1. An image processing apparatus comprising: a job execution unit that executes a processing job of image data; a log generation unit that generates image log information for identifying the processing job executed by the job execution unit and identifying the image data processed in the processing job; a log storage unit that stores the image log information generated by the log generation unit; a feature amount extraction unit that extracts a feature amount of the image data identified by the image log information; an identity determination unit that compares feature amounts, which are extracted by the feature amount extraction unit from plural pieces of the image data identified by plural pieces of the image log information, to determine identity among the plural pieces of image data; and a replacement unit that replaces information to identify a piece of the plural pieces of image data which are determined to be identical with each other, with information to identify another piece of the plural pieces of image data which are determined to be identical with each other.