Different scaling and autocorrelation characteristics and their application to astronomical images are discussed: the structure function, the autocorrelation function, Fourier spectra and wavelet spectra. The choice of the mathematical tool is of great importance for the scaling analysis of images. The structure function, for example, cannot resolve scales which are close to the dominating larg...

Abstract— This paper derives two discrete motion models for 3D pose recovery starting from the stochastic differential equations that describe the object’s motion in continuous time. The velocity is considered first as a Wiener process, which underlies the very often-used constant velocity model, and second as an Ornstein-Uhlenbeck process. Analysis of the autocorrelation signal derived in expe...

As spatial autocorrelation latent in georeferenced data increases, the amount of duplicate information contained in these data also increases. This property suggests the research question asking what the number of independent observations, ay n*, is that is equivalent o the sample size, n, of a data set. This is the notion of effective sample size. Intuitively speaking, when zero spatial autoco...

In two recent papers, a description is given of a means of obtaining an arbitrarily narrow peak in the calculation of the autocorrelation function [J. C. Brown, and M. S. Puckette, "Calculation of a narrowed autocorrelation function," J. Acoust. Sec. Am. 85, 1595-1601 (1989) ] or era narrow valley in the calculation of an inverse autocorrelation [J. C. Brown, and M. S. Puekette, "Musical inform...

We present a technique for measuring transient microscopic dynamics within deep tissue with sub-second temporal resolution, using diffusing-wave spectroscopy with gated single-photon avalanche photodiodes (APDs) combined with standard ungated multi-tau correlators. Using the temporal autocorrelation function of a reference signal allows to correct the temporal intensity autocorrelation function...

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the inf...

In this paper, we propose an improved autocorrelation function (ACF) based watermarking. The autocorrelation function based watermarking has been known to be one of the effective watermarking schemes that are resilient to geometric transform attacks. In this watermarking scheme, both the peaks in the autocorrelation function of a marked image and the embedded watermark should survive after vari...

We consider the task of estimating an operator from sampled data. The operator, which is described by a rational transfer function, is applied to continuous-time white noise and the resulting continuous-time process is sampled uniformly. The main question we are addressing is whether the stochastic properties of the time series that originates from the sample values of the process allows one to...