Image Zooming Based On A Type Of Partial Differential Equations

In this paper, we analyze the deficiency in usual interpolation and the known partialdifferential equations methods for image zooming. Based on the general partial differentialequation approach to image zoom and the feature of image zooming and the predictableof the edge for zoomed image, we propose a new type of linear partial differential equationsmodel for image zooming:hereΩis a bounded image subset of R² with Lipschitz boundary (?)Ω, x=(x₁,x₂)∈R², T＞0,β(x)∈L^∞((?)), g(x) is an edge-stopping function,φ(x) is the initial image, I(x) is theedge image, constantε＞0.We demonstrate the existence, uniqueness and stability for the solution in W_p^2,1(Ω_T)of the proposed model, at last, we give the actual results of our model in image zooming.The experimental results show that our method work fast and efficient. So our model isa meaningful, reasonable and effective image zooming model based on partial differentialequation not only in theory but also in practice.