Image-based modeling
Digital Visual Effects Yung-Yu Chuang
with slides by Richard Szeliski, Steve Seitz and Alexei Efros
Outline
• Models from multiple (sparse) images
– Structure from motion – Facade
• Models from single images
– Tour into pictures – Single view metrology – Other approaches
Models from multiple images (Façade, Debevec et. al. 1996)
Facade
• Use a sparse set of images
• Calibrated camera (intrinsic only)
• Designed specifically for modeling architecture
• Use a set of blocks to approximate architecture
• Three components:
– geometry reconstruction – texture mapping
– model refinement
Idea Idea
Geometric modeling
A block is a geometric primitive with a small set of parameters
Hierarchical modeling for a scene
Rotation and translation could be constrained
Reasons for block modeling
• Architectural scenes are well modeled by geometric primitives.
• Blocks provide a high level abstraction, easier to manage and add constraints.
• No need to infer surfaces from discrete features; blocks essentially provide prior models for architectures.
• Hierarchical block modeling effectively reduces
the number of parameters for robustness and
efficiency.
Reconstruction
minimize
Reconstruction
Reconstruction
nonlinear w.r.t.
camera and model
Results
3 of 12 photographs
Results
Texture mapping Texture mapping in real world
Demo movie Michael Naimark,
San Francisco Museum
of Modern Art, 1984
Texture mapping Texture mapping
View-dependent texture mapping View-dependent texture mapping
model VDTM
VDTM single
texture
map
View-dependent texture mapping Model-based stereo
• Use stereo to refine the geometry
known camera viewpoints
Stereo
scene point
optical center
image plane
Stereo
• Basic Principle: Triangulation
– Gives reconstruction as intersection of two rays – Requires
• calibration
• point correspondence
Stereo correspondence
• Determine Pixel Correspondence
– Pairs of points that correspond to same scene point
• Epipolar Constraint
– Reduces correspondence problem to 1D search along conjugate epipolar lines
epipolar plane epipolar line epipolar line
Finding correspondences
• apply feature matching criterion (e.g., correlation or Lucas-Kanade) at all pixels simultaneously
• search only over epipolar lines (much fewer candidate positions)
Image registration (revisited)
• How do we determine correspondences?
– block matching or SSD (sum squared differences)
d is the disparity (horizontal motion)
• How big should the neighborhood be?
Neighborhood size
• Smaller neighborhood: more details
• Larger neighborhood: fewer isolated mistakes
w = 3 w = 20
Depth from disparity
f
x x’
baseline
z
C C’
X
f input image (1 of 2)
[Szeliski & Kang ‘95]
depth map 3D rendering
– Camera calibration errors – Poor image resolution – Occlusions
– Violations of brightness constancy (specular reflections) – Large motions
– Low-contrast image regions
Stereo reconstruction pipeline
• Steps
– Calibrate cameras – Rectify images – Compute disparity – Estimate depth
• What will cause errors?
Model-based stereo
key image
offset image
warped offset image
Results
Comparisons
single texture, flat VDTM, flat
VDTM, model- based stereo
Final results
Kite photography
Final results
Results Results
Commercial packages
• Autodesk REALVIZ ImageModeler
The Matrix
Cinefex #79, October 1999.
The Matrix
• Academy Awards for Scientific and Technical achievement for 2000
To George Borshukov, Kim Libreri and Dan Piponi for the development of a system for image-based rendering allowing choreographed camera movements through computer graphic reconstructed sets.
This was used in The Matrix and Mission Impossible II; See The Matrix Disc #2 for more details
Models from single images
Vanishing points
• Vanishing point
– projection of a point at infinity
image plane
camera center
ground plane vanishing point
Vanishing points (2D)
image plane
camera center
line on ground plane vanishing point
Vanishing points
• Properties
– Any two parallel lines have the same vanishing point v
– The ray from C through v is parallel to the lines – An image may have more than one vanishing point
image plane
camera center C
line on ground plane vanishing point V
line on ground plane
Vanishing lines
• Multiple Vanishing Points
– Any set of parallel lines on the plane define a vanishing point
– The union of all of these vanishing points is the horizon line
• also called vanishing line
– Note that different planes define different vanishing lines
v1 v2
Computing vanishing points
• Properties
– Pis a point at infinity, v is its projection – They depend only on line direction
– Parallel lines P0+ tD, P1+ tD intersect at P
V
D P P 0t
0 /
1 / / /
1
Z Y X
Z Z
Y Y
X X
Z Z
Y Y
X X
t D
D D t
t D t P
D t P
D t P
tD P
tD P
tD P
P P
ΠP
v P0
D
Tour into pictures
• Create a 3D “theatre stage” of five billboards
• Specify foreground objects through bounding polygons
• Use camera transformations to navigate through the scene
Tour into pictures The idea
• Many scenes (especially paintings), can be represented as an axis-aligned box volume (i.e. a stage)
• Key assumptions:
– All walls of volume are orthogonal
– Camera view plane is parallel to back of volume – Camera up is normal to volume bottom
– Volume bottom is y=0
• Can use the vanishing point to fit the box to the
particular Scene!
