A combination of nanoscale imaging techniques such as atomic force microscopy and scanning electron microscopy are used to investigate the relationship between surface morphology and height statistics of GaN cap layers in InGaN/GaN light emitting diode heterostructures. The investigated samples were grown in two very different growth regimes which lead to distinct characteristic superficial landscapes. We also report here on the introduction of a new methodological approach that adapt the concept of height-height correlation function, a well known statistical tool in the field of studies on rough surfaces. We evaluate to which extent the geometrical properties of the constitutive 'bricks' (hillocks for ammonia assisted molecular beam epitaxial film) and structural defects (dislocation pits for metal organic vapor phase epitaxial film) affects the statistical properties of heights of these GaN surfaces. Finally, we have studied the spatial distribution of dislocation pits in both the samples to assess the quantitative differences between these heterostructures of very distinct surface morphology. (C) 2016 Elsevier Ltd. All rights reserved.