Presentation on theme: "Image Rectification for Stereo Vision"— Presentation transcript:
1 Image Rectification for Stereo Vision Charles LoopZhengyou ZhangMicrosoft ResearchPlease remind the audience that this is all completely confidential. We are in the midst of the patent process and certainly do not want to jeopardize that effort in any way.1
2 Problem Statement rectification Compute a pair of 2D projective transforms (homographies)rectificationOriginal imagesRectified images
3 Motivations To simplify stereo matching: Instead of comparing pixels on skew lines, we now only compare pixels on the same scan lines.Graphics applications: view morphingProblem:Rectifying homographies are not uniqueGoal: to develop a technique based ongeometrically well-defined criteria minimizing image distortion due to rectification
4 Epipolar Geometry Epipoles anywhere Epipole at Fundamental matrix CC’Epipoles anywhereFundamental matrixF: a 3x3 rank-2 matrixEpipole atFundamental matrix
5 Stereo Image Rectification Compute H and H’ such thatCompute rectified image points:Problem:H and H’ are not unique.
6 Properties of H and H’ (I) Consider each row of H and H’ as a line:Recall: both e and e’ are sent to [1 0 0]TObservations (I):v and w must go through the epipole ev’ and w’ must go through the epipole e’u and u’ are irrelevant to rectification
7 Properties of H and H’ (II) Observation (II):Lines v and v’, and lines w and w’ must be corresponding epipolar lines.Observation (III):Lines w and w’ define the rectifying plane.
8 Decomposition of H Special projective transform: Similarity transform: Shearing transform:
9 Special Projective Transform (I) Sends the epipole to infinityepipolar lines become parallelCaptures all image distortion due to projective transformationSubgoal: Make Hp as affine as possible.
10 Special Projective Transform (II) How to do it?Let original image point bethe transformed point will beObservation:If all weights are equal, then there is no distortion.Key idea:minimize the variation of wi over all pixelswith weight
11 Similarity TransformRotate and translate images such that the epipolar lines are horizontally aligned.Images are now rectified.
12 Shearing TransformFree to scale and translate in the horizontal direction.Subgoal:Preserve original image resolution as close as possible.