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Correcting Projector Distortions on Planar Screens via Homography. Daniel Hirt. Projector Devices Today. More affordable Smaller Some are even low-cost and compact. A Common Setup of a Projector Device. Mounted on ceiling. Another Common Setup. Placed on table. - PowerPoint PPT Presentation
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Correcting Projector Distortions on Planar Screens via Homography
Daniel Hirt
Projector Devices Today
• More affordable• Smaller• Some are even low-cost and compact
A Common Setup of a Projector Device
Mounted on ceiling
Another Common Setup
Placed on table
• Cause distortions• Mild deviations may cause mild distortions,
oftenly referred to as “keystone effect”
Deviations from Recommeded Setup
Basic Distortion Correction
• Most projectors offer a limited range of methods to correct a distorted image.
• Usually only “keystone correction” is available, and require manual operation.
Problem Solved?
• “Keystone Correction” features in projectors does not overcome all distortions.
• Some distortions might be caused by extreme conditions of projector placement.
Projection Correction On Planar Screens
• Recall the perspective projection formula, give a 3D point (x,y,z).
• We can use this to correct our image, but...• We do not have any 3D information
Approaches to Get 3D Information
• Rectified Calibrated Stereo (two cameras)• Determine calibration values for:– Projector– Camera
• Each of the above can give enough information for us to correct the distorted image
However, We Need to Also Know
• Intrinsic Parameters– Focal length– Principal point– Lens distortion
• Extrinsic Parameters– Translation– Rotation
Note: not all are actually required to be able to get a correction, but we need to have most for each of the participants (camera, projector)
Chosen Approach - Homography
• Popular in image and video analysis• Offers a simpler approach for planar-to-planar
projection problems
Using Homography
• A point (x1,y1) is projected from one plane to another point (x2,y2)
x1,y1
x2,y2
• We represent these points in homogenous coordinates
Using Homography
• In homogenous coordinates we get the following pinhole model
Using Homography
• Applying properties of homogenous representation where z=0 in points on planars, we get:
1
Solving an 8-DOF system
Method and Setup
Steps
• Get at least 4 correspondence points (usually the four corners) to solve 8-DOF system.
• Solve the homography matrix from corresponding points in captured projected image (webcam) to reference straight image.
• Apply persepective warp: H*(reference image)– “pre-warping”
• Re-project the pre-warped image
Raised Issues
The model is a good approximation• Some factors are added but are not
considered in the model:– Projector and webcam’s native distortions
• In practice, we need to improve the process, for more flexibility.
Improvement
• Project a chessboard pattern: 6x8 squares (5x7 inner corners)
• Detects 35 corresponding points• Scale-down the reference image to
approximate to the size of the captured image (factor of resize: diagonals on inner corners)
• Solves the Homography using RANSAC with the 35 sample points
Setup and Results
-Laptop Computer-Webcam-Pico Projector-Program using OpenCV 2.4.3 library (Linux OS)
Results
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