  Surface reconstruction from point clouds is a fundamental challenge in
computer graphics and medical imaging. In this paper, we explore the
application of advanced neural network architectures for the accurate and
efficient reconstruction of surfaces from data points. We introduce a novel
variant of the Highway network (Hw) called Square-Highway (SqrHw) within the
context of multilayer perceptrons and investigate its performance alongside
plain neural networks and a simplified Hw in various numerical examples. These
examples include the reconstruction of simple and complex surfaces, such as
spheres, human hands, and intricate models like the Stanford Bunny. We analyze
the impact of factors such as the number of hidden layers, interior and
exterior points, and data distribution on surface reconstruction quality. Our
results show that the proposed SqrHw architecture outperforms other neural
network configurations, achieving faster convergence and higher-quality surface
reconstructions. Additionally, we demonstrate the SqrHw's ability to predict
surfaces over missing data, a valuable feature for challenging applications
like medical imaging. Furthermore, our study delves into further details,
demonstrating that the proposed method based on highway networks yields more
stable weight norms and backpropagation gradients compared to the Plain Network
architecture. This research not only advances the field of computer graphics
but also holds utility for other purposes such as function interpolation and
physics-informed neural networks, which integrate multilayer perceptrons into
their algorithms.
