Presentation on theme: "Correcting Projector Distortions on Planar Screens via Homography Daniel Hirt."— Presentation transcript:
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 library (Linux OS)