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

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Outline

• Models from multiple (sparse) images

– Structure from motion – Facade

• Models from single images

– Tour into pictures

– Single view metrology – Other approaches

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Models from multiple images

(Façade, Debevec et. al.

1996)

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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

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Idea

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Idea

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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

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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.

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Reconstruction

minimize

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Reconstruction

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Reconstruction

nonlinear w.r.t.

camera and model

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Results

3 of 12 photographs

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Results

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Texture mapping

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Texture mapping in real world

Demo movie

Michael Naimark,

San Francisco Museum

of Modern Art, 1984

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Texture mapping

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Texture mapping

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View-dependent texture mapping

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View-dependent texture mapping

model VDTM

VDTM single

texture

map

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View-dependent texture mapping

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Model-based stereo

• Use stereo to refine the geometry

known known camera camera viewpoints viewpoints

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Stereo

scene point scene point

optical center optical center

image plane image plane

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Stereo

• Basic Principle: Triangulation

– Gives reconstruction as intersection of two rays – Requires

• calibration

• point correspondence

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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 lineepipolar line epipolar line

epipolar line

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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)

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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?

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Neighborhood size

• Smaller neighborhood: more details

• Larger neighborhood: fewer isolated mistakes

w = 3 w = 20

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Depth from disparity

f

x x’

baseline

z

C C’

X

f

input image (1 of 2)

[Szeliski & Kang ‘95]

depth map 3D rendering

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– 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?

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Model-based stereo

key image

offset image

warped offset image

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Results

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Comparisons

single texture, flat VDTM, flat

VDTM, model- based stereo

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Final results

Kite photography

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Final results

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Results

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Results

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Commercial packages

• Autodesk REALVIZ ImageModeler

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The Matrix

Cinefex #79, October 1999.

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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

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Models from single

images

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Vanishing points

• Vanishing point

– projection of a point at infinity

image plane

camera center

ground plane vanishing point

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Vanishing points (2D)

image plane

camera center

line on ground plane vanishing point

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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

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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

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Computing vanishing points

• Properties

– P is 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  ₀ t

















































 _

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

tD P

P P

 ΠP

v

P₀

D

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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

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Tour into pictures

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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!

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Fitting the box volume

• User controls the inner box and the vanishing

point placement (6 DOF)

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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)

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Example

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Example

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glTip

• http://www.cs.ust.hk/~cpegnel/glTIP/

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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

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1 2 3 4

Measurements on planes

Approach: unwarp then measure What kind of warp is this?

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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’

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Solving for homographies

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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

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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

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Measuring height

1 2 3 4

5 5.4

2.8 3.3

Camera height

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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

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Criminisi et al., ICCV 99

• Load in an image

• Click on lines parallel to X axis – repeat for Y, Z axes

• Compute vanishing points

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Vanishing point Vanishing

line

Vanishing point

Vertical vanishing point

(at infinity)

Criminisi et al., ICCV 99

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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

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Results

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Zhang et. al. CVPR 2001

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Zhang et. al. CVPR 2001

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Oh et. al. SIGGRAPH 2001

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Oh et. al. SIGGRAPH 2001

video

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Automatic popup

Input

Ground

Vertical

Sky

Geometric Labels Cut’n’Fold 3D Model

Image

Learned Models

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Geometric cues

Color

Location

Texture

Perspective

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Automatic popup

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Results

Automatic Photo Pop-up Input Images

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Results

This approach works roughly for 35% of images.

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Failures

Labeling Errors

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Failures

Foreground Objects

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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.