3D photography

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3D photography

Digital Visual Effects, Spring 2008 Yung-Yu Chuang

2008/5/13

with slides by Szymon Rusinkiewicz, Richard Szeliski, Steve Seitz and Brian Curless

Announcements

• Project #3 is due on 5/19. Two videos. Send us links only.

• We may have final project proposal

presentation on 5/27. Please send me your team members and topic by 5/26.

• Final project demo day will be 1:30pm on 6/25 (Wed). Room to be announced.

3D photography

• Acquisition of geometry and material

Range acquisition

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Range acquisition taxonomy

range range acquisition acquisition

contact contact

transmissive transmissive

reflective reflective

nonnon--opticaloptical

optical optical

industrial CT industrial CT mechanical

mechanical (CMM, jointed arm)(CMM, jointed arm)

radar radar sonar sonar ultrasound

ultrasound MRI MRI

ultrasonic trackers ultrasonic trackers magnetic trackers magnetic trackers inertial

inertial (gyroscope, accelerometer)(gyroscope, accelerometer)

Range acquisition taxonomy

optical optical methods methods

passive passive

active active

shape from X:

stereo stereo motion motion shading shading texture texture focus focus defocus defocus

active variants of passive methods active variants of passive methods

Stereo w. projected texture Stereo w. projected texture Active depth from defocus Active depth from defocus Photometric stereo Photometric stereo

time of flight time of flight

triangulation triangulation

Outline

• Passive approaches

– Stereo

– Multiview approach

• Active approaches

– Triangulation – Shadow scanning

• Active variants of passive approaches

– Photometric stereo

– Example-based photometric stereo

Passive approaches

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Public Library, Stereoscopic Looking Room, Chicago, by Phillips, 1923

Stereo Stereo

• One distinguishable point being observed

– The preimage can be found at the intersection of the rays from the focal points to the image points

Stereo

• Many points being observed

– Need some method to establish correspondences

Components of stereo vision systems

• Camera calibration

• Image rectification: simplifies the search for correspondences

• Correspondence: which item in the left image corresponds to which item in the right image

• Reconstruction: recovers 3-D information from the 2-D correspondences

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Epipolar geometry

• Epipolar constraint: corresponding points must lie on conjugate epipolar lines

– Search for correspondences becomes a 1-D problem

0 '

^Τ

Fx = x

Image rectification

• Warp images such that conjugate

epipolar lines become collinear and parallel to u axis

Disparity

• With rectified images, disparity is just (horizontal) displacement of corresponding features in the two images

– Disparity = 0 for distant points – Larger disparity for closer points

– Depth of point proportional to 1/disparity

Reconstruction

• Geometric

– Construct the line segment perpendicular to R and R' that intersects both rays and take its mid-point

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Basic stereo algorithm

For each epipolar line

For each pixel in the left image

• compare with every pixel on same epipolar line in right image

• pick pixel with minimum match cost

Improvement: match windows

Basic stereo algorithm

• For each pixel

– For each disparity

• For each pixel in window – Compute difference

– Find disparity with minimum SSD

Reverse order of loops

• For each disparity

– For each pixel

• For each pixel in window – Compute difference

• Find disparity with minimum SSD at each pixel

Incremental computation

• Given SSD of a window, at some disparity

Image 1 Image 1

Image 2 Image 2

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Incremental computation

• Want: SSD at next location

Image 1 Image 1

Image 2 Image 2

Incremental computation

• Subtract contributions from leftmost column, add contributions from rightmost column

Image 1 Image 1

Image 2 Image 2

++ ++ ++ ++ ++

-- -- -- -- -- -- -- -- -- --

++ ++ ++ ++ ++

Selecting window size

• Small window: more detail, but more noise

• Large window: more robustness, less detail

• Example:

Selecting window size

3 pixel window

3 pixel window 20 pixel window20 pixel window

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Non-square windows

• Compromise: have a large window, but higher weight near the center

• Example: Gaussian

• Example: Shifted windows

Ordering constraint

• Order of matching features usually the same in both images

• But not always: occlusion

Dynamic programming

• Treat feature correspondence as graph problem

Left image Left image features features

Right image features Right image features

1

1 22 33 44 1

1 2 2 3 3 4 4

Cost of edges = Cost of edges =

similarity of similarity of regions between regions between image features image features

Dynamic programming

• Find min-cost path through graph

Left image Left image features features

Right image features Right image features

1

1 22 33 44 1

1 2 2 3 3 4 4

1 1

33 44 11 2 2 2

2 33 44

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Energy minimization

• Another approach to improve quality of correspondences

• Assumption: disparities vary (mostly) smoothly

• Minimize energy function:

E_data+λE_smoothness

• E_data: how well does disparity match data

• E_smoothness: how well does disparity match that of neighbors – regularization

Energy minimization

• If data and energy terms are nice (continuous, smooth, etc.) can try to minimize via gradient descent, etc.

