1. An image processing apparatus for performing processing on image data which is formed of a predetermined number of pixel data obtained by an image-capturing device including a predetermined number of pixels and having a time integrating function, apparatus comprising; an area specifying unit configured to specify one of: (1) a non-mixed area formed of a foreground area consisting of foreground object components which form a foreground object of the image data and a background area consisting of background object components which form a background object of the image data, and (2) a mixed area in which the foreground object components and the background object components are mixed; a processing unit configured to simultaneously perform processing for separating the foreground object components and the background object components from the pixel data of the mixed area, and processing for eliminating motion blur from the separated foreground object components; and an equal-portion detection unit configured for detecting an equal portion consisting of adjacent pixel data of the foreground area whose values are substantially equal to each other, wherein said processing unit simultaneously performs at least the processing for separating the foreground object components and the background object components from the pixel data of the mixed area and the processing for eliminating motion blur from the separated foreground object components based on the detected equal portion and area result from the area specifying unit.