Vanishing Point Detection in the Hough Transform Space
Depth estimation from monocular images can be retrieved from the perspective distortion. One major effect of this distortion is that a set of parallel lines in the real world converges into a single point in the image plane. The estimation of the co-ordin
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Abstract. Depth estimation from monocular images can be retrieved from the perspective distortion. One major effect of this distortion is that a set of parallel lines in the real world converges into a single point in the image plane. The estimation of the co-ordinates of the vanishing point can be retrieved directly on the Hough Transformation space or polar plane. In fact the vanishing point in the image plane is mapped in the polar plane into a sine curve that can be estimated with a simple linear system.
1 Introduction In monocular images depth estimation, if no particular prior knowledge of the scene is given, can be retrieved in many real images by the perspective distortion. One major effect is that a set of parallel lines in the three dimensional space in the image space converges to a single point called the vanishing point. This point in the image plane gives important information on the distance of the objects in the scene and of the three--dimensional structure. In Sedgwick [2] some features of the vanishing point are given. Since this point is the projection of a point at the infinite with respect to the point of observation, a finite motion of the point of observation produces a movement of the vanishing point in the image that is negligible. This is called invariance to motion. This feature must be taken into account when considering sequential images of a moving point of observation. In this work an analytical method to determine the vanishing point in the Hough Parameters Space is presented. This method is computationally equivalent to others but has the advantage that in the Hough Plane the vanishing point has a precise shape that can be searched optimally. The algorithm to detect the vanishing point was also implemented and the results from real images are shown. This same algorithm can be used to detect the focus of expansion in moving scenes to determine the speed of objects in the three dimensional space. The next section provides a brief background on the problem and a few previous solutions. Section 3 outlines the proposed approach. Section 4 shows our preliminary results. Finally, conclusions and directions for the future work are stated. P. Amestoy et al. (Eds.): Euro-Par’99, LNCS 1685, pp. 987-994, 1999. Springer-Verlag Berlin Heidelberg 1999
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Andrea Matessi and Luca Lombardi
2 Perspective Projection and Notations Let us analyse the perspective projection and the transformation of a point of the real world into the image. The scene or the camera co-ordinates are set to define the Cartesian system XYZ where the Z-axis is the camera optical axis. Let the point (0,0,-f) be the viewpoint or the centre of the lens of the camera. Thus the image plane (x, y) coincides with the XY-plane. The parameter f refers to the focal length. In perspective projection a point in the real world (X, Y, Z) is mapped onto the intersection (x, y) of the XY-plane with the straight line that passes through the (X,Y,Z) point and the viewpoint. From Fig. 1 and from the similitude of triangles it is not diff
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