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, 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 for extracting, 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 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, wherein said relational-expression generating means 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.