• In practice, disparities only piecewise smooth

• Design smoothness function that doesn’t penalize large jumps too much

– Example: V(α,β)=min(|α−β|, K)

Stereo as energy minimization

• Matching Cost Formulated as Energy

– “data” term penalizing bad matches

– “neighborhood term” encouraging spatial smoothness

) , (

) , ( ) , ,

(x y d x y x d y

D = I −J +

similar) something

(or

d2 and d1 labels with pixels adjacent of

cost

2 1 2 1, ) (

d d d d V

−

=

∑

⁺

=

) 2 , 2 ( ), 1 , 1 (

2 , 2 1 , 1 )

, (

, ) ( , )

, , (

y x y x neighbors

y x y x y

x

y

x V d d

d y x D E

Energy minimization

• Hard to find global minima of non-smooth functions

– Many local minima – Provably NP-hard

• Practical algorithms look for approximate minima (e.g., simulated annealing)

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Energy minimization via graph cuts

Labels (disparities)

d₁ d₂ d₃

edge weight

edge weight ) , , (x y d₃ D

) , (d₁ d₁ V

• Graph Cost

– Matching cost between images – Neighborhood matching term

– Goal: figure out which labels are connected to which pixels

d₁ d₂ d₃

Energy minimization via graph cuts

d₁ d₂ d₃

• Graph Cut

– Delete enough edges so that

• each pixel is (transitively) connected to exactly one label node

– Cost of a cut: sum of deleted edge weights – Finding min cost cut equivalent to finding global

minimum of energy function

Computing a multiway cut

• With 2 labels: classical min-cut problem

– Solvable by standard flow algorithms

• polynomial time in theory, nearly linear in practice

– More than 2 terminals: NP-hard

[Dahlhaus et al., STOC ‘92]

• Efficient approximation algorithms exist

– Within a factor of 2 of optimal

– Computes local minimum in a strong sense

• even very large moves will not improve the energy

– Yuri Boykov, Olga Veksler and Ramin Zabih, Fast Approximate Energy Minimization via Graph Cuts, International Conference on Computer Vision, September 1999.

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Move examples

Starting point

Red-blue swap move

Green expansion move

The swap move algorithm

1. Start with an arbitrary labeling

2. Cycle through every label pair (A,B) in some order

2.1 Find the lowest E labeling within a single AB-swap 2.2 Go there if E is lower than the current labeling

3. If E did not decrease in the cycle, we’re done Otherwise, go to step 2

Original graph

A B

AB subgraph

(run min-cut on this graph) B

A

The expansion move algorithm

1. Start with an arbitrary labeling

2. Cycle through every label A in some order

2.1 Find the lowest E labeling within a single A-expansion 2.2 Go there if it E is lower than the current labeling

3. If E did not decrease in the cycle, we’re done Otherwise, go to step 2

Stereo results

ground truth scene

– Data from University of Tsukuba

http://cat.middlebury.edu/stereo/

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Results with window correlation

normalized correlation (best window size)

ground truth

Results with graph cuts

ground truth graph cuts

(Potts model E, expansion move algorithm)

Stereo evaluation Stereo—best algorithms

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Volumetric multiview approaches

• Goal: find a model consistent with images

• “Model-centric” (vs. image-centric)

• Typically use discretized volume (voxel grid)

• For each voxel, compute occupied / free (for some algorithms, also color, etc.)

Photo consistency

• Result: not necessarily the correct scene

• Many scenes produce the same images

All scenes All scenes

Photo

Photo--consistent scenesconsistent scenes True scene

True scene

Reconstructed Reconstructed

scene scene

Silhouette carving

• Find silhouettes in all images

• Exact version:

– Back-project all silhouettes, find intersection

Binary Images Binary Images

Silhouette carving

• Find silhouettes in all images

• Exact version:

– Back-project all silhouettes, find intersection

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Silhouette carving

• Limit of silhouette carving is visual hull or line hull

• Complement of lines that don’t intersect object

• In general not the same as object

– Can’t recover “pits” in object

• Not the same as convex hull

Silhouette carving

• Discrete version:

– Loop over all voxels in some volume

– If projection into images lies inside all silhouettes, mark as occupied

– Else mark as free

Silhouette carving Voxel coloring

• Seitz and Dyer, 1997

• In addition to free / occupied, store color at each voxel

• Explicitly accounts for occlusion

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Voxel coloring

• Basic idea: sweep through a voxel grid

– Project each voxel into each image in which it is visible

– If colors in images agree, mark voxel with color – Else, mark voxel as empty

• Agreement of colors based on comparing standard deviation of colors to threshold

Voxel coloring and occlusion

• Problem: which voxels are visible?

