A note on the gradient of a multi-image

Abstract

Gradient based edge detection techniques can be extended to multispectral images in various ways: difference operators can be applied to each component of a multi-image, and the results can be combined, e.g., taking the RMS, or the sum, or the maximum of their absolute values. In all of these approaches the image-components do not actually cooperate with one another, i.e., edge evidence along a given direction in one component does not reinforce edge evidence along the same direction in other components. To avoid this, the use of the tensor gradient of multi-images regarded as vector fields is suggested. Explicit formulas for the direction along which the rate of change is maximum, as well as for the maximum rate of change itself, are derived. Digital approximations are obtained by surface fitting.