Image oversegmentation creates small, compact, and irregularly shaped regions subject to further clustering. Consideration of texture characteristics can improve the resulting quality of the clustering process. Existing methods based on an orthogonal transform into frequency domain can extract texture features of arbitrarily shaped regions only from inscribed rectangles. We propose a method for extracting texture features of entire arbitrarily shaped image regions using orthogonal transforms. Furthermore, we introduce a mathematically correct method for unifying spectral dimensions that is necessary for accurate comparison and classification of spectra with different dimensions. The proposed method is particularly suitable for classifying areas with periodic and quasiperiodic textures. Our approach exploits the texture periodification property of certain orthogonal transforms that is based on insertion of zeros into the spectrum. We identified some of those orthogonal transforms which possess this important property and also provide mathematical proofs of our claims. Last, we show that inclusion of luminance and chrominance components into the feature vector increases the precision of the proposed method which then becomes suitable for natural scene images as well.