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Mine-like object classification from sidescan sonar images is of great interest for mine counter measure (MCM) operations. Because the shadow cast by an object is often the most distinct feature of a sidescan image, a standard procedure is to perform classification based on features extracted from the shadow. The classification can then be performed by extracting features from the shadow and comparing this to training data to determine the object. In this paper, a superellipse fitting approach to classifying mine-like objects in sidescan sonar images is presented. Superellipses provide a compact and efficient way of representing different mine-like shapes. Through variation of a simple parameter of the superellipse function different shapes such as ellipses, rhomboids, and rectangles can be easily generated. This paper proposes a classification of the shape based directly on a parameter of the superellipse known as the squareness parameter. The first step in this procedure extracts the contour of the shadow given by an unsupervised Markovian segmentation algorithm. Afterwards, a superellipse is fitted by minimizing the Euclidean distance between points on the shadow contour and the superellipse. As the term being minimized is nonlinear, a closed-form solution is not available. Hence, the parameters of the superellipse are estimated by the Nelder-Mead simplex technique. The method was then applied to sidescan data to assess its ability to recover and classify objects. This resulted in a recovery rate of 70% (34 of the 48 mine-like objects) and a classification rate of better than 80% (39 of the 48 mine-like objects).