Scale-imprecision space

It is argued that image measurements should satisfy two requirements of physical plausibility: the measurements are of non-zero scale and non-zero imprecision; and two required invariances, nothing is lost by expanding the image and nothing is lost by increasing the contrast of the image. A model of measurements satisfying these constraints, based on blurring the graph of the incident luminance, is described. Within this framework, several types of filtering can be expressed: mean filtering (ordinary scale space); median filtering: and mode filtering. It is found that of these possibilities, a system based on mode filtering produces interesting results. In particular, edges-defined as discontinuities-naturally appear, and their behaviour over scale and imprecision is presented.