In this paper, an approach for the classification and localization of geometric shapes, e.g., man-made objects or different types of geological features, in sonar images is presented. It is applied to a concrete application case, namely the detection and classification of naval mines. The approach consists of three steps. In the first step, the sonar image is segmented by a new active contours algorithm. To deal with the significant noise on sonar images, the assumption is used that the segmenting contours of highlight and shadow areas of objects are geometric shapes that can be described by superellipses. It is shown here that this superellipse constraint, which can cover a wide range from box-shaped to round objects, can directly be incorporated into an active contours method without an additional edge framework. In addition to its robustness to noise, our superellipse-driven active contours approach has the advantage that it is adaptable to the intensity distribution properties of sonar images. The second step consists of the actual classification including a pose estimation using a standard naive Bayes classifier on the superellipse parameters that are computed by the segmentation in the first step. Robustness is further boosted in a novel third step in which the classification is verified in a top-down process. Based on the results of the bottom-up processes, i.e., the segmentation in step one and the pose estimation from the superellipse parameters plus the class estimation by the classifier in step two, it is possible to simulate what the input sonar image should look like if the results are correct. If this model-based top-down simulation is similar to the original sensor image, the classification result is accepted; otherwise it is rejected. To this end, different measures are compared to compute the similarity between the real sensor image and the anticipated image generated from the classification and localization hypothesis. Finally, our approach is evaluated with a challenging real-world data set of 213 synthetic aperture sonar sidescan images from sea trials with mock-up mines.