1. An arc detecting apparatus comprising: an input unit that inputs an image; a line-segment detector that detects line segments from the image; a determiner that determines whether two of the line segments are associable with each other, on a basis of positions of the two line segments and angles of the two line segments relative to corresponding references; and an arc detector that detects an arc approximated by at least two line segments including the two line segments, on a basis of the two line segments being associated with each other according to a result of the determination.