1. A motion vector detector comprising: a searcher configured to search for, in each block in a first input image having a resolution of interest that is a predetermined resolution, an area having a high degree of correlation with a second input image having the resolution of interest, and generate a first flow that represents a set of motion vectors having the resolution of interest; a resolution converter configured to generate a second flow that represents a set of motion vectors having the resolution of interest by changing a set of motion vectors having a lower resolution than the resolution of interest to have a higher resolution; a synthesizer configured to generate a third flow that represents a set of motion vectors having the resolution of interest by combining motion vectors included in the first flow and motion vectors included in the second flow in such a way that a gradient-technique objective function is optimized; and a corrector configured to generate a set of motion vectors having the resolution of interest by optimizing a gradient-technique objective function having initial value set to the third flow.