3D shape is a crucial but heavily underutilized cue in object recognition, mostly due to the lack of a good generic shape representation. With the recent boost of inexpensive 2.5D depth sensors (e.g. Microsoft Kinect), it is even more urgent to have a useful 3D shape model in an object recognition pipeline. Furthermore, when the recognition has low confidence, it is important to have a fail-safe mode for object recognition systems to intelligently choose the best view to obtain extra observation from another viewpoint, in order to reduce the uncertainty as much as possible. To this end, we propose to represent a geometric 3D shape as a probability distribution of binary variables on a 3D voxel grid, using a Convolutional Deep Belief Network. Our model naturally supports object recognition from 2.5D depth map, and view planning for object recognition. We construct a large-scale 3D computer graphics dataset to train our model, and conduct extensive experiments to study this new representation.