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Image processing tasks have traditionally involved the use of square operators on regular rectangular image lattices. For many years the concept of using hexagonal pixels for image capture has been investigated, and several advantages of such an approach have been highlighted. Therefore, we present a design procedure for hexagonal gradient operators, developed within the finite element framework, for use on hexagonal pixel based images. In order to evaluate the approach we generate pseudo hexagonal images via resizing and resampling which also allows us to present results visually without the use of hexagonal lattice capture or display hardware. We provide comparative results with existing gradient operators, both rectangular and hexagonal.