  This paper presents a feature encoding method of complex 3D objects for
high-level semantic features. Recent approaches to object recognition methods
become important for semantic simultaneous localization and mapping (SLAM).
However, there is a lack of consideration of the probabilistic observation
model for 3D objects, as the shape of a 3D object basically follows a complex
probability distribution. Furthermore, since the mobile robot equipped with a
range sensor observes only a single view, much information of the object shape
is discarded. These limitations are the major obstacles to semantic SLAM and
view-independent loop closure using 3D object shapes as features. In order to
enable the numerical analysis for the Bayesian inference, we approximate the
true observation model of 3D objects to tractable distributions. Since the
observation likelihood can be obtained from the generative model, we formulate
the true generative model for 3D object with the Bayesian networks. To capture
these complex distributions, we apply a variational auto-encoder. To analyze
the approximated distributions and encoded features, we perform classification
with maximum likelihood estimation and shape retrieval.
