DNN-based Parameterization for B-Spline Curve Approximation

B-spline curve parameterization is a complex nonlinear and non-convex optimization problem. Traditional optimization methods often struggle with local minima and are computationally expensive, especially in high-dimensional spaces. We proposes a deep neural network (DNN)-based method to efficiently solve the parameterization problem in B-spline curve approximation. The designed parameterization network (PNet) maps the initial parameterization to an optimized one, transforming the problem into a search for suitable network parameters in a high-dimensional feature space. Due to the over-parameterization nature of DNNs, PNet is robust to initial conditions and less prone to local minima. Furthermore, the smooth regularization and top-$K$ loss function are introduced to further enhance optimization performance. Experimental results show that PNet achieves high-precision approximation with remarkable efficiency, even for large-scale point clouds.