Arbitrary factor image interpolation using geodesic distance weighted 2D autoregressive modeling

Least square regression has been widely used in image interpolation. Some existing regression-based interpolation methods used ordinary least squares (OLS) to formulate cost functions. These methods usually have difficulties at object boundaries because OLS is sensitive to outliers. Weighted least squares (WLS) is then adopted to solve the outlier problem. Some weighting schemes have been proposed in the literature. In this paper we propose to use geodesic distance weighting in that geodesic distance can simultaneously measure both the spatial distance and color difference. Another contribution of this paper is that we propose an optimization scheme that can handle arbitrary factor interpolation. The idea is to separate the problem into two parts, an adaptive pixel correlation model and a convolution based image degradation model. Geodesic distance weighted 2D autoregressive model is used to model the pixel correlation which preserves local geometry. The convolution based image degradation model provides the flexibility to handle arbitrary interpolation factor. The entire problem is formulated as a WLS problem constrained by a linear equality.