An image processing apparatus comprising: an interface configured to acquire a stereo image that includes a standard image and a reference image captured from different viewpoints; and a processor configured to perform low-rank approximation by singular value decomposition on the standard image and the reference image, and calculate a parallax by performing stereo matching processing between the standard image and the reference image that are subjected to the low-rank approximation by the singular value decomposition, wherein the processor is further configured to decompose the standard image and the reference image acquired by the interface into a left singular value matrix, a first diagonal matrix, and a right singular value matrix, wherein an inner product of the left singular value matrix, a second diagonal matrix obtained by lowering a rank of the first diagonal matrix, and the right singular value matrix are defined as the standard image and the reference image that are subjected to the low-rank approximation by the singular value decomposition, and determine a rank of the second diagonal matrix, based on a desired characteristics amount in each of the standard image and the reference image that are subjected to the low-rank approximation by the singular value decomposition, wherein the processor is further configured to vary the desired characteristics amount according to areas of the standard image and the reference image. an interface configured to acquire a stereo image that includes a standard image and a reference image captured from different viewpoints; and a processor configured to perform low-rank approximation by singular value decomposition on the standard image and the reference image, and calculate a parallax by performing stereo matching processing between the standard image and the reference image that are subjected to the low-rank approximation by the singular value decomposition, wherein the processor is further configured to decompose the standard image and the reference image acquired by the interface into a left singular value matrix, a first diagonal matrix, and a right singular value matrix, wherein an inner product of the left singular value matrix, a second diagonal matrix obtained by lowering a rank of the first diagonal matrix, and the right singular value matrix are defined as the standard image and the reference image that are subjected to the low-rank approximation by the singular value decomposition, and determine a rank of the second diagonal matrix, based on a desired characteristics amount in each of the standard image and the reference image that are subjected to the low-rank approximation by the singular value decomposition, wherein the processor is further configured to vary the desired characteristics amount according to areas of the standard image and the reference image. decompose the standard image and the reference image acquired by the interface into a left singular value matrix, a first diagonal matrix, and a right singular value matrix, wherein an inner product of the left singular value matrix, a second diagonal matrix obtained by lowering a rank of the first diagonal matrix, and the right singular value matrix are defined as the standard image and the reference image that are subjected to the low-rank approximation by the singular value decomposition, and determine a rank of the second diagonal matrix, based on a desired characteristics amount in each of the standard image and the reference image that are subjected to the low-rank approximation by the singular value decomposition, wherein the processor is further configured to vary the desired characteristics amount according to areas of the standard image and the reference image.