Fitting the box volume
• User controls the inner box and the vanishing point placement (6 DOF)
Foreground Objects
• Use separate billboard for each
• For this to work, three separate images used:
– Original image.
– Mask to isolate desired foreground images.
– Background with objects removed
Foreground Objects
• Add vertical rectangles for each foreground object
• Can compute 3D coordinates P0, P1 since they are on known plane.
• P2, P3 can be computed as before (similar triangles)
Example
Example glTip
• http://www.cs.ust.hk/~cpegnel/glTIP/
3D Truth in Old Masters Criminisi et al. ICCV 1999
1. Find world coordinates (X,Y,Z) for a few points 2. Connect the points with planes to model geometry
– Texture map the planes
1 2 3 4
1 2 3 4
Measurements on planes
Approach: unwarp then measure What kind of warp is this?
Image rectification
To unwarp (rectify) an image
• solve for homography H given p and p’
• solve equations of the form: wp’ = Hp – linear in unknowns: w and coefficients of H – H is defined up to an arbitrary scale factor – how many points are necessary to solve for H?
p p’
Solving for homographies Solving for homographies
A h 0
• Defines a least squares problem:
2n × 9 9 2n
– Since h is only defined up to scale, solve for unit vector ĥ
– Works with 4 or more points
Finding world coordinates (X,Y,Z)
1. Define the ground plane (Z=0)
2. Compute points (X,Y,0) on that plane 3. Compute the heights Z of all other points
Measuring height
1 2 3 4 5 5.4
2.8 3.3
Camera height
q1
Computing vanishing points
• Intersect p
1q
1with p
2q
2v
p1
p2 q2
• Least squares version
– Better to use more than two lines and compute the “closest”
point of intersection
– See notes by Bob Collins for one good way of doing this:
• http://www-2.cs.cmu.edu/~ph/869/www/notes/vanishing.txt
Criminisi et al., ICCV 99
• Load in an image
• Click on lines parallel to X axis – repeat for Y, Z axes
• Compute vanishing points
Vanishing point Vanishing
line
Vanishing point
Vertical vanishing point
(at infinity)
Criminisi et al., ICCV 99 Criminisi et al., ICCV 99
• Load in an image
• Click on lines parallel to X axis – repeat for Y, Z axes
• Compute vanishing points
• Specify 3D and 2D positions of 4 points on reference plane
• Compute homography H
• Specify a reference height
• Compute 3D positions of several points
• Create a 3D model from these points
• Extract texture maps
• Output a VRML model
Results Zhang et. al. CVPR 2001
Zhang et. al. CVPR 2001 Oh et. al. SIGGRAPH 2001
Oh et. al. SIGGRAPH 2001
video
Automatic popup
Input
Ground
Vertical
Sky
Geometric Labels Cut’n’Fold 3D Model
Image
Learned Models
Geometric cues
Color
Location
Texture
Perspective
Automatic popup
Results
Automatic Photo Pop-up Input Images
Results
This approach works roughly for 35% of images.
Failures
Labeling Errors
Failures
Foreground Objects
3-sweep The Avengers
• video
References
• P. Debevec, C. Taylor and J. Malik. Modeling and Rendering Architecture from Photographs: A Hybrid Geometry- and Image- Based Approach, SIGGRAPH 1996.
• Y. Horry, K. Anjyo and K. Arai. Tour Into the Picture: Using a Spidery Mesh Interface to Make Animation from a Single Image, SIGGRAPH 1997.
• A. Criminisi, I. Reid and A. Zisserman. Single View Metrology, ICCV 1999.
• L. Zhang, G. Dugas-Phocion, J.-S. Samson and S. Seitz. Single View Modeling of Free-Form Scenes, CVPR 2001.
• B. Oh, M. Chen, J. Dorsey and F. Durand. Image-Based Modeling and Photo Editing, SIGGRAPH 2001.
• D. Hoiem, A. Efros and M. Hebert. Automatic Photo Pop-up, SIGGRAPH 2005.
