A non-parametric method of, and system for, dimensioning an object of arbitrary shape, captures a three-dimensional (3D) point cloud of data points over a field of view containing the object and a base surface on which the object is positioned, detects a base plane indicative of the base surface from the point cloud, extracts the data points of the object from the point cloud, processes the extracted data points of the object to obtain a convex hull, and fits a bounding box of minimum volume to enclose the convex hull. The bounding box has a pair of mutually orthogonal planar faces, and the fitting is performed by orienting one of the faces to be generally perpendicular to the base plane, and by simultaneously orienting the other of the faces to be generally parallel to the base plane.