Presentation on theme: "Zhengyou Zhang Vision Technology Group Microsoft Research"— Presentation transcript:
1Zhengyou Zhang Vision Technology Group Microsoft Research Flexible Camera Calibration by Viewing a Plane from Unknown OrientationsZhengyou ZhangVision Technology GroupMicrosoft 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 StatementDetermine the characteristics of a camera (focal length, aspect ratio, principal point) from visual information (images)
3MotivationsRecovery of 3D Euclidean structure from images is essential for many applications.This requires camera calibration.Look for a flexible and robust technique, suitable for desktop vision systems.(such that it can be used by the general public)Examples include:virtual world navigation. We are familiar with Euclidean world. If we don’t know the camera internal parameters, we can at best obtain projective structure. It would need a lot of training for human being to navigate successfully in a projective world.Vision-based user interface. How far is the person from the screen? Where is s/he looking at?Product advertisement. An on-line customer would prefer to check the exact Euclidean shape, rather than projective distorted one.
4Classical Approach (Photogrammetry) Use precisely known 3D pointsDecision theory group focuses on solving problems with probability and decision theory. Focus is on making application of these methods practical. Related methods, approximations, heuristics from AI, OR, Statistics, Economics are applied as needed. Groups’s work typically motivated by real-world problems, e.g., those posed by MS product and systems groups.Known displacementShortcomings: Not flexiblevery expensive to make such a calibration apparatus.3
5Futuristic Approach (Self-calibration) Move the camera in a static environmentmatch feature points across imagesmake use of rigidity constraintDecision theory group focuses on solving problems with probability and decision theory. Focus is on making application of these methods practical. Related methods, approximations, heuristics from AI, OR, Statistics, Economics are applied as needed. Groups’s work typically motivated by real-world problems, e.g., those posed by MS product and systems groups.Shortcoming: Not always reliabletoo many parameters to estimate3
6Realistic Approach (my new method) Use only one planePrint a pattern on a paperAttach the paper on a planar surfaceShow the plane freely a few times to the cameraAdvantages:Flexible!Robust?Yes. See RESULTS
8Plane projection For convenience, assume the plane at z = 0. mThe relation between image points and model points is then given by:with
9What do we get from one image? We can obtain two equations in 6 intermediate homogeneous parameters.Given H, which is defined up to a scale factor,And let, we haveThis yields
10Geometric interpretation Plane at infinityAbsolute conicC
11Linear Equations Let symmetric Define up to a scale factor Rewrite as linear equations:symmetric
12What do we get from 2 images? If we impose = 0, which is usually the case with modern cameras, we can solve all the other camera intrinsic parameters.How about more images?Better! More constraints than unknowns.
13Solution Show the plane under n different orientations (n > 1) Estimate the n homography matrices(analytic solution followed by MLE)Solve analytically the 6 intermediate parameters (defined up to a scale factor)Extract the five intrinsic parametersCompute the extrinsic parametersRefine all parameters with MLE
27ConclusionWe have developed a flexible and robust technique for camera calibration.Analytical solution exists.MLE improves the analytical solution.We need at least two images if c = 0.We can use as many images of the plane as possible to improve the accuracy.
28It really works!Currently used routinely in both Vision and Graphics Groups.Binary executable will be distributed on the Web to the public soon.Source code will also be made available.