Texel-based image classification with orthogonal bases

Periodic variations in patterns within a group of pixels provide important information about the surface of interest and can be used to identify objects or regions. Hence, a proper analysis can be applied to extract particular features according to some specific image properties. Recently, texture analysis using orthogonal polynomials has gained attention since polynomials characterize the pseudo-periodic behavior of textures through the projection of the pattern of interest over a group of kernel functions. However, the maximum polynomial order is often linked to the size of the texture, which implies in many cases, a complex calculation and introduces instability in higher orders leading to computational errors. In this paper, we address this issue and explore a pre-processing stage to compute the optimal size of the window of analysis called “texel.” We propose Haralick-based metrics to find the main oscillation period, such that, it represents the fundamental texture and captures the minimum information, which is sufficient for classification tasks. This procedure avoids the computation of large polynomials and reduces substantially the feature space with small classification errors. Our proposal is also compared against different fixed-size windows. We also show similarities between full-image representations and the ones based on texels in terms of visual structures and feature vectors using two different orthogonal bases: Tchebichef and Hermite polynomials. Finally, we assess the performance of the proposal using well-known texture databases found in the literature.