HIGH-QUALITY IMAGE RESIZING USING OBLIQUE PROJECTION OPERATORS

The standard interpolation approach to image resizing is to fit the or iginal picture with a continuous model and resample the function at th e desired rate. However, one can obtain more accurate results if one a pplies a filter prior to sampling, a fact well known from sampling the ory, The optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space. Unfortunately, the optimal pr ojection prefilter is difficult to implement when sine or high order s pline functions are used. In this paper, we propose to resize the imag e using an oblique rather than an orthogonal projection operator in or der to make use of faster, simpler, and more general algorithms. We sh ow that we can achieve almost the same result as with the orthogonal p rojection provided that we use the same approximation space. The main advantage is that it becomes perfectly feasible to use higher order mo dels (e.g, splines of degree n greater than or equal to 3), We develop the theoretical background and present a simple and practical impleme ntation procedure using B-splines, Our experiments show that the propo sed algorithm consistently outperforms the standard interpolation meth ods and that it provides essentially the same performance as the optim al procedure (least squares solution) with considerably fewer computat ions. The method works for arbitrary scaling factors and is applicable to both image enlargement and reduction.