The quantification of local surface complexity in the human cortex has shown to be of interest in investigating population differences as well as developmental changes in neurodegenerative or neurodevelopment diseases. We propose a novel assessment method that represents local complexity as the difference between the observed distributions of local surface topology to its best-fit basic topology model within a given local neighborhood. This distribution difference is estimated via Earth Move Distance (EMD) over the histogram within the local neighborhood of the surface topology quantified via the Shape Index (SI) measure. The EMD scores have a range from simple complexity (0.0), which indicates a consistent local surface topology, up to high complexity (1.0), which indicates a highly variable local surface topology. The basic topology models are categorized as 9 geometric situation modeling situations such as crowns, ridges and fundi of cortical gyro and sulci. We apply a geodesic kernel to calculate the local SI histogram distribution within a given region. In our experiments, we obtained the results of local complexity that shows generally higher complexity in the gyral/sulcal wall regions and lower complexity in some gyral ridges and lowest complexity in sulcal fundus areas. In addition, we show expected, preliminary results of increased surface complexity across most of the cortical surface within the first years of postnatal life, hypothesized to be due to the changes such as development of sulcal pits.