Gradient fusion operators for vector-valued image processing

While classical image processing algorithms were designed for scalar-valued (binary or grayscale) images, new technologies have made it commonplace to work with vector-valued ones. These technologies can involve new types of sensors, as in remote sensing, but also mathematical models leading to an increased cardinality at each pixel. This work analyzes the role of first-order differentiation in vector-valued images; specifically, we explore a novel operator to produce a 2D vector from a Jacobian matrix, in order to represent the variation in a vector-valued image as a planar feature