Color image analysis in a vector field

A color image can be defined by a function (vector field) F:V2→V3 where V2 is a 2-dimensional pixel coordinate space and V3 is a 3-dimensional color space with r, g, b color signals transformed to CIE L*a*b* uniform color space. The derivative of the vector field F´(x) is characterized by the Jacobian matrix. The largest singular value of Jacobian matrix shows the vector gradient magnitude. In this paper we show that the detected edges obtained from the largest singular value are more accurate and finer than the edges obtained by the differential operator method