Euclidean proximity function in image processing

In image processing measuring and valuing a distance between two points is important. The obtained values can be used for determining whether two points are close to each other or to define weights for a filter concentrated around a central element. While there are measures of proximity, neither of them was defined with a such use in mind, mostly concentrating on problem of an optimization. The idea is to turn the Euclidean distance between two points into a measure of how close (or far) two points are from each other, basing on two given ranges. The function was mostly obtained by a theoretical analysis supported with a mathematical calculation and examples of use. As it was proven in the work, the obtained function can be implemented not only to measure proximity, but also as a flexible kernel for image filters, allowing for blurring or edge-detection.