Fractional brownian motion: a maximum likelihood estimator and its application to image texture

Fractals have been shown to be useful in characterizing texture in a variety of contexts. Use of this methodology normally involves measurement of a parameter H, which is directly related to fractal dimension. In this work the basic theory of fractional Brownian motion is extended to the discrete case. It is shown that the power spectral density of such a discrete process is only approximately proportional to |f|a instead of in direct proportion as in the continuous case. An asymptotic Cramer-Rao bound is derived for the variance of an estimate of H. Subsequently, a maximum likelihood estimator (MLE) is developed to estimate H. It is shown that the variance of this estimator nearly achieves the minimum bound. A generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the MLE when the discrete fractional Brownian process is contaminated with additive Gaussian noise. The results show that even at signal-to-noise ratios of 30 dB, significant errors in estimation of H can result when noise is present. The MLE is then applied to X-ray images of the human calcaneus to demonstrate how the line-to-line formulation can be applied to the two-dimensional case. These results indicate that it has strong potential for quantifying texture.     

Laser spectroscopic measurement of quenching and doublet mixing rates of the Na(3P(3/2, 1/2)) doublet in a propane-air flame

We have measured the quenching rate of the Na 3P level and the doublet mixing rates of the Na 3P(3/2) and 3P(1/2) levels in a propane-air flame at atmospheric pressure. To obtain these rates, subnanosecond time-resolved fluorescence measurements were made using a mode-locked dye laser and the time-correlated single-photon counting method. Our results are 1.4 x 10(9) s(-1) for the quenching rate and 3.0 x 10(9) s(-1) for the 3P(3/2) --> 3P(1/2) mixing rate.     

Anomalous refractive indices of the amplifying medium in a waveguide CO2 laser

The relative changes in refractive index of the amplifying medium in a waveguide CO2 laser have been measured as a function of the inlet and outlet pressures, discharge current, gas flow rate, and intracavity power using an interferometric technique. The experiments have been made for two gas mixing ratios over a wide range of the inlet pressure. Saturated phenomena of the refractive index have been observed for increasing inlet pressure. The output power and the variation in impedance of the amplifying medium have been simultaneously measured. The dependence of the refractive index on the inlet pressure in the absence of the discharge, the electron density, and the estimation of errors in measurements are discussed.