1. A stereo image processing apparatus comprising: an acquiring section that acquires stereo images including a target image and a reference image; a decimating section that decimates the target image and the reference image to create a decimated target image and a decimated reference image; a first calculation section that calculates the amount of displacement in pixels between the decimated target image and the decimated reference image; a filtering section that reverses a sequence of data consisting of brightness values in the decimated target image to calculate an inverted phase filter coefficient, and filters the decimated reference image using the calculated inverted phase filter coefficient to output the results of filtering; and a second calculation section that detects a peak in the results of filtering outputted from the filtering section to calculate the amount of displacement in sub-pixels between the decimated target image and the decimated reference image.