• Solution: constrain camera views

– When a voxel is considered, necessary occlusion information must be available

– Sweep occluders before occludees

– Constrain camera positions to allow this sweep

Voxel coloring sweep order

Scene Scene Traversal Traversal

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Voxel coloring camera positions

Inward-looking

Cameras above scene

Outward-looking

Cameras inside scene

Seitz Seitz

Image acquisition

•Calibrated Turntable

•360° rotation (21 images) Selected Dinosaur Images

Selected Dinosaur Images

Selected Flower Images Selected Flower Images

Voxel coloring results

Dinosaur Reconstruction Dinosaur Reconstruction

72 K voxels colored 72 K voxels colored 7.6 M voxels tested 7.6 M voxels tested 7 min. to compute 7 min. to compute on a 250MHz SGI on a 250MHz SGI

Flower Reconstruction Flower Reconstruction

70 K voxels colored 70 K voxels colored 7.6 M voxels tested 7.6 M voxels tested 7 min. to compute 7 min. to compute on a 250MHz SGI on a 250MHz SGI

Space carving

Image 1

Image 1 Image NImage N

…...…...

Initialize to a volume V containing the true scene Initialize to a volume V containing the true scene

Repeat until convergence Repeat until convergence

Choose a voxel on the current surface Choose a voxel on the current surface

Carve if not photo

Carve if not photo--consistentconsistent Project to visible input images Project to visible input images

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Multi-pass plane sweep

• Faster alternative:

– Sweep plane in each of 6 principal directions – Consider cameras on only one side of plane – Repeat until convergence

Multi-pass plane sweep

True Scene Reconstruction

Multi-pass plane sweep Multi-pass plane sweep

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Multi-pass plane sweep Multi-pass plane sweep

Input image (1 of 45)

Input image (1 of 45) ReconstructionReconstruction

Reconstruction Reconstruction Reconstruction

Reconstruction

Space carving results: African violet

Input image Input image (1 of 100) (1 of 100)

Reconstruction Reconstruction

Space carving results: hand

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Active approaches

Time of flight

• Basic idea: send out pulse of light (usually laser), time how long it takes to return

t c

r= Δ

2 1c t

r= Δ

2 1

Laser scanning (triangulation)

• Optical triangulation

– Project a single stripe of laser light – Scan it across the surface of the object

– This is a very precise version of structured light scanning

• Other patterns are possible

Direction of travel Object

CCD

CCD image plane

Laser

Cylindrical lens Laser sheet

Digital Michelangelo Project

http://graphics.stanford.edu/projects/mich/

Cyberware

face and hand full body

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XYZRGB XYZRGB

Shadow scanning

Desk Lamp

Camera

Stick or pencil

Desk

http://www.vision.caltech.edu/bouguetj/ICCV98/

Basic idea

• Calibration issues:

– where’s the camera wrt. ground plane?

– where’s the shadow plane?

• depends on light source position, shadow edge

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Two Plane Version

• Advantages

– don’t need to pre-calibrate the light source

– shadow plane determined from two shadow edges

Estimating shadow lines

Shadow scanning in action

accuracy: 0.1mm over 10cm ~ 0.1% error

Results

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Textured objects

accuracy: 1mm over 50cm ~ 0.5% error

Scanning with the sun

accuracy: 1cm over 2m

~ 0.5% error

Scanning with the sun

Active variants of

passive approaches

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The BRDF

• The Bidirectional Reflection Distribution Function

– Given an incoming ray and outgoing ray what proportion of the incoming light is reflected along outgoing ray?

surface normal

γ ρ(l,v) (l n)

I = × ⋅

Diffuse reflection (Lambertian)

L V P N

kd

v l, )=

ρ( albedo

Assuming that light strength is 1.

