1. An image processing apparatus, comprising: a brightness gradient calculating unit that calculates brightness gradient strength and a brightness gradient direction in each pixel of an interpolation image corresponding to an enlarged image including pixels inserted between pixels of an image before enlargement; a contour extracting unit that determines a pixel indicating the contour in said interpolation image, using said brightness gradient strength and said brightness gradient direction; and a contour correcting unit that specifies a first isolation pixel isolated by the predetermined distance from each pixel indicating the contour in a brightness gradient direction of the pixel indicating the contour and a second isolation pixel isolated by said predetermined distance from each pixel in a 180°-rotation direction of said direction, for each pixel indicating the contour, corrects colors of the pixels between the pixel indicating said contour and said first isolation pixel with a color of said first isolation pixel, and corrects the colors of the pixels whose colors are not corrected with the color of said first isolation pixel among the pixels between said first isolation pixel and said second isolation pixel with a color of said second isolation pixel.