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Introduction to Structured Light (SL) Systems and SL Based Phase Unwrapping R. Garcia & A. Zakhor EECS Department UC Berkeley www-video.eecs.berkeley.edu/research

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Outline Background Structured Light Basics Phase Unwrapping Our Algorithms Results Summary

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Determining Depth of a Scene Many applications: – Biomedical – Industrial – Entertainment – Navigation Methods for Determining Depth – Triangulation – Time of flight – Depth from (de)focus – Other… 3

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Triangulation Based Depth Methods Scene observed from multiple views Correspondences between views solved Must know intrinsic and extrinsic parameters for each view Two categories – Passive: Stereo – multiple cameras – Active: Structured Light – camera with projector or other light source used [S. Narasimhan] 4 IJ Cam IJ ProjectorCam

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Traditional Stereo Need 2 or more views of the scene Scene texture used to identify correspondences across views Dense stereo remains an active research area in computer vision – Algorithms and new Middlebury vision Given rectified images, triangulation is simple Using similar triangles: [Mirmehdi] 5

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Potential Problem with Stereo Stereo works well on “textured” images

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Potential Problem with Stereo Stereo can fail with lack of texture ? ?

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Structured Light (SL) SL places “texture” onto the scene Projector patterns identify each scene region Classes of patterns – Temporal – Spatial – Other Survey of patterns [J. Salvi et al., 2004] 8

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Temporal Coding Multiple frames are projected to identify scene regions Camera pixel’s intensity change used for correspondence Scene assumed to be static 9

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Encodes unique information into small regions. Fewer captures Less dense reconstruction Spatial Coding 10

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Spatial Coding Recognize this?

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Other Coding Methods Spacetime Coding – Zhang et al., “Spacetime Stereo: Shape Recovery for Dynamic Scenes”, 2003 – Davis et al., “Spacetime Stereo: A Unifying Framework for Depth from Triangulation”, 2003 Viewpoint Coding – Young et al., “Viewpoint-Coded Structured Light”,

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Structured Light v. Stereo Advantages of SL: – SL does not require a richly textured scene – Solving correspondences is not expensive – Each scene point scene receives a unique code Advantages of Stereo: – No interference with observed scene – Only need acquisitions at one time for capture; SL often needs multiple images – Too much texture can be problematic for SL. 13

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Outline Background Structured Light Basics Phase Unwrapping Our Algorithms Results Summary

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Structured Light Geometry Geometry of SL is simple Triangulation performed by ray-plane intersection Intrinsic and extrinsic parameters needed – Calibration matrix for camera and projector – Transformation between coordinate frame of camera and projector

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Triangulation Left Cam Projector 16 Intrinsic and extrinsic parameters

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Triangulation Left Cam Projector 17

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SL for Dynamic Scene Capture SL capable of capturing dynamic scenes Want to limit capture time when capturing dynamic scenes “One-shot” approaches require single capture Trade-off – Fewer frames -> lower capture resolution – More frames -> more sensitive to scene motion 18

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Overview of Phase Shifted Structured Light (SL) Systems Project patterns to find correspondences between camera and projector Phase shifted sinusoidal patterns: – Fast capture: 3 shots – Simple to decode – Insensitive to blur – Used in optical metrology M periods

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Example: Scene Illuminated with Phase-Shifted Sinusoids I1I1 I3I3 I2I2 Wrapped Phase Unwrapped Phase M periods in sinusoid Need to unwrap phase

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Outline Background Structured Light Basics Phase Unwrapping Our Algorithms Results Summary

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What is Phase Unwrapping? Phase values usually expressed from [-π, π) Would like to recover original continuous phase measurement

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Overview of Phase Unwrapping Unwrapping assumptions: – Single continuous object in scene – Slowly varying depth; discontinuities less than |π| 2D phase unwrapping results in relative phase: – Need absolute phase for triangulation. Wrapped Phase Unwrapped Phase

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Creating Point Cloud

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Stereo-Assisted Phase Unwrapping Stereo assisted phase unwrapping [Wiese 2007]: – Results in absolute phase – Deals with depth discontinuities System Setup: Two cameras, single projector Cam 1 Cam 2 Projector A B C D

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Overview of Phase Unwrapping with two Cameras [Weise et al. 2007] To resolve the absolute phase for a camera pixel: 1.Determine wrapped phase for all pixels in first and second camera 2.Project a ray from pixel in camera 1 with wrapped phase 3.Project M planes from the projector corresponding to in space 4.Find the M intersections of the M planes with the ray in (1) in 3D space, 5.Project onto camera 2 6.Compare the M phase values at M pixel locations in camera 2 to the and choose the closest 26..

