Object modeling is a multifaceted and active area of research in image analysis, manufacturing, and computational geometry. In image analysis, the focus of this paper, objects may be described in terms of their shape and appearance. Geometric features that are invariant to scale, rotation and translation are essential for proper modeling of shape. Deformable random objects, common in biomedical imaging, do not carry distinct features and suffer from multiple sources of uncertainty, including resolution, size, location and occlusion. Registration involves generating the transformation parameters for mapping a source to a target, while categorization involves matching entities into classes. Both processes, involve mapping attributes of objects with respect to each other, and robust features together with proper similarity measures are keys for good performance. This article examines the issues of features, similarity measures for registration and categorization of small-size deformable random objects; a case study of lung nodules in chest CT is used as an example. We show that feature descriptors capturing textural contents are more effective for these types of objects. The paper includes survey and evaluations of several modern feature descriptors that have been introduced in the computer vision and image analysis literature.