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, and configured to perform the Hough transform using all points in the specified image whose pixel values each exceed zero; a counting part configured to add a value weighted by a feature quantity of a point in the specified image to a count value stored 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, each point in the specified image having an individual feature quantity which weights a particular value to be added to the count value corresponding to a value set of coordinates (a,b,r) in the Hough space to which the each point 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 value exceeds a first threshold.