Real-time extraction of features from range images can play an important role in computer vision tasks such as localisation and navigation. Developing operators that can characterise features in a range image, such as jump, crease, or smooth edges, is challenging, due to both the irregular spatial distribution of range image data and the nature of the features themselves. We present adaptive gradient operators that can automatically change shape to accommodate irregular data distribution; through appropriate analysis of the output responses, we show that the operators can also be specialised to characterise particular types of range image features.