Interpolation is essential in digital image processing, especially magnification. Many different approaches to interpolation specific to magnification have been developed in an effort to overcome the shortcomings of bilinear and bicubic interpolation. One of these approaches, Constraint-Based Interpolation, produces an image that is free of jaggies and has less blurring than bilinear or bicubic interpolation. Although Constraint-Based Interpolation produces a visually pleasing image, there are user-chosen parameters that make the algorithm difficult to use. In this thesis we propose a method for automatic selection of those parameters and an extension of Constraint-Based Interpolation to other forms of image manipulation, such as skew, rotation, warp, or any other invertable image transformation. By extending Constaint-Based Interpolation the same improvements observed in magnification could be observed in these other image transformations.