1. A motion vector detection apparatus comprising: a layering unit configured to generate layers with different resolutions for each of a first image and a second image, the first image and the second image being to be displayed at times different from each other, each of the resolutions indicating a number of first blocks which are set to a corresponding layer; a first extraction unit configured to extract, as a space candidate vector, a motion vector assigned to a first reference block, the first reference block being located in a layer which corresponds to the first image and to which a target block belongs; a second extraction unit configured to extract, as a time candidate vector, a motion vector assigned to a second reference block, the second reference block being located in a layer which corresponds to a third image and has a resolution identical to a resolution of the layer which corresponds to the first image and to which the target block belongs, the third image being to be displayed at a time different from the times; a third extraction unit configured to extract, as a layer candidate vector, a motion vector assigned to a third reference block, the third reference block being located in a layer which corresponds to the first image and has a lower resolution than the resolution of the layer which corresponds to the first image and to which the target block belongs; and a determination unit configured to determine a motion vector to be assigned to the target block, based on first correlations between the target block and second blocks, the second blocks being located in a layer which corresponds to the second image and being specified by assigning, to the target block, the space candidate vector, the time candidate vector, and the layer candidate vector, wherein the first extraction unit, the second extraction unit, the third extraction unit, and the determination unit perform recursive processing.