1. A method for stitching together images taken through a fisheye lens in order to produce a 360-degree spherical panorama, wherein the method is applied to an electronic device so that the electronic device is enabled to read at least two real-site images taken respectively from different positions by at least one digital still camera mounted with a fisheye lens, the method comprising the steps, to be performed by the electronic device, of: acquiring a plurality of parameters of the fisheye lens that correspond to the different positions, the parameters comprising a plurality of internal parameters and an external parameter, wherein the internal parameters are focal lengths of the fisheye lens, an offset of a center of the fisheye lens, and an aberration coefficient of the fisheye lens, and the internal parameters are acquired by taking images of a plurality of calibration plates respectively placed on different inner walls of a light box, registering the images taken of the calibration plates, and determining the internal parameters through an optimization algorithm; and the external parameter is a three-dimensional relationship between the different positions from which the real-site images are respectively taken through the fisheye lens; and wherein the fisheye lens has an imaging property defined by Ū(u,v)=f(L,M X ) describing how a point X (X,Y,Z) in a three-dimensional space is projected to a point Ū(u,v) in a two-dimensional imaging plane of the fisheye lens to form a pixel in a two-dimensional image, with M representing the external parameter of the fisheye lens, L representing the internal parameters of the fisheye lens, f representing a projection-based relationship, and X representing coordinates of lattice points of a checkerboard lattice on each said calibration plate; acquiring a vignetting coefficient of the fisheye lens, and performing brightness compensation on the real-site images according to the vignetting coefficient in order to eliminate a vignetting effect; projecting the real-site images onto a spherical surface according to the internal parameters and the external parameter, and spreading out the spherical surface to form a two-dimensional spread-out picture; performing image registration on overlap areas of the real-site images projected on the two-dimensional spread-out picture, calculating a registration parameter of each corresponding pair of pixels in the overlap areas through an interpolation smoothing operation after obtaining an image registration parameter of each corresponding pair of image sections of the overlap areas, and adjusting an offset of each corresponding pair of said pixels in the overlap areas according to a corresponding said registration parameter in order to align images in the overlap areas; performing brightness and hue registration and adjustment on the overlap areas of the real-site images projected on the two-dimensional spread-out picture, calculating brightness and hue adjustment values for each corresponding pair of said image sections, and adjusting brightness and hues of the overlap areas of the real-site images according to the brightness and hue adjustment values through an interpolation smoothing operation in order to achieve consistency in brightness and hue; and performing image fusion on the overlap areas of the real-site images to eliminate any noticeable seam and thereby produce a 360-degree spherical panorama.