Validation of Fringe-Projection Measurements Using Inverse Fringe Projection

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Validation of Fringe-Projection Measurements
Using Inverse Fringe Projection

• By Mohammad Qudeisat
• Supervisor Dr. Francis Lilley

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Headlines

• Introduction
• Problem Statement
• Inverse Fringe Projection
• Introduction to the idea
• Camera-Projector mapping
• Generating and using the inverse fringe image
• Calculating errors in the object phase-map
• Summary
• Future Work

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Introduction

• 3D shape measurement is a very common problem and
  has many applications.
• One common approach for 3D shape measurement is
  using fringe-projection.
• Basically, a straight fringe pattern is projected
  on the object and then captured by a camera.
• The object shape deforms the fringe pattern.
• We analyze deformations in the fringe pattern to
  calculate the depth map of the object.

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3D Shape Measurement using Fringe Projection

• Step 1 Generate a straight fringe pattern
• Step 2 Project the fringe pattern on the object.

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3D Shape Measurement using Fringe Projection contd

• Step 3 Calculate the phase map.
• Step 4 Use the phase map to obtain the depth
  map through a process that relates phase changes
  to depth changes, called System Calibration.

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Problem Statement

• Fringe projection measurements can contain errors
  (noise, sharp edges, ripples, etc).
• We need a way by which we can validate our
  measurements.
• Repeating the measurement will not produce very
  different results.
• Measuring the object shape with a different
  device can be a solution, but it produces a
  different perspective of the object shape
  Complexity, Cost and Completeness.
• We need to validate our measurements using the
  same devices used in the measurement process.

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Inverse-Fringe Projection The Idea

• To measure an object, we project a straight
  fringe pattern on the object and capture a
  deformed fringe pattern and use it to calculate
  the phase map.
• Inverse-Fringe Projection method reverses the
  whole operation.
• From the phase map obtained in step 1, we
  generate a deformed fringe pattern such that when
  projected on the object it produces a straight
  fringe pattern on the camera.

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Inverse-Fringe Projection The Idea
From This
We generate and project this
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Inverse-Fringe Projection The Idea
We want to capture something like this
And we practically capture this image
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Measurement Validation steps using Inverse-Fringe
Projection

• Camera-Projector Mapping
• Defining the wanted camera image
• Generating and projecting the Inverse-Fringe
  pattern
• Capturing the fringe image using the camera
• Calculating the phase-error map, that is, the
  phase difference between the wanted and the
  captured phase maps

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Step 1 Camera-Projector mapping

• For each pixel in the camera, we need to find the
  corresponding pixel(s) in the projector in
  sub-pixel accuracy.

This is how camera pixels see projector pixels.
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Camera-Projector mapping

• How to find the projector pixel (or location)
  pp(i,j) that corresponds to camera pixel pc(l,m)?
• Idea Project horizontal and vertical fringe
  patterns and calculate the phase-map for both the
  projected and the captured patterns.
• Camera and projector pixels that have equal
  horizontal and vertical phase values correspond
  to each other.

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Camera-Projector mapping (Procedure)

• Project and grab a horizontal fringe pattern
• Project and grab vertical fringe pattern
• Calculate the horizontal and vertical phase maps
  for the camera and the projector
• For each pixel in the camera, find the
  corresponding pixel(s) in the projector by
  matching the horizontal and vertical phase values
  in the camera image with their counterparts in
  the projector image, use interpolation for
  sub-pixel accuracy
• Now we have a map that relates camera pixels to
  projector pixels

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Camera Projector Mapping Horizontal
Correspondence
Projected
Grabbed (Camera)
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Camera-Projector mapping (Procedure) - Example

• For camera pixel (100,100)
• Horizontal phase value 50.71
• Vertical phase value 36.94
• We search projector phase maps
• Horizontal phase map
• Pixels (, 123), (,124) have phase values
  50.20, 50.83
• Vertical Phase map
• Pixels (270, ), (271, ) have phase values
  36.75, 37.44
• Using linear interpolation we find that pixel
  (100,100) in the camera corresponds to pixel
  (270.34, 123.871) in the projector
• We repeat the procedure for all camera pixels to
  get a complete correspondence between camera and
  projector pixels.

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Step 2 Defining the wanted-fringe image

• The easiest step Normally, we want to capture a
  straight fringe pattern

Something similar to this image
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Step 3 Generating the inverse-fringe image

• The inverse fringe image is a function of both
  the camera-projector mapping and the wanted
  fringe image.
• Iinv Iwl(i,j), m(i,j)
• For each pixel in the projected image pp(i,j)
  find the (supposed-to-be) corresponding camera
  pixel pc(l,m) from the Camera-Projector mapping
  with sub-pixel accuracy
• Fill the projector pixel pp(i,j) with the
  intensity value of the wanted camera image at
  pixel pc(l,m)
• Repeat the operation for all projector pixels
  that are in the view of the camera

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Step 4 Using the Inverse-Fringe image

• Project the inverse-fringe image on the object
• Capture the image using the camera

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Step 5 Calculating the phase-error map

• Ideally, the projected inverse-fringe image will
  be captured as a completely straight fringe
  pattern
• In practice, there are always various types of
  errors
• These errors originate from the object phase map
  and propagate to the Camera-Projector mapping
• Errors in the mapping result in an inverse fringe
  image that does NOT produce a 100 straight
  fringe image on the camera
• To calculate the phase-error map, simply
  calculate the difference between the wanted
  inverse fringe image and the captured inverse
  fringe image.

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Calculating the phase-error map

• So we will calculate the phase difference between
  these two images

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Calculating the phase-error map

• And the result is

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Another Example with a major error
Depth map
Captured inverse-fringe image
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Another Example with major error
Error phase-map
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Summary

• A measurement validation method using
  inverse-fringe projection technique was proposed.
• This method is simple, accurate and does not need
  any additional hardware.
• Using this method, phase-map errors can be
  detected and quantitatively measured.

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Future Work

• Currently, the method can quantitatively measure
  errors in the phase map.
• We aim to achieve a quantitative measure of
  errors in the depth map.
• Currently, this method can only detect errors.
• We aim to have the ability to correct errors.
• I am also working on reducing the computational
  complexity of the algorithm to be used in our
  real-time fringe-projection measurement system.

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Thank You

• Thank You for Listening.