Photometric stereo

N L1

L2

V L3

• Can write this as a matrix equation:

Solving the equations

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More than three lights

• Get better results by using more lights

• Least squares solution:

• Solve for N, k_d as before

Trick for handling shadows

• Weight each equation by the pixel brightness:

• Gives weighted least-squares matrix equation:

• Solve for N, k_das before

Photometric Stereo Setup Procedure

• Calibrate camera

• Calibrate light directions/intensities

• Photographing objects (HDR recommended)

• Estimate normals

• Estimate depth

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Estimating light directions

• Trick: place a chrome sphere in the scene

– the location of the highlight tells you where the light source is

• Use a ruler

Photographing objects

Normalize light intensities Estimate normals

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Depth from normals Results

Limitations

• Big problems

– doesn’t work for shiny things, semi-translucent things

– shadows, inter-reflections

• Smaller problems

– calibration requirements

• measure light source directions, intensities

• camera response function

Example-based photometric stereo

• Estimate 3D shape by varying illumination, fixed camera

• Operating conditions

– any opaque material – distant camera, lighting – reference object available

– no shadows, interreflections, transparency

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same surface normal

“Orientation consistency”

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Virtual views

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Velvet Virtual Views

Brushed Fur Virtual Views

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Active stereo with structured light

• Project “structured” light patterns onto the object

– simplifies the correspondence problem

camera 2 camera 1

projector

camera 1

projector Li Zhang’s one-shot stereo

Spacetime Stereo

http://grail.cs.washington.edu/projects/stfaces/

3D Model Acquisition Pipeline

3D Scanner 3D Scanner 3D Scanner

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3D Model Acquisition Pipeline

View Planning View Planning View Planning

3D Model Acquisition Pipeline

Alignment Alignment Alignment View Planning

View Planning View Planning

3D Model Acquisition Pipeline

Alignment Alignment Alignment

Merging Merging Merging View Planning

View

View PlanningPlanning

Volumetric reconstruction

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Signed distance function Results

The Digital Michelangelo Project

• Goal: scan 10 sculptures by Michelangelo

• High-resolution (“quarter-millimeter”) geometry

• Stanford University, led by Marc Levoy

Systems, projects and applications

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Scanning the David

height of gantry: 7.5 meters weight of gantry: 800 kilograms

Range processing pipeline

• steps

1. manual initial alignment 2. ICP to one existing scan

3. automatic ICP of all overlapping pairs 4. global relaxation to spread out error 5. merging using volumetric method

• 480 individually aimed scans

• 2 billion polygons

• 7,000 color images

• 32 gigabytes

• 30 nights of scanning

• 22 people

Statistics about the scan

photograph 1.0 mm computer model

Comparison

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Results The Great Buddha Project

• Great Buddha of Kamakura

• Original made of wood, completed 1243

• Covered in bronze and gold leaf, 1267

• Approx. 15 m tall

• Goal: preservation of cultural heritage

• Institute of Industrial Science, University of Tokyo, led by Katsushi

Katsushi IkeuchiIkeuchi

Scanner

• Cyrax range scanner by Cyra Technologies

• Laser pulse time-of-flight

• Accuracy: 4 mm

• Range: 100 m

Processing

• 20 range images (a few million points)

• Simultaneous all-to-all ICP

• Variant of volumetric merging (parallelized)

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Results Applications in VFX

• 3D scanning

• Hybrid camera for IMAX

• View interpolation

3D scanning

XYZRGB Inc.

IMAX 3D

• 6K resolution, 42 linear bits per pixel

• For CG, it typically takes 6 hours for a frame

• 45-minute IMAX 3D CG film requires a 100-CPU rendering farm full-time for about a year just for rendering

• For live-action, camera is bulky (like a refrigerator)

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Hybrid stereo camera Live-action sequence

Hybrid input

left

right

Hybrid input

left

right

left

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Combine multiple hires to lores Results

View interpolation

Bullet time video

View interpolation

High-quality video view interpolation

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Final project

• Assigned: 5/14

• Due: 6/25 Wednesday

• Proposal and midterm report on 5/27

Final project

• Research (1-2 people)

• System (1-3 people)

• Film (3-4 people)

Research

• Define a problem and try to solve it

• You don’t need to solve it all, but have to make a reasonable progress, for example, solve a simplified version.

• Find inspirations from SIGGRAPH/CVPR/ICCV papers

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System

• Implement existing algorithm into a useful system such as implementing SIGGRAPH

2006/2007/2008 or CVPR/ICCV 2006/2007/2008 papers

Film

• It must be an “effect” film.

• You can use any tools as you want. But, I assume that you have to write some on your own.

• Find inspirations from

Gatech’s vfx course

http://www.cc.gatech.edu/classes/AY2004/cs4480_spring/

independent film makers

http://www.peerlessproductions.com/

ADs/films/YouTube

• Submit two videos, final and making-of.