1. A method for taking a panorama mosaic photograph, comprising: (a) displaying a partial image of a previously taken image as a guide image on a display showing a current image to be taken and taking a number of images, in sequence, constituting the panorama mosaic photograph according to a photography operation; (b) projecting the taken images onto a common cylindrically curved surface; and (c) joining the projected images into a single image, wherein the step (b) is performed according to equation (12) below I ⁡ ( f ⁢ u R 2 - u 2 , f ⁢ v R 2 - u 2 ) ( 12 ) wherein a focal length of images is f; a rotational angle between images is θ; an image coordinate system with an image center at an origin is (x,y); a pixel at location (x,y) in image I is I(x,y); a cylindrical coordinate with radius R is (u,v)=(Rθ,v); and pixel value corresponding to (u,v) satisfies the equation (12).