Image magnification using fractional order level set reconstruction

A new fractional order MCM function is proposed for image magnification in this paper. The traditional MCM function of integer order is generalized to fractional order, through introducing a fractional order term to the energy function of level set models. The fractional order level set model is to solve a typical fractional order variational problem through deducing an fractional order Euler-Lagrange equation for minimizing the modified energy function. The equations are actually complicated partial differential equations (PDE) of fractional order and a numerical implementation based on G-L fractional derivative definition is used to solve it. Theoretic analysis reveals that the proposed fractional order MCM function can be viewed as generalization of the traditional MCM function. At last, the proposed fractional order MCM function is implemented and tested on a series of contrary experiments, which demonstrate that fractional order MCM function can obtain better image magnification results than the corresponding integral one.