  In this article, we propose the novel concept of Belief Scene Graphs, which
are utility-driven extensions of partial 3D scene graphs, that enable efficient
high-level task planning with partial information. We propose a graph-based
learning methodology for the computation of belief (also referred to as
expectation) on any given 3D scene graph, which is then used to strategically
add new nodes (referred to as blind nodes) that are relevant to a robotic
mission. We propose the method of Computation of Expectation based on
Correlation Information (CECI), to reasonably approximate real
Belief/Expectation, by learning histograms from available training data. A
novel Graph Convolutional Neural Network (GCN) model is developed, to learn
CECI from a repository of 3D scene graphs. As no database of 3D scene graphs
exists for the training of the novel CECI model, we present a novel methodology
for generating a 3D scene graph dataset based on semantically annotated
real-life 3D spaces. The generated dataset is then utilized to train the
proposed CECI model and for extensive validation of the proposed method. We
establish the novel concept of \textit{Belief Scene Graphs} (BSG), as a core
component to integrate expectations into abstract representations. This new
concept is an evolution of the classical 3D scene graph concept and aims to
enable high-level reasoning for task planning and optimization of a variety of
robotics missions. The efficacy of the overall framework has been evaluated in
an object search scenario, and has also been tested in a real-life experiment
to emulate human common sense of unseen-objects. For a video of the article,
showcasing the experimental demonstration, please refer to the following link:
https://youtu.be/hsGlSCa12iY
