Abstract: From a visual point of view, the shape of an image is mainly determined by the edges. Conventional polynomial interpolation of image enlarging methods would produce blurred edges, while edge-directed interpolation based methods would cause detail distortion in the non-edge areas. A new method for image enlarging is presented. The image is enlarged in two steps. In the first step, a fitting surface is constructed to interpolate the image data. To remove the zigzagging artifact, for each pixel, a fitting patch is constructed using edge information as constraints. The combination of all the patches forms the fitting surface which has the shape suggested by image data. Each point on the fitting surface can be regarded as a sampling point taken from a unit square domain, which means that when the fitting surface is used to enlarge the image, each sampling domain of the enlarged pixels is also a unit square, causing the enlarged image to lose some details. To make the enlarged image keep the details as much as possible, the sampling domain of the enlarged pixels should be less than a unit square. Then, in the second step, using the points taken from the fitting surface, new pixels are computed using constrained optimization technique to form the enlarged image, the size of the sampling domain of the enlarged pixels is inversely proportional to the size of the enlarged image. The enlarged image has a quadratic polynomial precision. Comparison results of the new method with other methods are included.