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Image-based modeling

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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

(2)

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.

(3)

Reconstruction

minimize

Reconstruction

Reconstruction

nonlinear w.r.t.

camera and model

Results

3 of 12 photographs

(4)

Results

Texture mapping Texture mapping in real world

Demo movie Michael Naimark,

San Francisco Museum

of Modern Art, 1984

(5)

Texture mapping Texture mapping

View-dependent texture mapping View-dependent texture mapping

model VDTM

VDTM single

texture

map

(6)

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

(7)

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

(8)

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

(9)

Comparisons

single texture, flat VDTM, flat

VDTM, model- based stereo

Final results

Kite photography

Final results

(10)

Results Results

Commercial packages

• Autodesk REALVIZ ImageModeler

The Matrix

Cinefex #79, October 1999.

(11)

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

(12)

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

(13)

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

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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/

(15)

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’

(16)

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

(17)

q1

Computing vanishing points

• Intersect p

1

q

1

with p

2

q

2

v

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

(18)

Results Zhang et. al. CVPR 2001

Zhang et. al. CVPR 2001 Oh et. al. SIGGRAPH 2001

(19)

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

(20)

Results

Automatic Photo Pop-up Input Images

Results

This approach works roughly for 35% of images.

Failures

Labeling Errors

Failures

Foreground Objects

(21)

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.

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