A method for recovery of compact volumetric models for shape representation and segmentation in computer vision is introduced. The models are superquadrics with parametric deformations (bending, tapering, and cavity deformation). The input for the model recovery is three-dimensional range points. We define an energy or cost function whose value depends on the distance of points from the model's surface and on the overall size of the model. Model recovery is formulated as a least-squares minimization of the cost function for all range points belonging to a single part. The initial estimate required for minimization is the rough position, orientation and size of the object. During the iterative gradient descent minimization process, all model parameters are adjusted simultaneously, recovering position, orientation, size and shape of the model, such that most of the given range points lie close to the model's surface. Because of the ambiguity of superquadric models, the same shape can be described with different sets of parameters. A specific solution among several acceptable solutions, which are all minima in the parameter space, can be reached by constraining the search to a part of the parameter space. The many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization. Segmentation is defined as a description of objects or scenes in terms of the adopted shape vocabulary. Model recovery of an object consisting of several parts starts by computing the rough position, orientation and size of the whole object. By allowing a variable number of range points in a model, a model can actively search for a better fit (by compressing itself and expanding) resulting in a subdivision of the object into a model representing the largest part of the object and points belonging to the rest of the scene. Using the same method, the remaining points can be recursively subdivided into parts each represented with a single compact volumetric model. Results using real range data show that the recovered models are stable and that the recovery procedure is fast.