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Multivariate morphological granulometric texture classification using Walsh and wavelet features

As introduced by Matheron, granulometries depend on a single sizing parameter for each structuring element forming the filter. The size distributions resulting from these granulometries have been used successfully to classify texture by using as features the moments of the normalized size distribution. The present paper extends the concept of granulometry in such a way that each structuring element has its own sizing parameter and the resulting size distribution is multivariate. Classification is accomplished by taking either the Walsh or wavelet transform of the multivariate size distribution, obtaining a reduced feature set by applying the Karhunen-Loeve transform to decorrelate the Walsh or wavelet features, and classifying the textures via a Gaussian maximum-likelihood classifier.