Image-based modeling
Digital Visual Effects g Yung-Yu Chuang
with slides by Richard Szeliski, Steve Seitz and Alexei Efros
Outline
• Models from multiple (sparse) images
St t f ti
– Structure from motion – Facade
d l f l
• 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
C lib d (i i i l )
• Calibrated camera (intrinsic only)
• Designed specifically for modeling architecture
• Use a set of blocks to approximate architecture
• Three components:
g t t ti
– geometry reconstruction – texture mapping
d l fi t
– model refinement
Idea Idea
Geometric modeling
A block is a geometric primitive with a small set of parameters with a small set of parameters
Hi hi l d li f
Hierarchical modeling for a scene
Rotation and translation could be constrained
Reasons for block modeling
• Architectural scenes are well modeled by geometric primitives
geometric primitives.
• Blocks provide a high level abstraction, easier
t d dd t i t
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 p
efficiency.
Reconstruction
minimize
Reconstruction
Reconstruction
li
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
model VDTM
VDTM single
texture VDTM
texture
map
View-dependent texture mapping Model-based stereo
• Use stereo to refine the geometry
known known camera camera viewpoints viewpoints
Stereo
scene point scene point
i l
i l
optical center optical center
image plane image plane
Stereo
• Basic Principle: Triangulation
– Gives reconstruction as intersection of two raysy – Requires
• calibration i
• point correspondence
Stereo correspondence
• Determine Pixel Correspondence
P i f i t th t d t i t
– Pairs of points that correspond to same scene point
epipolar plane epipolar lineepipolar line epipolar line
epipolar line
p p p
• Epipolar Constraint
– Reduces correspondence problem to 1D search along conjugate epipolar lines
Finding correspondences
• apply feature matching criterion (e.g., correlation or Lucas-Kanade) at all pixels correlation or Lucas Kanade) at all pixels simultaneously
• search only over epipolar lines (much fewer y p p ( candidate positions)
Image registration (revisited)
• How do we determine correspondences? How do we determine correspondences?
– block matching or SSD (sum squared differences)
d i th di it (h i t l ti ) d is the disparity (horizontal motion)
• How big should the neighborhood be?
Neighborhood size
• Smaller neighborhood: more details
L i hb h d f i l d i k
• Larger neighborhood: fewer isolated mistakes
w = 3 w = 20
Depth from disparity
input image (1 of 2)
[Szeliski & Kang ‘95]
depth map 3D rendering
X
[Szeliski & Kang 95]
z
f
x x’
f baseline
C C’
Stereo reconstruction pipeline
• Steps
Calibrate cameras – Calibrate cameras – Rectify images – Compute disparityp p y – Estimate depth
– Camera calibration errors
• What will cause errors?
– Poor image resolution – Occlusions
– Violations of brightness constancy (specular reflections) – Large motions
Low contrast image regions – Low-contrast image regions
Model-based stereo
key image warped offset image
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
achievement for 2000
To George Borshukov, Kim Libreri and Dan Pi i f th d l t f t f Piponi for the development of a system for image-based rendering allowing choreographed
t th h t hi
camera movements through computer graphic reconstructed sets.
This was used in The Matrix and Mission I ibl II S Th M i Di #2 f Impossible II; See The Matrix Disc #2 for more details
Models from single images Models from single images
Vanishing points
image plane
camera center
vanishing point
center
ground plane
• Vanishing point
g p
• Vanishing point
– projection of a point at infinity
Vanishing points (2D)
image plane
camera center
vanishing point
center
line on ground planeg p
Vanishing points
image plane
camera center
vanishing point V
center C
line on ground plane line on ground plane
• Properties
g p
p
– 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 pointg y g p
Vanishing lines
v1 v2
Multiple Vanishing Points
• Multiple Vanishing Points
– Any set of parallel lines on the plane define a vanishing point
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
Computing vanishing points
V
D P P 0t P0
D
/ / /
Y X Y
Y X X Y Y
X X
t
D D D t
t P
D t P tD P
tD P
P P
• Properties
0 /
1 / 1
Z Z
Z Z Z
t D
t D t P tD P
ΠP
• Properties
v– Pis a point at infinity, v is its projection – They depend only on line direction
ΠP
v
They depend only on line direction
– Parallel lines P0+ tD, P1+ tD intersect at P
Tour into pictures
• Create a 3D “theatre stage” of
• Create a 3D theatre stage of five billboards
• Specify foreground objects p y g j 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 represented as an axis-aligned box volume (i.e. a stage)
K ti
• 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!
particular Scene!
