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Two-Point Perspective Single View Geometry

Two-Point Perspective Single View Geometry. an extended tour into the picture…. 15-862 Final Project Faustinus Kevin Gozali ( fkg@andrew.cmu.edu ). v eye. X. vp l. vp r. z. y. x. Image Plane. Two-point Perspective World. Camera/eye at (0,0,h) h = dist(horizon, bottom of image)

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Two-Point Perspective Single View Geometry

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  1. Two-Point Perspective Single View Geometry an extended tour into the picture… 15-862 Final Project Faustinus Kevin Gozali (fkg@andrew.cmu.edu) 15-862 Fall 2006

  2. veye X vpl vpr z y x Image Plane Two-point Perspective World • Camera/eye at (0,0,h) • h = dist(horizon, bottom of image) • Camera vanishes at the center of horizon (veye) • Image plane parallel to x and z axis • Center at (0,f,h) • Two vanishing points (vpl, vpr) 15-862 Fall 2006

  3. veye X vpl vpr z y x Image Plane Our Assumptions • Horizontal Horizon line • This holds for two-point perspective • 1 VP to the left, 1 to the right • Baselines below horizon • Uniform heights for all walls base line 15-862 Fall 2006

  4. veye X vpl vpr z y x Image Plane Vanishing Point Calculation • User specifies parallel lines • Compute intersection point with Least Square Method = VP • Method described by Bob Collins • http://www.cs.cmu.edu/~ph/869/www/notes/vanishing.txt • Simply doing MLdivide doesn’t work • Done separately for VPleft and VPright 15-862 Fall 2006

  5. The Horizon Line • Calculated based on 2 VPs • Assumption: horizontal horizon in image plane • Or, user can specify directly 15-862 Fall 2006

  6. Selecting Base Lines • User specifies base-lines • For each desired vertical wall • Assumption: must be below horizon 15-862 Fall 2006

  7. Side View z y Camera (0,0,h) veye horizon line dy h f base point depth (3Dy) Image Plane Computing Depth (y-axis) • Similar to 1-point perspective • Based on height ratios • Camera height as reference • Recall: image plane at y = f 15-862 Fall 2006

  8. veye X dx2 dx1 2Dx2 2Dx1 Image Plane Computing Location in x-axis • Using calculated depths (y) • Compute horizontal distance from veye in image plane • Recall: left side is x-, right side is x+ • Horizontal distance amplified using depth ratio to camera height • Farther points are amplified more 15-862 Fall 2006

  9. Specifying Height • After 3D location is computed • Compute Height Scales • Ratio for each base point to camera height • Extend walls vertically upward • Height of the base-point closest to the camera as reference • User picks the desired height, then compute 3Dheight 15-862 Fall 2006

  10. Ground Surface • Ground surface is a prefect rectangle at z = 0 • Create Ground mask • Up to the farthest base-point • Warp texture (using Homography) • Point correspondences have to consider 3D depth! • Create 3D surface 15-862 Fall 2006

  11. Vertical Walls • Similar to ground processing • All walls are perfect rectangle • No mask is needed • Warp texture using Homography • Consider distance of each base point as width • Uniform height • Create 3D model • Intersects the ground plane correctly 15-862 Fall 2006

  12. 3D Model Generation • Define the surfaces • Based on (3Dx, 3Dy, 3Dheight) • Wrap textures • Observe model 15-862 Fall 2006

  13. Fun with Texture Sources • Texture Interpolation • approximately evening view • Blending • Half morning half night • Use this for 3D model 15-862 Fall 2006

  14. Texture Examples 15-862 Fall 2006

  15. Gallery 15-862 Fall 2006

  16. Gallery 15-862 Fall 2006

  17. Gallery 15-862 Fall 2006

  18. Gallery 15-862 Fall 2006

  19. References [1] Chu, Siu-Hang, Animating Chinese Landscape Paintings and Panoramas. A Thesis Submitted to the Hong Kong University of Science and Technology, August 2001. [2] Hoeim, Derek; Efros, A. Alexei; Herbert, Martial. Automatic Photo Pop-up. Robotics Institute, Carnegie Melon University, Pittsburgh PA, USA. http://www.cs.cmu.edu/~dhoiem/projects/popup [3] Single View Reconstruction Lecture slides. http://graphics.cs.cmu.edu/courses/15-463/2006_fall/www/Lectures/SingleViewReconstruction.pdf [4] Perspective Drawing. An online tutorial. http://www.lems.brown.edu/vision/people/leymarie/SkiP/May98/Boehm1.html [5] Horry, Yoichi; Anjyo, Ken-ichi; Arai, Kiyoshi. Tour Into the Picture: Using a Spidery Mesh Interface to Make Animation from a Single Image. Hitachi, Ltd. [6] Collins, Bob. A guide to compute vanishing points. http://www.cs.cmu.edu/~ph/869/www/notes/vanishing.txt 15-862 Fall 2006

  20. Q&A Questions? 15-862 Fall 2006

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