Highway Networks for Improved Surface Reconstruction: The Role of Residuals and Weight Updates

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.