1. A motion vector detection apparatus comprising: a layering unit configured to generate at least three 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, wherein the third extraction unit uses, as the layer candidate vector, a zero vector when the resolution of the layer which corresponds to the first image and to which a target block belongs is identical to a lowest resolution; and a determination unit configured to select, as an optimum candidate vector, one of the space candidate vector, the time candidate vector, and the layer candidate vector, the optimum candidate vector having a highest first correlation of 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, generate local vectors by varying the optimum candidate vector, select one of the local vectors as an optimum vector, the optimum vector having a highest second correlation of second correlations between target block and third blocks, the third blocks corresponding to the second image and being specified by the local vectors, and determine the optimum vector as a motion vector for the target block, wherein the extracting the motion vector assigned to the first reference block, the extracting the motion vector assigned to the second reference block, the extracting the motion vector assigned to the third reference block, and the determining are performed for each of the layers with the different resolutions.