Feature classes for 1D, 2nd order image structure arise from natural image maximum likelihood statistics

Much is understood of how quantitative aspects of image structure are measured by VI simple cells, but less about how qualitative structure is determined from these measurements. We review Geometric Texton Theory (GTT) that aims to describe this step from quantitative to qualitative. GTT proposes that qualitative feature categories arise through consideration of the maximum likelihood (ML) explanations of image measurements. It posits that a pair of output vectors of an ensemble of co-localised neurons signal the same feature category if and only if the corresponding ML explanations are qualitatively similar. We present mathematical and empirical results relevant to GTT for the limited case of measurement by 1D filters of up to 2nd order. The mathematical results identify the simplest explanations for measurements by such filters, while the empirical results identify the ML. We find that the ML explanations are not the most simple under any of the definitions of simple that we examined. However, the ML explanations do have properties predicted by GTT. In particular they change rapidly and qualitatively for certain narrow regions of measurement space, while remaining qualitative stable between those transition regions. Three feature categories arise naturally from the data: light bars, dark bars and edges. The results are consistent with GTT.