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I. IntroductionThe vanishing point (VP), caused by the perspective effects of 3D-to-2D projection, is one of the invariant features in the estimation of image depth, object dimension, and 3D structure. Since these features are widely used in the fields of computer vision, various techniques regarding precise VP detection (VPD) are rigorously studied. In general, architectural objects have enough parallel lines, stretched in vertical or horizontal directions in 3D space that these lines are clustered and the cross points in 2D projection are accumulated in space in order to detect VPs Barnard [2] proposed a Gaussian sphere as a bounded space into which lines in the 2D image space are projected, and thereby, both the finite and infinite VPs can be detected effectively. Tuytelaars and others [6] proposed a space-bounding technique for the unbounded parameter space of a cascade Hough transform in order to detect VPs and lines.

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