5Deviations from Recommeded Setup Cause distortionsMild deviations may cause mild distortions, oftenly referred to as “keystone effect”
6Basic 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.
7Problem Solved?“Keystone Correction” features in projectors does not overcome all distortions.Some distortions might be caused by extreme conditions of projector placement.
8Projection 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
9Approaches to Get 3D Information Rectified Calibrated Stereo (two cameras)Determine calibration values for:ProjectorCameraEach of the above can give enough information for us to correct the distorted image
10However, We Need to Also Know Intrinsic ParametersFocal lengthPrincipal pointLens distortionExtrinsic ParametersTranslationRotationNote: 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)
11Chosen Approach - Homography Popular in image and video analysisOffers a simpler approach for planar-to-planar projection problems
12Using HomographyA point (x1,y1) is projected from one plane to another point (x2,y2)x1,y1x2,y2We represent these points in homogenous coordinates
13Using HomographyIn homogenous coordinates we get the following pinhole model
14Using Homography Solving an 8-DOF system Applying properties of homogenous representation where z=0 in points on planars, we get:1Solving an 8-DOF system
16StepsGet 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
17Raised Issues The model is a good approximation Some factors are added but are not considered in the model:Projector and webcam’s native distortionsIn practice, we need to improve the process, for more flexibility.
18ImprovementProject a chessboard pattern: 6x8 squares (5x7 inner corners)Detects 35 corresponding pointsScale-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
19Setup and Results -Laptop Computer -Webcam -Pico Projector -Program using OpenCV library (Linux OS)