Feature extraction in image data has been investigated for many years, and more recently the problem of processing images containing irregularly distributed data has become prominent. Range data are now commonly used in the areas of image processing and computer vision. However, due to the data irregularity found in range images that occurs with a variety of image sensors, direct image processing, in particular edge detection, is a nontrivial problem. Typically, irregular range data would require to be interpolated to a regular grid prior to processing. One example of an edge detection technique that can be directly applied to range images is the scan-line approximation, but this does not employ exact data locations. Therefore, we present novel Laplacian operators that can be applied directly to irregularly distributed data, and in particular we focus on application to irregularly distributed 3-D range data for the purpose of edge detection. Within the data distribution framework commonly occurring in range data acquisition devices, our results illustrate that the approach works well over a range of levels of irregularity of data distribution. The use of Laplacian operators on range data is also found to be much less susceptible to noise than the traditional use of Laplacian operators on intensity images.