Bilinear Factorization Research Articles

A perspective factorization method for Euclidean reconstruction with uncalibrated cameras

AbstractStructure from motion (SFM), which is recovering camera motion and scene structure from image sequences, has various applications, such as scene modelling, robot navigation, object recognition and virtual reality. Most of previous research on SFM requires the use of intrinsically calibrated cameras. In this paper we describe a factorization‐based method to recover Euclidean structure from multiple perspective views with uncalibrated cameras. The method first performs a projective reconstruction using a bilinear factorization algorithm, and then converts the projective solution to a Euclidean one by enforcing metric constraints. The process of updating a projective solution to a full metric one is referred as normalization in most factorization‐based SFM methods. We present three normalization algorithms which enforce Euclidean constraints on camera calibration parameters to recover the scene structure and the camera calibration simultaneously, assuming zero skew cameras. The first two algorithms are linear, one for dealing with the case that only the focal lengths are unknown, and another for the case that the focal lengths and the constant principal point are unknown. The third algorithm is bilinear, dealing with the case that the focal lengths, the principal points and the aspect ratios are all unknown. The results of experiments are presented. Copyright © 2002 John Wiley & Sons, Ltd.

Theory of magnetostatic forward volume wave convolvers

The present paper reports a theory for MSFVW convolvers which incorporates the underlying nonlinear multiplication and spatial integration processes as well as the inherent dispersiveness of the MSFVW's. The double-frequency convolution signal is assumed to be picked up by a full-turn microstrip loop lying on the YIG-film surface and to be generated by contra-propagating signals that are either cw or time-limited cw pulses. Computations of the convolver bilinearity factor F T indicate an efficient convolution process over a wide bandwidth, with values of F T that are of the same order as, or better than, the reported experimental results for MSW convolution in a YIG cylindrical or plate geometry. The distortion in the convolution signal caused by the pronounced dispersive behaviour of MSFVW's is significantly weaker than what one might have expected. This result is a consequence of the rather small bandwidth on either side of the carrier frequency of the cw pulses which contributes to the integral function representing the induced convolution pick-up signal.

Narrow-aperture chirp transducers for SAW convolvers

Narrow-aperture SAW beams can be generated efficiently using chirp transducers, thus avoiding the need for beam compression in convolvers. The transducers can be designed such as to compensate for phase errors due to dispersive SAW propagation. Experimental confirmation was obtained using convolvers with 120 MHz bandwidth and 16 μs interaction length, and a bilinearity factor of -65 dBm was achieved.

Convolution with magnetoelastic Rayleigh waves on bulk YIG

This letter reports the observation of the most efficient convolution of magnetoelastic Rayleigh waves on bulk YIG reported to date. With 83-MHz input signals launched in opposite directions using ZnO transducers, an internal bilinearity factor of -31 dBm which is comparable to that of the best Si-LiNbO 3 convolver has been realized.

S.A.W. convolver using secondary electrons

Nonlinear interaction of oppositely-directed s.a.w. with secondary electrons was investigated. It was shown that the bilinear factor of this system is about 40 dB higher than one in the best known coupled semiconductor-piezoelectric structure.

Efficiency of the surface-acoustic-wave diode convolver

The diode convolver performs signal processing, for example correlation, by mixing two input waveforms in an array of diodes, each diode being connected to a tap on a surface acoustic wave delay line. This paper gives the theory for the device efficiency, for a parallel circuit arrangement of taps and diodes. The effect of stray capacity is also analyzed. An experimental 31-tap device used hybrid circuitry in order to allow close spacing of the taps, giving a tap-to-tap propagation time of 90 ns. The efficiency agrees well with theory, showing that the bilinearity factor is maximized for an intermediate value of the bias current. The maximum bilinearity factor, relating external powers, was -34 dBm.

Signal processing with surface waves via the double acousto-optic interaction

Optical diffraction by two successive surface acoustic waves was used to achieve various signal-processing operations. Expressions were derived for the frequency spectrum and bilinearity factor associated with this double interaction and these formulas were verified experimentally using Fabry-Perot interferometry. An aperture function formalism was used to demonstrate that the doubly diffracted field corresponds in form to that required for real-time convolution. The addition of a simple lens system extended the capability of this technique to a full range of processing functions. The following operations were demonstrated for pulses of the order of 1 μs: squaring convolution, squaring correlation, variable time expansion, variable time compression, time inversion, and image scanning. This processor is characterized by large bandwidth since the diffraction takes place in the Raman-Nath limit up to GHz frequencies.

A SAW planar piezoelectric convolver

An increase of the dynamic range of a surface-wave piezo-electric convolver can be obtained by increasing its bilinear factor. We show that this can be done by reducing the acoustic beamwidth in the interaction region. A lower limit of beamwidth is found through the study of the guided modes in the convolver plate. A 600-BT product device using nonsymmetrical couplers to obtain the beamwidth reduction is described. The main characteristics-bandwidth, dynamic range, spurious signals-are given and we show a linear FM pulse autocorrelation performed in this device.

Acoustic convolver using multistrip beamwidth compressors

A degenerate nonlinear surface-wave convolver has been built from nonsymmetrical couplers working as beamwidth compressors to increase the acoustic power density and thus the bilinear merit factor. The measured results are compared with those of the classical LiNbO3 convolver, and the practical advantages of this new structure are pointed out. To demonstrate the device capability, the autocorrelation function of a linear f.m. pulse whose b.t. product was 120 has been performed.

Convolution with magnetostatic waves in a y.i.g. rod

Mixing of oppositely directed magnetostatic waves has been demonstrated in an axially magnetised y.i.g. rod. Using both single and double pulses, convolution has been achieved at 1275 MHz. Measurements and preliminary theory indicate a substantially greater bilinearity factor than that obtainable with devices currently available.