Numerical subgrid Bi-cubic methods of partial differential equations in image segmentation

Image segmentation is a core research in the image processing and computer vision. In this paper, we suggest a Bi-cubic spline phase transition potential and elaborate a Bi-Cubic spline phase transition potential development. In the image segmentation, we develop the new approach to apply the novel computational fluid dynamics in the boundary with subgrid. The numerical subgrid Bi-cubic method with Bi-Cubic spline for minimizing the piecewise constant energy functional is very efficient, robust and fast in the image segmentation with a multispecies multiphase segmentation models. The subgrid Bi-cubic spline is applied on the boundary with subgrid and the regular grid is applied on the non-boundary. The model generates a multispecies multiphase distribution with Bi-Cubic spline and we can extract the image segments with multispecies multiphase. Finally, we analyze the models and show the numerical results. Numerical results are presented with OCR (Optical Character Recognition) and the medical image.