The Morphological Equivalent of Gaussian Scale-Space

Abstract

An image is the result of a physical measurement, e.g. the luminance on the retina or the distance from the observer to the “depicted” objects. All physical measurements are the result of the interaction of a measurement probe of finite spatial and temporal size with the physical world. The size of the measurement probe determines at what scale the world is observed. This observation scale is often called the inner scale as it is proportional to the size of the smallest details that can be meaningful distinguished in the image.