with other algorithms. L-band polarimetric synthetic aperture radar (SAR) images of Camp Roberts, CA, are used to substantiate this theory     

Motion estimation in the frequency domain using fuzzy c-planesclustering

A previous work explicitly models the discontinuous motion estimation problem in the frequency domain where the motion parameters are estimated using a harmonic retrieval approach. The vertical and horizontal components of the motion are independently estimated from the locations of the peaks of respective periodogram analyses and they are paired to obtain the motion vectors using a procedure proposed by Chen, Giannakis, Nandhakumar (see IEEE Trans. Image Processing, vol.7, p.1242-56, 1998). In this paper, we present a more efficient method that replaces the motion component pairing task and hence eliminates the problems of the pairing method described by Chen et al. The method described in this paper uses the fuzzy c-planes (FCP) clustering approach to fit planes to three-dimensional (3-D) frequency domain data obtained from the peaks of the periodograms. Experimental results are provided to demonstrate the effectiveness of the proposed method.     

Hierarchical motion estimation in Hadamard transform domain

The authors propose a hierarchical motion estimation algorithm in which the sum of the absolute difference in the Hadamard transform domain is used as its matching measure. The computational complexity of this algorithm was reduced to ~5.6% while the image degradation of its reconstructed image quality was <0.1 dB on average, compared with that of the full search in the pixel domain     

3D face recognition in the Fourier domain using deformed circular curves

One of the most significant problems in image and vision applications is the efficient representation of a target image containing a large amount of data with high complexity. The ability to analyze high dimensional signals in a lower dimension without losing their information, has been crucial in the field of image processing. This paper proposes an approach to 3D face recognition using dimensionality reduction based on deformed circular curves, on the shortest geodesic distances, and on the properties of the Fourier Transform. Measured geodesic distances information generates a matrix whose entities are geodesic distances between the reference point and an arbitrary point on a 3D object, and an one-dimensional vector is generated by reshaping the matrix without losing the original properties of the target object. Following the property of the Fourier Transform, symmetry of the magnitude response, the original signal can be analyzed in the lower dimensional space without loss of inherent characteristics. This paper mainly deal with the efficient representation and recognition algorithm using deformed circular curves and the simulation shows promising result for recognition of geometric face information.     

Fractional Fourier transform of the Gaussian and fractional domain signal support

The fractional Fourier transform (FrFT) provides an important extension to conventional Fourier theory for the analysis and synthesis of linear chirp signals. It is a parameterised transform which can be used to provide extremely compact representations. The representation is maximally compressed when the transform parameter, /spl alpha/, is matched to the chirp rate of the input signal. Existing proofs are extended to demonstrate that the fractional Fourier transform of the Gaussian function also has Gaussian support. Furthermore, expressions are developed which allow calculation of the spread of the signal representation for a Gaussian windowed linear chirp signal in any fractional domain. Both continuous and discrete cases are considered. The fractional domains exhibiting minimum and maximum support for a given signal define the limit on joint time-frequency resolution available under the FrFT. This is equated with a restatement of the uncertainty principle for linear chirp signals and the fractional Fourier domains. The calculated values for the fractional domain support are tested empirically through comparison with the discrete transform output for a synthetic signal with known parameters. It is shown that the same expressions are appropriate for predicting the support of the ordinary Fourier transform of a Gaussian windowed linear chirp signal.     

Fourier domain reconstruction of synthetic focus acoustic imaging system

This letter presents a new numerical reconstruction procedure for the synthetic focus system which improves the transversal resolution in acoustic B-scope imaging. It involves calculations in Fourier domain and could be made especially efficient by the use of now commonly available hardwired FFT processors. Computer simulation demonstrates the feasibility of the procedure.     

Time domain algorithm for the estimation of two sinusoidalfrequencies

A computationally simple algorithm is presented that measures one or two frequencies using lookup tables and simple adders. The algorithm is based on a real-time processing of instantaneous frequency and envelope. The algorithm provides a maximum likelihood estimate in the single frequency case. Oversampling is required and the algorithm cannot estimate three or more frequencies. A complete error analysis is presented along with simulation results     

Improved parameter estimation by noise compensation in the time-scale domain

It was shown recently that parameter estimation can be performed directly in the time-scale domain by isolating regions wherein the prediction error can be attributed to the error of individual dynamic model parameters [1]. Based on these single-parameter equations of the prediction error, individual model parameters error can be estimated for iterative parameter estimation. An added benefit of this parameter estimation method, besides its unique convergence characteristics, is the added capacity for direct noise compensation in the time-scale domain. This paper explores this benefit by introducing a noise compensation method that estimates the distortion by noise of the prediction error in the time-scale domain and incorporates that as a confidence factor to bias the estimation of individual parameters error. This method is shown to improve the precision of the estimated parameters when the confidence factors accurately represent the noise distortion of the prediction error.     

Coarse frequency estimation using the discrete Fourier transform (Corresp.)

The discrete Fourier transform (DFT) is applied as a coarse estimator of the frequency of a sine wave in Gaussian noise. Probability of anomaly and the variance of the estimation error are determined by computer simulation for several DFT block sizes as a function of signal energy-to-noise density ratiomathcal{E}/N_0. Several data windows are considered, but uniform weighting gives the best performance.