Shape transformation based on the modified Lengyel-Epstein model

Shape transformation has broad application prospects infields such as computer graphics and biomedical modeling. This paper presents an innovative model that not only enhances shape transformation applications but also demonstrates remarkable performance in tasks such as image dehazing and segmentation, underscoring its versatility and value in computer vision. In this paper, a novel method is proposed, which is suitable for shape transformation. This method is based on Lengyel-Epstein (LE) model and a minor adjustment to the original LE model is that v0-v replaces u in the system. Five point difference scheme and seven point difference scheme are adopted to discrete the Laplace operator in two-dimensional (2D) and three-dimensional (3D) space. Through a series of numerical experiments, we have demonstrated that the proposed model effectively achieves shape transformation in both 2D and 3D spaces. Additionally, simulations of image dehazing and segmentation show promising results. Thus, the modified LE model offers a novel approach applicable to a variety of computer vision tasks.