1. An object detection apparatus, comprising: an image input unit configured to receive an image; an image feature quantity extraction unit configured to extract a predetermined image feature quantity from the image to generate a feature-quantity extraction image; a symmetry evaluation unit configured to evaluate, for every processing target pixel in the feature-quantity extraction image, first-direction symmetry of an image area around the processing target pixel based on an image feature quantity of pixels around the processing target pixel, and calculate a symmetry width in a first direction, the first-direction symmetry being symmetry in the first direction; a center detection unit configured to detect the target pixel as a symmetry center pixel when the evaluated symmetry for the target pixel exceeds a predetermined reference; and an object area detection unit configured to detect an object width in the first direction for an object having symmetry included in the image based on the symmetry width of each symmetry center pixel, and detect an object width in a second direction orthogonal to the first direction based on distribution of each symmetry center pixel in the second direction.