1. By: Mohammad Qudeisat Supervisor: Dr. Francis Lilley
Validation of Fringe-Projection Measurements Using Inverse Fringe Projection
By: Mohammad Qudeisat
Supervisor: Dr. Francis Lilley

2. 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

3. 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.

4. 3D Shape Measurement using Fringe Projection
Step 1: Generate a straight fringe pattern
Step 2: Project the fringe pattern on the object.

5. 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”.

6. 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.

7. 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.

8. Inverse-Fringe Projection – The Idea
From This
We generate and project this

9. Inverse-Fringe Projection – The Idea
We want to capture something like this
And we practically capture this image

10. 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

11. 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.

12. 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.

13. 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

14. Camera – Projector Mapping – Horizontal Correspondence
Projected
Grabbed (Camera)

15. 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, ) in the projector
We repeat the procedure for all camera pixels to get a complete correspondence between camera and projector pixels.

16. Step 2: Defining the wanted-fringe image
The easiest step: Normally, we want to capture a straight fringe pattern
Something similar to this image

17. 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

18. Step 4: Using the Inverse-Fringe image
Project the inverse-fringe image on the object
Capture the image using the camera

19. 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.

20. Calculating the phase-error map
So we will calculate the phase difference between these two images

21. Calculating the phase-error map
And the result is:

22. Another Example with a major error
Depth map
Captured inverse-fringe image

23. Another Example with major error
Error phase-map

24. 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.

25. 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.

26. Thank You
Thank You for Listening.