1. An image processing apparatus that carries out a modification process on a pre-modification image to generate a post-modification image within an image modification area, the image processing apparatus comprising: a target block setting unit that establishes a target block as a destination of the modification process, the target block constituting the image modification area; a block modification unit that generates an image within the target block by storing an image included in a referent block, which is associated with the target block, into a source memory area, and by referring the image included in the referent block stored in the source memory area as a source of the modification process; a block scanning unit that generates entirety of the post-modification image by sequentially shifting the target block to a different position within the image modification area, and by causing the block modification unit to generate an image within the target block after each shift; a maximum block size computing unit that computes a maximum block size of the referent block associated with the target block situated any available position, the maximum block being computed prior to generation of the image of the target block by the block modification unit; and a source memory area allocating unit that allocates the source memory area capable of storing an image of a size equal to the maximum block size computed by the maximum block size computing unit.