We demonstrate how known convolution techniques for uncertain data can be used to set the shapes of structuring elements in adaptive mathematical morphology, enabling robust morphological processing of partially occluded or otherwise incomplete data. Results are presented for filtering of both gray-scale images containing missing data and 3D profile data where information is missing due to occlusion effects. The latter demonstrates the intended use of the method: enhancement of crack signatures in a surface inspection system for casted steel.The presented method is able to disregard unreliable data in a systematic and robust way, enabling adaptive morphological processing of the available information while avoiding any false edges or other unwanted features introduced by the values of faulty pixels.