Multispectral sensors constitute a core
earth observation imaging technology generating massive high-dimensional
observations acquired across multiple time instances. The collected
multitemporal remote sensed data contain rich information for Earth
monitoring applications, from flood detection to crop classification. To
easily classify such naturally multidimensional data, conventional
low-order deep learning models unavoidably toss away valuable
information residing across the available dimensions. In this work, we
extend state-of-the-art convolutional network models based on the U-Net
architecture to their high-dimensional analogs, which can naturally
capture multidimensional dependencies and correlations. We introduce
several model architectures, both of low as well as of high order, and
we quantify the achieved classification performance vis-à-vis the latest
state-of-the-art methods. The experimental analysis on observations
from Landsat-8 reveals that approaches based on low-order U-Net models
exhibit poor classification performance and are outperformed by our
proposed high-dimensional U-Net scheme.