1. An image processing apparatus for processing image data which is formed of a predetermined number of pixel data obtained by an image-capturing device including a predetermined number of pixels, the pixels having a time integrating function, said image processing apparatus comprising: relational-expression generating means for extracting, in correspondence with a designated pixel of a designated frame of the image data, the pixel data of a peripheral frame around the designated frame as background pixel data corresponding to a background object which forms a background among a plurality of objects of the image data, and also for extracting designated pixel data of the designated pixel contained in the designated frame so as to generate a plurality of relational expressions concerning the designated pixel indicating a relationship between the designated pixel data and the background pixel data; mixture-ratio detection means for detecting a mixture ratio indicating a mixture state of the plurality of objects in the real world concerning the designated pixel based on the relational expressions; predictive-error calculation means for calculating a predictive error by substituting the mixture ratio detected by said mixture-ratio detection means into the relational expressions; covered background area/uncovered background area specifying means for specifying, based on the predictive error, whether an area to which the designated pixel belongs is a mixed area in which the plurality of objects are mixed and is also a covered background area formed at a leading end in a moving direction of a foreground object which forms a foreground among the plurality of objects, or is the mixed area and is also an uncovered background area formed at a trailing end in the moving direction of the foreground object; and foreground area/background area specifying means for specifying whether the area to which the designated pixel belongs is a foreground area consisting of only foreground object components which form the foreground object or a background area consisting of only background object components which form the background object.