Use of discrete gradient operators for the automatic determination of vanishing points: Comparative analysis

Thales’ second theorem can be used for the automatic detection of the vanishing points of an image. This paper explores its reliability and accuracy according to the type of operator used for the detection of edges. An algorithm has been used which processes a photographic image according to the operator selected. The result is a point cloud which is then used to find the desired solution. The comparison between the four discrete gradient operators (Frei-Chen, Prewitt, Roberts and Sobel) has been made taking into account the resolution of the image and the number of vanishing points. The results obtained show that Frei-Chen’s operator shows good performance in determining vanishing points with respect to the spatial X axis, Sobel’s operator is the best for determining the vanishing point with respect to the spatial Y axis, Roberts’ operator gives good results for calculating vanishing points in both spatial axes, and Prewitt’s operator is not appropriate for processing this type of image.

► An algorithm has been developed to obtain vanishing points automatically.
► The algorithm is based on Thales’ second theorem.
► Frei-Chen, Prewitt, Roberts and Sobel discrete gradient operators have been examined.
► The variables have been the image resolution and the number of vanishing points.
► The Roberts method has been shown to be the best for calculating vanishing points.