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In this paper, we introduce a curve evolution approach to image magnification based on a generalization of the Mumford-Shah functional. This work is a natural extension of the curve evolution implementation of the Mumford-Shah functional presented by the authors in previous work. In particular, by considering the image magnification problem as a structured case of the missing data problem, we generalize the data fidelity term of the original Mumford-Shah energy functional by incorporating a spatially varying penalty to accommodate those pixels with missing measurements. This generalization leads us to a PDE-based approach for simultaneous image magnification, segmentation, and smoothing, thereby extending the traditional applications of the Mumford-Shah functional which only considers simultaneous segmentation and smoothing. This novel approach for image magnification is more global and much less susceptible to blurring or blockiness artifacts as compared to other more traditional magnification techniques, and has the additional attractive denoising capability.

A Curve Evolution Approach to Medical Image Magnification via the Mumford-Shah Functional