Discrete Algorithm Of Image Interpolation

Digital image processing-the manipulation of images by computer-is a relatively recent development it terms of humans' ancient fascination with visual stimuli. In its short history, it has been applied to practically every type of imagery, with varying degrees of success. The inherent subjective appeal of pictorial displays attracts perhaps a disproportionate amount of attention from scientist and lay person alike.Like other multidisciplinary fields, digital image processing suffers from myths, misunderstandings, misconceptions,and misinformation. It is a broad umbrella under which fall diverse aspects of optics, electronics, mathematics, photography, and computer technology.It is plagued with imprecise and often contradictory jargon taken from many different fields.Geometric operation change the spatial relationships among the objects in an image. Such operations may be thought of as moving things around within the image. Actually, a geometric operation is much more general than that, since point in the input image may move to any position in the output image. Such an unconstrained geometric operation would almost certainly scramble the image content, so geometric operations are generally constrained to preserve some semblance of order.Two separate algorithms are required for a geometric operation.First , there must be an algorithm that defines the spatial transformation itself. This specifies the "motion" of each pixel as it "moves" from this initial to its final position in the image. Also required is an algorithm for gray-level interpolation.This is necessary because, in general, integer x,y positions in the input image map to fractional(non- integer) positions in the output image and conversely.In the input image f(x, y), the gray-level value are defined only at integral values of x and y. Eq. listed above,however, will in general dictate that the gray-level value for g(x,y) be taken from f(x,y) at fractional(non-integral) coordinate positions. If the geometric operation is considered a mapping from f to g, pixels in f can map to positions between pixel in g and vice versa. For the purposes of this discussion, we stipulate that pixels be located exactly coordinates of the sampling grid.In this paper , we provide an algorithm of image interpolation based on near-neighborhood principle. Gray-level value of the interpolated pixel is approximately equal to weighted arithmetic sum of the term, gray-level value of the pixels near the interpolated pixel, and computing the weighted functions is very important for this interpolation algorithm. In order to interpolate the image, we point out a mathematical description about the near-neighborhood principle and construct weighted functions which satisfy the conditions listed bellow:αk(s,t),k = 1...4 are weighted functions:(1)αk(s,t) is non-positive, i.e.(2)αk(s,t) is normal, i.e. and(3)Given (s,t),d^(s,t)(i,j) andαk(s,t) is anti-order, k = 2i + j + 1. IfandthenThe image interpolated is also smoothed by the interpolated algorithm at the same time. At last I provide a compensation algorithm to sharp the edges of the objects in the image. The gray-value of the nearest pixels which are in the same scanning-line is more than a given threshold, within the edge of the same object in the image. I compensate the gray-value of the interpolated node between the pixels, so as to sharp the edges of objects. The compensation algorithm is based on the normal vector of the four-pixel near the interpolated node in order to compute the compensation value. In order to be fit for the edges in the different conditions, I choose the parameterωadaptively. While the edge is strong, the correspond parameterωis weak. The program is based on Matlab 6.5. The numerical experiments show that our algorithm can keep the original texture of the image unchanged and sharp the texture of the edges to some degree.