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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

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

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.

3D Shape Measurement using Fringe Projection

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

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”.

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.

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.

Inverse-Fringe Projection – The Idea

We want to capture something like this

And we practically capture this image

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

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.

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.

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

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.

Step 2: Defining the wanted-fringe image

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

Something similar to this image

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 = Iw[l(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

Step 4: Using the Inverse-Fringe image

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

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.

Calculating the phase-error map

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

Calculating the phase-error map

- And the result is:

Another Example with major error

Error phase-map

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.

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.

Thank You

Thank You for Listening.

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