Model-based segmentation approaches have been proven to produce very accurate segmentation results while simultaneously providing an anatomic labeling for the segmented structures. However, variations of the anatomy, as they are often encountered e.g. on the drainage pattern of the pulmonary veins to the left atrium, cannot be represented by a single model. Automatic model selection extends the model-based segmentation approach to handling significant variational anatomies without user interaction. Using models for the three most common anatomical variations of the left atrium, we propose a method that uses an estimation of the local fit of different models to select the best fitting model automatically. Our approach employs the support vector machine for the automatic model selection. The method was evaluated on 42 very accurate segmentations of MRI scans using three different models. The correct model was chosen in 88.1% of the cases. In a second experiment, reflecting average segmentation results, the model corresponding to the clinical classification was automatically found in 78.0% of the cases.