  Understanding the 3D geometric structure of the Earth's surface has been an
active research topic in photogrammetry and remote sensing community for
decades, serving as an essential building block for various applications such
as 3D digital city modeling, change detection, and city management. Previous
researches have extensively studied the problem of height estimation from
aerial images based on stereo or multi-view image matching. These methods
require two or more images from different perspectives to reconstruct 3D
coordinates with camera information provided. In this paper, we deal with the
ambiguous and unsolved problem of height estimation from a single aerial image.
Driven by the great success of deep learning, especially deep convolution
neural networks (CNNs), some researches have proposed to estimate height
information from a single aerial image by training a deep CNN model with
large-scale annotated datasets. These methods treat height estimation as a
regression problem and directly use an encoder-decoder network to regress the
height values. In this paper, we proposed to divide height values into
spacing-increasing intervals and transform the regression problem into an
ordinal regression problem, using an ordinal loss for network training. To
enable multi-scale feature extraction, we further incorporate an Atrous Spatial
Pyramid Pooling (ASPP) module to extract features from multiple dilated
convolution layers. After that, a post-processing technique is designed to
transform the predicted height map of each patch into a seamless height map.
Finally, we conduct extensive experiments on ISPRS Vaihingen and Potsdam
datasets. Experimental results demonstrate significantly better performance of
our method compared to the state-of-the-art methods.
