1. An image processing device comprising: a brightness information calculation portion that calculates brightness information of an image signal that is input and that forms a two-dimensional image made from pixels; a normal direction estimation portion that estimates a normal direction for each pixel, or each region made of a plurality of pixels, from the brightness information, and obtains a normal direction vector that is a three-dimensional vector for each pixel or for each region based on the estimated normal direction; a corrected gradation derivation portion that finds a correction amount of the brightness information based on the normal direction vector that is obtained by the normal direction estimation portion, and corrects the brightness information of the image signal based on the correction amount of the brightness information; and a processor that controls at least one of the brightness information calculation portion, the normal direction estimation portion, and the corrected gradation derivation portion, wherein the normal direction estimation portion (i) sets a third direction component value for each pixel or each region to a first value that is a predetermined value, the third direction component value being a value of a component of a third direction that is not included on a plane that is formed by the two-dimensional image, and (ii) obtains the normal direction vector from values of three direction components including: (1) a first direction component value that is a value of a component of a first direction; and (2) a second direction component value that is a value of a component of a second direction, the first direction component value and the second direction component value serving as two-dimensional coordinate information for determining a pixel position of a pixel in the two-dimensional image, and wherein the normal direction estimation portion sets, for a plurality of pixels, the third direction component value to the same value as the first value and determines the normal direction value for each pixel or for each region.