A Global Approach for the Detection of Vanishing Points and Mutually Orthogonal Vanishing Directions

Discovery of Sets of Mutually Orthogonal Vanishing Points in Videos

“…Input: Most works start from lines [6,9], or line segments [3,21,26,11,29,12,34,2]. Some approaches employ continuous image gradients or texture [27,25,23] and thresholded edges images [30].…”

“…Line-VP consistency and VP refinement: The consistency between an estimated VP and the image lines is usually measured using line endpoint distances in the image, used by us and [29,12,4,2,17], the angular differences in the image [26,8], with explicit probabilistic modeling of the line end point errors [35], or with angles between normals of interpretation planes in the Gaussian sphere [21,24,20]. We sample MOVP candidates on the Gaussian sphere because testing for orthogonality directly translates to vector cross products, but revert to image-space fitting errors for refinement to avoid distorted errors and to attenuate dependance on (potentially) noisy internal camera calibration.…”

“…Efficient search [26,8], direct clustering [29,17], multi-line RANSAC [4,34], EM procedures [1,15,27,12,35], or MCMC inference [28] are among the methods employed directly on the accumulator space. If a discretization is enforced on the accumalator space, the solutions are found by voting schemes [21,24,20,23] or inference over graphical models [30,2].…”

“…The VP computation or refinement with given associated lines is commonly done by Hough voting and nonmaximum suppression [21,24,20,32,23], by solving a quadratic program [2], implicitly in an ExpectationMaximization (EM) setting [1,27,29,35], or by linear least-squares, as in [15].…”

“…Accumulator space: The intersections of imaged lines are computed in the (unbounded) image space [26,27,29,9,2,35] or on a (bounded) Gaussian unit sphere, as introduced in [3] and used in [21,24,20,1,15,11,12,4,22,28].…”