1. 12/15/200615-862 Fall 2006 Two-Point Perspective Single View Geometry 15-862 Final Project Faustinus Kevin Gozali (fkg@andrew.cmu.edu) an extended tour into the picture…

2. 12/15/200615-862 Fall 20062 Two-point Perspective World  Camera/eye at (0,0,h) h = dist(horizon, bottom of image)  Camera vanishes at the center of horizon (v eye )  Image plane parallel to x and z axis Center at (0,f,h)  Two vanishing points (vp l, vp r ) X vp r vp l v eye Image Plane x z y

3. 12/15/200615-862 Fall 20063 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 X vp r vp l v eye Image Plane x z y base line

4. 12/15/200615-862 Fall 20064 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 http://www.cs.cmu.edu/~ph/869/www/notes/vanishing.txt Simply doing MLdivide doesn’t work  Done separately for VP left and VP right X vp r vp l v eye Image Plane x z y

5. 12/15/200615-862 Fall 20065 The Horizon Line  Calculated based on 2 VPs  Assumption: horizontal horizon in image plane  Or, user can specify directly

6. 12/15/200615-862 Fall 20066 Selecting Base Lines  User specifies base-lines For each desired vertical wall  Assumption: must be below horizon

7. 12/15/200615-862 Fall 20067 Computing Depth (y-axis)  Similar to 1-point perspective  Based on height ratios Camera height as reference Recall: image plane at y = f v eye Image Plane y zSide View dy h base point depth (3D y )f Camera (0,0,h)horizon line

8. 12/15/200615-862 Fall 20068 Computing Location in x-axis  Using calculated depths (y)  Compute horizontal distance from v eye 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 X v eye Image Plane dx 2 dx 1 2D x1 2D x2

9. 12/15/200615-862 Fall 20069 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 3D height

10. 12/15/200615-862 Fall 200610 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

11. 12/15/200615-862 Fall 200611 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

12. 12/15/200615-862 Fall 200612 3D Model Generation  Define the surfaces Based on (3D x, 3D y, 3D height )  Wrap textures  Observe model

13. 12/15/200615-862 Fall 200613 Fun with Texture Sources  Texture Interpolation approximately evening view  Blending Half morning half night  Use this for 3D model

14. 12/15/200615-862 Fall 200614 Texture Examples

15. 12/15/200615-862 Fall 200615 Gallery

16. 12/15/200615-862 Fall 200616 Gallery

17. 12/15/200615-862 Fall 200617 Gallery

18. 12/15/200615-862 Fall 200618 Gallery

19. 12/15/200615-862 Fall 200619 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 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.pdfhttp://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 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 http://www.cs.cmu.edu/~ph/869/www/notes/vanishing.txt

20. 12/15/200615-862 Fall 200620 Q&A Questions?