Fitting the box volume
• User controls the inner box and the vanishing point placement (6 DOF)
point placement (6 DOF)
Foreground Objects
• Use separate billboard for each billboard for each
• For this to work, three separate images used:
– Original image.
– Mask to isolate desired foreground images.
– Background with bj t d objects removed
Foreground Objects
• Add vertical rectangles for rectangles for each foreground object
object
• Can compute 3D Can compute 3D coordinates P0, P1 since they are on known plane.
• P2, P3 can be d computed as before (similar triangles) triangles)
Example
Example glTip
• http://www.cs.ust.hk/~cpegnel/glTIP/
Criminisi et al. ICCV 1999
1 Find world coordinates (X Y Z) for a few points 1. Find world coordinates (X,Y,Z) for a few points 2. Connect the points with planes to model geometry
Te t re map the planes – Texture map the planes
Measurements on planes
4 3 4
2 1
1 2 3 4
Approach: unwarp then measure What kind of warp is this?
Image rectification
p’
p p
To unwarp (rectify) an image
• solve for homography H given p and p’
l ti f th f ’ H
• solve equations of the form: wp’ = Hp – linear in unknowns: w and coefficients of H – H is defined up to an arbitrary scale factorp y – how many points are necessary to solve for H?
Solving for homographies
Solving for homographies
A h 0
A h 0
• Defines a least squares problem:
2n × 9 9 2n
• Defines a least squares problem:
– Since h is only defined up to scale solve for unit Since h is only defined up to scale, solve for unit vector ĥ
– Works with 4 or more pointsWorks with 4 or more points
Finding world coordinates (X,Y,Z)
1 Define the ground plane (Z 0) 1. Define the ground plane (Z=0)
2. Compute points (X,Y,0) on that plane 3 Comp te the heights Z of all other points 3. Compute the heights Z of all other points
Measuring height
5 5.4 4 5
3 3
Camera height
2 3 2.8
3.3
1 2
Computing vanishing points
v
q2 q1
p p2
• Intersect p
1q
1with p
2q
2p1
• 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: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
• Click on lines parallel to X axis – repeat for Y, Z axes
Compute vanishing points
• Compute vanishing points
Criminisi et al., ICCV 99
Vertical vanishing point
( t i fi it ) Vanishing
line
(at infinity) line
Vanishing point Vanishing
point point
p
Criminisi et al., ICCV 99
• Load in an image
• Click on lines parallel to X axis
• Click on lines parallel to X axis – repeat for Y, Z axes
Compute vanishing points
• Compute vanishing points
• Specify 3D and 2D positions of 4 points on reference plane
plane
• Compute homography H
• Specify a reference height
• Specify a reference height
• Compute 3D positions of several points
• Create a 3D model from these points
• Create a 3D model from these points
• Extract texture maps Output a VRML model
• 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
video
Automatic popup
Input Geometric Labels Cut’n’Fold 3D Model
Ground Imageg
Vertical
Sky Learned Models
Geometric cues
Color Texture
Location 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
References
• P. Debevec, C. Taylor and J. Malik. Modeling and Rendering Architecture from Photographs: A Hybrid Rendering Architecture from Photographs: A Hybrid Geometry- and Image-Based Approach, SIGGRAPH 1996.
• Y. Horry, K. Anjyo and K. Arai. Tour Into the Picture: y, jy 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 Ch J D d F D d I B d
• 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
• D. Hoiem, A. Efros and M. Hebert. Automatic Photo Pop-up, SIGGRAPH 2005.
