A general framework for low level vision

TLDR

Intensity images are treated as 2‑D surfaces embedded in 3‑D space for gray‑level images and in 5‑D space for color images. The authors aim to introduce a new geometrical framework that generates natural flows for image scale space and enhancement. The framework defines a geometrical model that yields natural flows for scale‑space and enhancement operations. The formulation unifies classical schemes through simple intensity‑contrast scaling, producing efficient algorithms, and naturally extends to multidimensional signals for powerful denoising and scale‑space methods.

Abstract

We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the (x, I) space. The image is, thereby, a two-dimensional (2-D) surface in three-dimensional (3-D) space for gray-level images, and 2-D surfaces in five dimensions for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms.