This paper presents the Discriminative Generalized Hough Transform (DGHT) as a robust and accurate method for the localization of epiphyseal regions in radiographs of the left hand. The technique utilizes a discriminative training approach to generate shape models with individual positive and negative model point weights for the Generalized Hough Transform. The framework incorporates a multi-level approach which reduces the searched region in two zooming steps, using specifically trained DGHT shape models. In addition to the standard method, a novel landmark combination approach is presented. Here, the N-best lists of individual landmark localizations are combined with anatomical constraints to achieve a globally optimal localization result for all 12 considered epiphyseal regions of interest. The technique has been applied to extract 12 epiphyseal regions of interest for a subsequent automatic bone age assessment. It achieved a localization success rate of 98.1% on a corpus with 412 left hand radiographs covering the age range from 3 to 19 years.