Although 2D Object detection has been largely improved in the past years with the advance of deep learning methods and the use of large labeled image datasets, 3D object detection from 2D imagery is a challenging problem in a variety of applications such as robotics, due to the lack of data and diversity of appearances and shapes of objects within a category. Google has just announced the launch of Objectron that has a novel data pipeline using mobile augmented reality session data. However, it also is corresponding to 2D-driven 3D object detection technique. This study explores more mature 2D object detection method, and applies its 2D projection to Objectron 3D lifting system. Most object detection methods use bounding boxes to encode and represent the object shape and location. In this work, we explore a stochastic representation of object regions using Gaussian distributions. We also present a similarity measure for the Gaussian distributions based on the Hellinger Distance, which can be viewed as a stochastic Intersection-over-Union. Our experimental results show that the proposed Gaussian representations are closer to annotated segmentation masks in available datasets. Thus, less accuracy problem that is one of several limitations of Objectron can be relaxed.