Figure 1

Principles of Beltrami flow. An image I(x, y) made up of a white square over black background (top) is viewed as a surface S = (x, y, I(x, y)) in a 3D space (bottom). The edges are seen as cliffs in the Z direction. At each point of the surface, the projection of the normal n (arrows in blue) to the Z direction (arrows in black) is the edge indicator in Equation (1), yielding little value at sharp edges. In uniform areas, however, the normal to the surface n runs parallel to Z and the projection thus yields maximum value.