A Scale-Free and Parameter-Free Image Edge Strength Measure

We present a family of image Slope Measures which are scale-free measures that are highest near image edges. They are defined at each pixel as the steepest of the (up, down, or bi-directional) intensity slopes to every other pixel. We list some useful mathematical properties such as intensity and rotation invariances and show a relationship to the maximal morphological dilations and erosions by cones. We discuss generalisations by using non-Euclidean distances or non-conical structuring functions, and extensions to colour, multi-spectral and higher-dimensional images. We present detailed pseudo-code for a fast doubly-recursive multi-resolution algorithm and give typical algorithm timings and visually demonstrate the measure as applied to standard test images. Reference C code for these algorithms is available on the internet at: https://github.com/xomexx/SlopeMeasures.