Presentation on theme: "Image Rectification for Stereo Vision"— Presentation transcript:
1Image 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
2Problem Statement rectification Compute a pair of 2D projective transforms (homographies)rectificationOriginal imagesRectified images
3Motivations 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
4Epipolar Geometry Epipoles anywhere Epipole at Fundamental matrix CC’Epipoles anywhereFundamental matrixF: a 3x3 rank-2 matrixEpipole atFundamental matrix
5Stereo Image Rectification Compute H and H’ such thatCompute rectified image points:Problem:H and H’ are not unique.
6Properties 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
7Properties 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.
8Decomposition of H Special projective transform: Similarity transform: Shearing transform:
9Special Projective Transform (I) Sends the epipole to infinityepipolar lines become parallelCaptures all image distortion due to projective transformationSubgoal: Make Hp as affine as possible.
10Special 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
11Similarity TransformRotate and translate images such that the epipolar lines are horizontally aligned.Images are now rectified.
12Shearing TransformFree to scale and translate in the horizontal direction.Subgoal:Preserve original image resolution as close as possible.