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Stereo Phase Unwrapping [Weise et. al. 2007] Left Cam Right Cam Projector 27

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Drawbacks of Stereo Phase Unwrapping Must be run twice. Possible to incorrectly assign absolute phase values to corresponding points between views. P A B C D Left CameraRight Camera 28

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Comparison of Stereo Assisted Phase Unwrapping with Merging Stereo and 3D (x,y,t)

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Temporal Inconsistencies Consecutive phase images highly correlated Correlated information not used during phase unwrapping Results in inconsistent unwrapping

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3D Phase Unwrapping Multi-dimensional phase unwrapping – 2D: traditional image processing – 3D: medical imaging (i.e. MRI)

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Overview of 3D (x,y,t) Phase Unwrapping Treat consecutive phase images as volume of phase values Edges defined between neighboring pixels Quality assigned to each pixel Inversely proportional to spatio-temporal second derivative Want to unwrap according to quality of edges

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3D Phase Unwrapping (cont.) Evaluate edges in a 3D volume from highest quality to lowest Evaluating edge = unwrapping pixels connected to it Unwrapped pixels connected in chains Grow the chain by adding pixels/edges in x, y, and t Chains merged together

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Outline Background Structured Light Basics Phase Unwrapping Our Algorithms Results Summary

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Consistent Stereo-Assisted Phase- Unwrapping Methods for Structured Light Systems

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Merging Stereo & 3D (x,y,t) Phase Unwrapping Goal: Solve for absolute phase offset of a chain by using stereo matching data. Approach: use quality to find phase offset probabilistically M periods in the sinusoidal pattern M possible phase offsets Find offset probability for each pixel in the chain, then combine them to find phase offset for the whole chain How to find phase offset for a pixel P: Use phase difference between wrapped phase at P and its corresponding M projected pixels to generate likelihood of each of the M phase offset values.

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Computing Phase Offset for an Entire Chain Combine offset probabilities for each pixel in the chain to determine phase offset for the whole chain Pixels in the same period Pixels in different periods

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Comparison with 3D (x,y,t) only Proposed 3D (x,y,t) Handling multiple disjoint objects Proposed algorithm avoids unwrapping low quality pixels by using stereo

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Comparison with Stereo Only Stereo Only Proposed Consecutive unwrapped phase frames and their difference

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Comparison of Stereo Assisted Phase Unwrapping with Merging Stereo and 3D (x,y,t)

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Stereo Phase Unwrapping [Weise et. al. 2007] Left Cam Right Cam Projector 41

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Proposed Method Perform unwrapping w.r.t. projector pixels rather than camera pixels Left Cam Right Cam Projector 42

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Overview of the proposed Method For each projector pixel with phase, find the corresponding epipolar line in each image. For each camera, find all points along the epipolar line with phase Find the 3D point in space resulting from intersection of rays resulting from these points with the plane for the projector: – N 1 points in 3D space for the left camera 1 A i – N 2 points in 3D space for the right camera 2 B i Find the corresponding pair of A i and B i closest in 3D space Assign global phase to corresponding pixels of the “best” pair of the two cameras Camera 1 Camera 2 43

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Projector Domain Stereo Method Left Cam Right Cam Projector 44 Top down view of the projector plane corresponding to the projector column with absolute phase theta

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Finding corresponding “pair” of points in 3D from the two cameras Compute pairwise distance for all pairs of points in the two views. The distance between the 3D locations of corresponding points is small. Compute possible correspondences for each projector pixel. Find the correct correspondence labeling for each projector pixel. – Use loopy belief propagation (LBP) B1B1 B2B2 A1A1 A2A2 A3A3 Distance B1B1 B2B2 A1A1 {A 1,B 1 }{A 1,B 2 } A2A2 {A 2,B 1 }{A 2,B 2 } A3A3 {A 3,B 1 }{A 3,B 2 } Possible Labels

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Loopy Belief Propagation Cost Function Minimize cost function: where: Labeling for projector image Set of projector pixels Projector pixel Locations of pixels in Cam A & B 3D distance cost threshold 3D location of image pixel 2D location of image pixel 4- connected pixel neighborhood 2D distance cost threshold 46

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Local Phase Unwrapping for Remaining Pixels Occluded pixels: – Corresponding pair are too far apart in 3D space – Use quality based local unwrapping Unwrapping order for remaining pixels depends on: – Density of stereo unwrapped points – Local derivatives Merge pixel density and derivative maps to generate quality map Unwrap from highest to lowest quality. Camera Points Computed via LBP 47 DensityLocal Derivative Merged

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Results Right Camera Proposed 48 Proposed method results in consistent phase results across cameras In a 700 frame sequence, our method: Has same accuracy in 80% of frames Has better than or equal accuracy in 96% of frames. Left Camera Proposed Left Camera [Weise et. al.]

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Results: Captured Dynamic Scene 49

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Dynamic Point Cloud

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Advantages of Projector Domain Unwrapping Only scene points illuminated by the projector can be reconstructed Unwrapping only needs to be performed once for any # of cameras more consistent and efficient. Computational complexity scales with projector resolution rather than image resolution. 51

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Conclusion Provided introduction to the structured light systems Presented two phase unwrapping algorithms: – A three-dimensional stereo-assisted phase unwrapping method – A projector-centric stereo-assisted unwrapping method Results in accurate, consistent phase maps across both views. Results in accurate 3D point clouds 52

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