1. A processing method for image interpolation, comprising: detecting whether an edge exists for a selected area in an original image by using an edge detection method, and determining an edge direction of the edge; on a normal direction to the edge direction, producing a contour by using a plurality of pixels in the original image to interpolate a plurality of contour pixels, wherein a destination pixel is located on the contour; identifying two extreme points from the contour pixels by judging a changing trend of a brightness value of the contour; determining whether the destination pixel is located at a transition area or a non-transition area; when the destination pixel is located at the non-transition area, calculating an interpolation adjust value according to the brightness values of the two extreme points and the brightness value of the destination pixel; and obtaining an interpolation result of the destination pixel by performing the interpolation on the selected area according to the interpolation adjust value, wherein the step of determining whether the destination pixel is located at the transition area or the non-transition area comprises: according to the brightness values of the two extreme points and the brightness value of the destination pixel, determining the brightness value of the destination pixel is near the brightness value of one extreme point of the two extreme points, and defining the closer extreme point as a destination extreme point; determining whether an inflexion point exists among the contour pixels from the location of the destination pixel toward an end of the destination extreme point; when the inflexion point exists among the contour pixels, the destination pixel is located at the non-transition area; and when the inflexion point does not exist among the contour pixels, the destination pixel is located at the transition area.