3D photography

3D photography

Digital Visual Effects Yung-Yu Chuang

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

3D photography

• Acquisition of geometry and material

Range acquisition

Range acquisition taxonomy

range acquisition

contact

transmissive

reflective non-optical optical

industrial CT

mechanical (CMM, jointed arm)

radar sonar ultrasound

MRI

ultrasonic trackers magnetic trackers

inertial (gyroscope, accelerometer)

Range acquisition taxonomy

optical methods

passive

active

shape from X:

stereo motion shading texture focus defocus

active variants of passive methods

Stereo w. projected texture Active depth from defocus Photometric stereo

time of flight 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

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 co rrespondences

• Correspondence: which item in the left image c orresponds to which item in the right image

• Reconstruction: recovers 3-D information from t he 2-D correspondences

Epipolar geometry

• Epipolar constraint: corresponding points must l ie on conjugate epipolar lines

– Search for correspondences becomes a 1-D problem

0

'

Fx 

x

Image rectification

• Warp images such tha t conjugate epipolar li nes become collinear and parallel to u axis

Disparity

• With rectified images, disparity is just (horizont al) displacement of corresponding features in th e 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

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 2

Incremental computation

• Want: SSD at next location

Image 1

Image 2

Incremental computation

• Subtract contributions from leftmost column, a dd contributions from rightmost column

Image 1

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 20 pixel window

Non-square windows

• Compromise: have a large window, but higher w eight 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 features

Right image features

1 2 3 4

1 2 3 4

Cost of edges = similarity of regions between

image features

Dynamic programming

• Find min-cost path through graph

Left image features

Right image features

1 2 3 4

1 2 3 4

1

34 1 2 2

3 4

Energy minimization

• Another approach to improve quality of corresp ondences

• Assumption: disparities vary (mostly) smoothly

• Minimize energy function:

E_data+lE_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, s mooth, etc.) can try to minimize via gradient d escent, etc.

• In practice, disparities only piecewise smooth

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

– Example: V(a,b)=min(|a-b|, K)

Stereo as energy minimization

• Matching Cost Formulated as Energy

– “data” term penalizing bad matches

– “neighborhood term” encouraging spatial smoothness

) , (

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, ,

( x y d x y x d y

D  I - J 

similar) something

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labels with

pixels adjacent

of cost

2 1

2 1, ) (

d d

d d V

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 ^

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) 2 , 2 ( ), 1 , 1 (

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y x y

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x y

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Energy minimization

• Hard to find global minima of non-smooth funct ions

– Many local minima – Provably NP-hard

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

Stereo results

ground truth scene

– Data from University of Tsukuba

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

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

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

Photo-consistent scenes True scene Reconstructed

scene

Silhouette carving

• Find silhouettes in all images

• Exact version:

– Back-project all silhouettes, find intersection

Binary Images

Silhouette carving

• Find silhouettes in all images

• Exact version:

– Back-project all silhouettes, find intersection

Silhouette carving

• Limit of silhouette carving is visual hull or line hull

• Complement of lines that don’t intersect obje ct

• 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, m ark 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

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 standa rd deviation of colors to threshold

Voxel coloring and occlusion

Voxel coloring and occlusion

• Problem: which voxels are visible?

• Solution: constrain camera views

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

– Sweep occluders before occludees

– Constrain camera positions to allow this sweep

Voxel coloring sweep order

Scene Traversal

Voxel coloring camera positions

Inward-looking

Cameras above scene

Outward-looking

Cameras inside scene

Seitz

Image acquisition

•Calibrated Turntable

•360° rotation (21 images)

Selected Dinosaur Images

Selected Flower Images

Voxel coloring results

Dinosaur Reconstruction

72 K voxels colored 7.6 M voxels tested

7 min. to compute on a 250MHz SGI

Flower Reconstruction

70 K voxels colored 7.6 M voxels tested

7 min. to compute on a 250MHz SGI

Space carving

Image 1 Image N

…...

Initialize to a volume V containing the true scene

Repeat until convergence

Choose a voxel on the current surface Carve if not photo-consistent

Project to visible input images

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

Multi-pass plane sweep

Multi-pass plane sweep

Input image (1 of 45) Reconstruction

Reconstruction Reconstruction

Space carving results: African violet

Input image (1 of 100)

Reconstruction

Space carving results: hand

Active approaches

Time of flight

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

t c

r  

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

Digital Michelangelo Project

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

Cyberware

face and hand full body

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

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

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

The BRDF

• The Bidirectional Reflection Distribution Function

– Given an incoming ray and outgoing ray

what proportion of the incoming light is reflected along outg oing ray?

surface normal



(l,v) (l n)

I   

Diffuse reflection (Lambertian)

kd

v l, ) 

( albedo

Assuming that light strength is 1.

Photometric stereo

N

L₁ L₂ V L₃

• Can write this as a matrix equation:

Solving the equations

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_d as before

Photometric Stereo Setup

Procedure

• Calibrate camera

• Calibrate light directions/intensities

• Photographing objects (HDR recommended)

• Estimate normals

• Estimate depth

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

Depth from normals

Results

Limitations

• Big problems

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

– 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

same surface normal

“Orientation consistency”

Virtual views

Velvet

Virtual Views

Brushed Fur

Virtual Views

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 Model Acquisition Pipeline

View Planning View Planning

3D Scanner 3D Scanner

3D Model Acquisition Pipeline

Alignment Alignment View Planning

View Planning

3D Scanner 3D Scanner

3D Model Acquisition Pipeline

3D Scanner 3D Scanner

Alignment Alignment

Merging Merging View Planning

View Planning

Volumetric reconstruction

Signed distance function

Results

The Digital Michelangelo Project

• Goal: scan 10 sculptures by Michelangelo

• High-resolution (“quarter-millimeter”) geometr y

• Stanford University, led by Marc Levoy

Systems, projects and applica

tions

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

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 Ikeuchi

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)

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 r endering farm full-time for about a year just for rendering

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

Hybrid stereo camera

Live-action sequence

Hybrid input

left

right

Hybrid input

left

right

left

Combine multiple hires to lores

Results

View interpolation

Bullet time video

View interpolation

High-quality video view interpolation