1. An apparatus for estimating dimensions of an object associated with an electro-optically readable code, comprising: a handheld device aimable at a scene containing the object supported on a base surface; a scanner supported by the device and operative for scanning the scene over a field of view to obtain a position of a reference point of the code associated with the object, and for reading the code; a dimensioning sensor supported by the device and operative, in automatic response to the reading of the code, for capturing a three-dimensional (3D) point cloud of data points of the scene; a controller for clustering the point cloud into data clusters, for locating the reference point of the code in one of the data clusters, for extracting from the point cloud the data points of the one data cluster belonging to the object, and for processing the extracted data points belonging to the object to estimate the dimensions of the object; and wherein the controller is operative for detecting a base plane indicative of the base surface from the point cloud, for processing the extracted data points belonging to the object to obtain a convex hull, and for fitting a bounding box of minimum volume to enclose the convex hull, the bounding box having a pair of mutually orthogonal planar faces, the controller being operative for orienting one of the faces to be generally perpendicular to the base plane, and for simultaneously orienting the other of the faces to be generally parallel to the base plane.