Classification Of Textures Using Second‐Order Spectra

. We consider the classification of textures as realizations of stationary random fields using non‐parametric estimates of their second‐order spectra. The random fields in each class are assumed to be stationary with the same spectrum, which we estimate from a finite sample by smoothing its periodogram. The classification rule can be interpreted as maximizing a mean square convergent approximation to the averaged log‐likelihood if the random fields are Gaussian, and in general as minimizing the discrepancy of the periodogram from the spectrum of the class. The limiting behaviour of the probability of misclassification as the sample size tends to infinity is studied under certain cumulant conditions. The classification rule is illustrated with real texture data.