Image Zooming Based On Anisotropic Diffusion

After analyzing some deficiency in conventional image interpolation methods and some recent partial differential equations(PDE) based image zooming methods, noting that the zooming image's edge should be consistent with the original image's, we present a new linear PDE for image zooming. Our model takes the following form:whereΩ(?)R² is the bounded rect region of the image to be zoomed, (?)Ωis the consistent boundary, T＞0,β(x)∈L^∞((?)), u₀(x, y) is the zoomed image using conventional image interpolation methods, e(x, y) is the edge image, s＞0,λ＞0 are constants.we'll prove the existence, uniqueness and stability of weak solution for the model, and prove that the weak solution is belonging to L²(0,T; H¹(Ω))∩C([0, T]; L²(Ω)) under some basic assumptions. Finally, the numerical experiments are completed with the explicit difference schemes. The result show that we can get good quality of zoomed image by using our model, and our method work fast and efficient. So our model is a meaningful, proper and having good image zooming effects PDE based image zooming model not only in theory but also in practice.