DETECTING BOUNDARIES IN A VECTOR FIELD

A vector gradient approach is proposed to detect boundaries in multidimensional data with multiple attributes (a vector field). It is used to extend a gradient edge detector to color images. The statistical effects of noise on the distribution of the amplitudes and directions of the vector gradient are characterized. The noise behavior of the L2 norm of the scalar gradients is also characterized for comparison. When the attribute components are highly correlated, as is often the case in color images, use of the vector gradient shows a small gain in signal-to-noise ratio over that of the L2 norm of the scalar gradients. This small gain may or may not be significant, depending on other measures an edge detector uses to deal with noise.