MCnet: A Neural Network Method for Mean Curvature Optimization on Image Surfaces - Zhili Wei; Wenming Tang; Yuanhao Gong (IEEE Access, 2024)
Mean curvature is fundamentally important for various research fields, including differential geometry in mathematics, cell membrane modeling in biophysics and image processing in computer vision. However, its optimization is a challenging task. Conventionally, its optimization can be carried out by Partial Differential Equations (mean curvature flows) or solved by Augmented Lagrangian Methods. These approaches are numerically slow because they have to satisfy several numerical stability constraints. To tackle this issue, in this paper, we propose to use deep neural networks for the mean curvature optimization. Our method has several advantages. First, the proposed network has only 0.046M parameters, leading to a compact model. Second, the proposed network can be trained on low resolution images but applied on any resolution images. Third, it is flexible in the loss function design and thus can be used as a generic optimization method. To numerically valid the effectiveness and efficiency of the proposed method, several experiments are conducted. The results confirm that the proposed method achieves lower energy than traditional methods and thus establishes a new the-state-of-the-art for mean curvature optimization. The proposed method can be applied in a large range applications, where mean curvature optimization is involved.