We introduce an object-based method to automatically classify topography from SRTM data. The new method relies on the concept of decomposing land-surface complexity into more homogeneous domains. An elevation layer is automatically segmented and classified at three scale levels that represent domains of complexity by using self-adaptive, data-driven techniques. For each domain, scales in the data are detected with the help of local variance and segmentation is performed at these appropriate scales. Objects resulting from segmentation are partitioned into sub-domains based on thresholds given by the mean values of elevation and standard deviation of elevation respectively. Results resemble reasonably patterns of existing global and regional classifications, displaying a level of detail close to manually drawn maps. Statistical evaluation indicates that most of classes satisfy the regionalization requirements of maximizing internal homogeneity while minimizing external homogeneity. Most objects have boundaries matching natural discontinuities at regional level. The method is simple and fully automated. The input data consist of only one layer, which does not need any pre-processing. Both segmentation and classification rely on only two parameters: elevation and standard deviation of elevation. The methodology is implemented as a customized process for the eCognition® software, available as online download. The results are embedded in a web application with functionalities of visualization and download.