1. A detection apparatus for detecting an arc in a specified image, comprising: a feature quantity calculating part configured to determine a feature quantity of each point in the specified image; a Hough transform part configured to convert an arc that passes through an arbitrary point in the specified image to a value set of coordinates (a,b,r) in a Hough space by defining orthogonal coordinates with respect to a reference point in the specified image and representing an arbitrary arc in the specified image using a value set of coordinates (a, b) of its center in an orthogonal coordinate system and a radius r; a counting part configured to add a value weighted by a feature quantity of a point in the specified image in a storage entry corresponding to a value set of coordinates (a,b,r) in the Hough space to which the point in the specified image is converted by the Hough transform part; and a detection part configured to detect the arc in the specified image by identifying a value set of coordinates (a,b,r) for which the count exceeds a first threshold.