This paper proposes a novel method for determining a three-dimensional (3D) bounding box to estimate pose (position and orientation) and size of a 3D object corresponding to a segmented object region in an image acquired by a single calibrated camera. The method is designed to work upon an object on the ground and to determine a bounding box aligned to the direction of the object, thereby reducing the number of degrees of freedom in localizing the bounding box to 5 from 9. Observations associated with the structural properties of back-projected object regions on the ground are suggested, which are useful for determining the object points expected to be on the ground. A suitable base is then estimated from the expected on-ground object points by applying to them an assumption of bilateral symmetry. A bounding box with this base is finally constructed by determining its height, such that back-projection of the constructed box onto the ground minimally encloses back-projection of the given object region. Through experiments with some 3D-modelled objects and real objects, we found that a bounding box aligned to the dominant direction estimated from edges with common direction looks natural, and the accuracy of the pose and size is enough for localizing actual on-ground objects in an industrial working space. The proposed method is expected to be used effectively in the fields of smart surveillance and autonomous navigation.