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The use of range data has become prominent in the field of computer vision. Due to the irregular nature of range data that occurs with a number of sensors, feature extraction is a complex and challenging problem. Feature extraction 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 Laplacian operators that can be applied to both regularly or irregularly distributed range data. We demonstrate that the feature maps generated using our approach on range data are much less susceptible to noise than the traditional use of Laplacian operators on intensity images.