Cultural Heritage Applications: Archaeological Ceramics and Building Restoration - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 129

describe them based on mixtures of ICA. Section 6.1.4 presents the experiments
and the results obtained in the sorting of ceramic pieces from four different
periods: Bronze Age, Iberian, Roman, and Middle Ages. Section 6.1.5 presents the
conclusions and future line of work.
We reported some preliminary results related to this archaeological application
which was presented in conference [ 6 ]. The following significant new contribu-
tions are presented in this application: rationale and selection of new ultrasonic
features; use of a classifier that is based on probabilistic semi-supervision of ICA
mixture models that are suitable for handling expert uncertainty; implementation
of an ad hoc device designed to avoid the uncontrolled conditions of a totally
manual measurement procedure; and demonstration of physical interpretation of
the results obtained by the proposed method in comparison with standard methods
used in archaeology. Therefore, this work provides the foundations to implement a
practical method to complement or even replace some of the destructive and time-
consuming techniques that are currently employed in archaeology.

6.1.2 Through-Transmission Model and Feature
Definition

A simplified model of ultrasonic through-transmission analysis is to consider that
the recorded signal is the convolution of the material reflectivity with a linear time
varying (LTV) system (see Fig. 6.1 ). The variant impulse response of the LTV is
the injected ultrasonic pulse travelling through the material, which bears the effects
of attenuation and dispersion that affect both its amplitude and frequency content.
Actually, some non-linearity may be incorporated into this simple model in some
specific cases; however, in general, the linear assumption is adequate for a large
number of situations, or is at least enough to be able to obtain practical solutions
yielding reasonable performance. Thus, the received signal x ð t Þ looks similar to the
one shown in Fig. 6.1 .
If we consider that x ð t Þ is a realization of a nonstationary stochastic process
x ð t fg having instantaneous power spectral density P x ð f ; t Þ; different ''ultrasonic
signatures'' us ð t Þ can be computed like those included in Eqs. ( 6.1 - 6.4 ).

R

f 2

f P x ð f ; t Þ df

f 1

Centroid frequency ð fc): us ð t Þ¼ f c ð t Þ¼ ð 6 : 1 Þ

R

f 2

P x ð f ; t Þ df

f 1

Maximum frequency fmax ð Þ : us ð t Þ¼ f max ð t Þ¼ max P x ð f ; t Þ ð 6 : 2 Þ

|{z}
f