Continuous casting is a highly efficient process used to produce most of the world steel production tonnage, but can cause cracks in the semi-finished steel product output. These cracks may cause problems further down the production chain, and detecting them early in the process would avoid unnecessary and costly processing of the defective goods. In order for a crack detection system to be accepted in industry, however, false detection of cracks in non-defective goods must be avoided. This is further complicated by the presence of scales; a brittle, often cracked, top layer originating from the casting process. We present an approach for an automated on-line crack detection system, based on 3D profile data of steel slab surfaces, utilizing morphological image processing and statistical classification by logistic regression. The initial segmentation successfully extracts 80% of the crack length present in the data, while discarding most potential pseudo-defects (non-defect surface features similar to defects). The subsequent statistical classification individually has a crack detection accuracy of over 80% (with respect to total segmented crack length), while discarding all remaining manually identified pseudo-defects. Taking more ambiguous regions into account gives a worst-case false classification of 131 mm within the 30 600 mm long sequence of 150 mm wide regions used as validation data. The combined system successfully identifies over 70% of the manually identified (unambiguous) crack length, while missing only a few crack regions containing short crack segments. The results provide proof-of-concept for a fully automated crack detection system based on the presented method.