  Depth estimation is a challenging task of 3D reconstruction to enhance the
accuracy sensing of environment awareness. This work brings a new solution with
a set of improvements, which increase the quantitative and qualitative
understanding of depth maps compared to existing methods. Recently, a
convolutional neural network (CNN) has demonstrated its extraordinary ability
in estimating depth maps from monocular videos. However, traditional CNN does
not support topological structure and they can work only on regular image
regions with determined size and weights. On the other hand, graph
convolutional networks (GCN) can handle the convolution on non-Euclidean data
and it can be applied to irregular image regions within a topological
structure. Therefore, in this work in order to preserve object geometric
appearances and distributions, we aim at exploiting GCN for a self-supervised
depth estimation model. Our model consists of two parallel auto-encoder
networks: the first is an auto-encoder that will depend on ResNet-50 and
extract the feature from the input image and on multi-scale GCN to estimate the
depth map. In turn, the second network will be used to estimate the ego-motion
vector (i.e., 3D pose) between two consecutive frames based on ResNet-18. Both
the estimated 3D pose and depth map will be used for constructing a target
image. A combination of loss functions related to photometric, projection, and
smoothness is used to cope with bad depth prediction and preserve the
discontinuities of the objects. In particular, our method provided comparable
and promising results with a high prediction accuracy of 89% on the publicly
KITTI and Make3D datasets along with a reduction of 40% in the number of
trainable parameters compared to the state of the art solutions. The source
code is publicly available at https://github.com/ArminMasoumian/GCNDepth.git
