1. A method for magnifying images and videos, applicable to an image processing device so that, upon inputting of a digital image thereinto, the image processing device outputs a magnified digital image according to a predetermined magnification ratio, the method comprising steps of: providing a preprocess module for executing a high-pass filtering process on the input image so as to extract a high-frequency portion thereof, wherein the high-frequency portion is used to perform high-frequency compensation on a magnification result of the input image; and for executing an image decomposition process on the input image so as to extract an image gradient of the input image by using a gradient operator and decompose the input image into plane regions and edge regions according to a predetermined fixed threshold, wherein the plane regions and the edge regions are labeled on the input image with labels; providing a composite up-scaling module for executing a magnification process on the plane regions and the edge regions of the input image, respectively, wherein the magnification process of the plane regions of the input image is based on a simple interpolation, while the magnification process of the edge regions is based on both a smart interpolation and the simple interpolation; for subsequently executing a confidence process on a result of the smart interpolation, wherein the result of the smart interpolation has higher confidence if an edge direction is clearer, and lower confidence if the edge direction is less clear; and for finally executing a weighted summation on the result of the smart interpolation and a result of the simple interpolation according to said confidence, wherein the composite up-scaling module executes the magnification processes on the original input image and the high-frequency portion thereof, respectively; and executing a fusion process by which the magnification result of the original input image is fused with a magnified result of the high-frequency portion to form an output image.