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The use of range images has become prominent in the field of computer vision. Due to the irregular nature of range image data that occurs with a number of sensors, edge detection techniques for range images are often based on scan line data approximations and hence do not employ exact data locations. We present a finite element based approach to the development of gradient operators that can be applied to both regularly and irregularly distributed range images. We have created synthetic irregularly distributed range images for each edge type, and the gradient operators developed are evaluated with respect to their performance in edge detection across varying levels of data irregularity.