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A question about relation of (K R T H)

asked 2014-01-20 11:55:01 -0500

我干过豪哥 gravatar image

H is homography matrix. R(r1,r2,r3)is a rotation matrix ,t is a translation matrix , k is a intrinsic matrix.I want to get H by R K T,so I use the equation (H = K(R|T).But I want to get the Homography matrix between two 2D images,and I only use r1 r2 just like H = K(r1,r2,T).Is that right?? Thank you for your reply!!

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answered 2014-01-21 03:03:00 -0500

jensenb gravatar image

Yes that is a correct assumption. To understand why, recall that a homography is an arbitrary linear mapping between two planes, in your case between a world plane and the image plane. The pinhole camera model specifies the projection of arbitrary 3d world points as

image description

A homography requires that the world points lie on a plane, adding an additional constraint to the projection equation above. Because the absolute position of the camera and plane in world coordinates is not relevant for the projection, only their relative pose to each other (specified by R and t), we can arbitrarily require that the 3d world points lie on the X-Y world plane (Z=0) without any loss of generality. This simplifies the projection equation down to

image description

This is the trick used by Zhang as part of his flexible camera calibration technique (used by OpenCV) for example.

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Thanks,Bro! I got Homography matrix like above.But I use the K,R refined Bundleadjuster in opencv stitch module to calculate Homography matrix.For example, I have four pic(P1,P2,P3,P4) to stitch a panorama,so I will calculate four H(H1,H2,H3,H4)correspoding to(P1 to P4),finally I try to use function warpPespective(H)to map Pic to the final pano instead of function remap(K,R)(opencvStitchmodule use remap to map pics to final pano).I tried to realize that idea this afternoon and failed.So I want to know ,is my idea right?

我干过豪哥 gravatar image我干过豪哥 ( 2014-01-21 05:53:52 -0500 )edit

I'm not so familiar with the stitching module, so this is just a guess, but the docs say that the rotations and translations are estimated pairwise between the images, so maybe you are applying the Homography between the wrong pairs, or in the wrong order?

jensenb gravatar imagejensenb ( 2014-01-21 07:14:45 -0500 )edit

I choose pairwise points manually instead of surf features.My purpose is that using Homography matrix to map the pics on the final pano instead of warp the image by K and R.And I have get a good final panorama by stitch moudle order.So I want to know ,is the idea"use homograph matrix to map pic insteadof stitch module" right?

我干过豪哥 gravatar image我干过豪哥 ( 2014-01-21 08:28:49 -0500 )edit
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Asked: 2014-01-20 11:55:01 -0500

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Last updated: Jan 21 '14