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: an extractor configured to extract, in correspondence with a designated pixel of a designated frame of the image data, mixed pixel data, which is the pixel data, in which a plurality of objects contained in the image data are mixed, from the designated frame and a peripheral frame around the designated frame in accordance with a motion of a foreground object which forms a foreground of the plurality of objects, and also to extract, in correspondence with the mixed pixel data, background pixel data, which is the pixel data, corresponding to a background object which forms a background of the plurality of objects, the background pixel data being associated with the corresponding mixed pixel data, from a frame different from the frames from which the mixed pixel data are extracted in accordance with a motion of the background object so as to generate a plurality of relational expressions indicating relationships between the mixed pixel data and the background pixel data concerning the designated pixel; and a detector configured to detect 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, wherein said extractor generates the plurality of relational expressions based on a first approximation in which components of the foreground object contained in the mixed pixel data change substantially linearly with respect to the positions of the pixels, and a second approximation in which the mixture ratio of the mixed pixel data extracted from the designated frame changes substantially linearly with respect to the positions of the pixels wherein the extractor and detector are implemented in hardware or a combination of hardware and software.