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Decompose Homography into Rotation matrix & Translation vector
var intrinsic:Vector.<Number> = new Vector.<Number>(9, true);
var intrinsicInverse:Vector.<Number> = new Vector.<Number>(9, true);
var R:Vector.<Number> = new Vector.<Number>( 9, true );
var t:Vector.<Number> = new Vector.<Number>( 3, true );
// SVD routine
var svd:SVD = new SVD();
// input homography[9] - 3x3 Matrix
// please note that homography should be computed
// using centered object/reference points coordinates
// for example coords from [0, 0], [320, 0], [320, 240], [0, 240]
// should be converted to [-160, -120], [160, -120], [160, 120], [-160, 120]
function computePose(homography:Vector.<Number>):Boolean
{
var h1:Vector.<Number> = Vector.<Number>([homography[0], homography[3], homography[6]]);
var h2:Vector.<Number> = Vector.<Number>([homography[1], homography[4], homography[7]]);
var h3:Vector.<Number> = Vector.<Number>([homography[2], homography[5], homography[8]]);
var invH1:Vector.<Number> = new Vector.<Number>(3, true);
var invC:Vector.<Number>;
var r1:Vector.<Number> = new Vector.<Number>(3, true);
var r2:Vector.<Number> = new Vector.<Number>(3, true);
var r3:Vector.<Number> = new Vector.<Number>(3, true);
var vT:Vector.<Number> = new Vector.<Number>(9, true);
//
invC = intrinsicInverse.concat();
// matrix multiplication [src1, src2, dst]
multMat(invC, h1, invH1);
var v0:Number = invH1[0];
var v1:Number = invH1[1];
var v2:Number = invH1[2];
var lambda:Number = Math.sqrt( v0 * v0 + v1 * v1 + v2 * v2 );
if (lambda == 0) return false;
lambda = 1.0 / lambda;
invC[0] *= lambda;
invC[1] *= lambda;
invC[2] *= lambda;
invC[3] *= lambda;
invC[4] *= lambda;
invC[5] *= lambda;
invC[6] *= lambda;
invC[7] *= lambda;
invC[8] *= lambda;
// Create normalized R1 & R2:
multMat(invC, h1, r1);
multMat(invC, h2, r2);
// Get R3 orthonormal to R1 and R2:
r3[0] = r1[1] * r2[2] - r1[2] * r2[1];
r3[1] = r1[2] * r2[0] - r1[0] * r2[2];
r3[2] = r1[0] * r2[1] - r1[1] * r2[0];
// Put the rotation column vectors in the rotation matrix:
// u can play with flip sign of rows here depending on how u apply 3D matrix
R[0] = r1[0];
R[1] = r2[0];
R[2] = r3[0];
R[3] = r1[1];
R[4] = r2[1];
R[5] = r3[1];
R[6] = r1[2];
R[7] = r2[2];
R[8] = r3[2];
// Calculate Translation Vector T:
multMat(invC, h3, t);
// Transformation of R into - in Frobenius sense - next orthonormal matrix:
svd.decompose( R, 3, 3 );
transposeMat( svd.V, vT );
multMat( svd.U, vT, R );
return true;
}
function setIntrinsicParams(fx:Number, fy:Number, cx:Number, cy:Number):void
{
intrinsic[0] = fx;
intrinsic[4] = fy;
intrinsic[2] = cx;
intrinsic[5] = cy;
intrinsic[8] = 1.0;
//
// Create inverse calibration matrix:
var tau:Number = fx / fy;
intrinsicInverse[0] = 1.0 / (tau*fy);
intrinsicInverse[1] = 0.0;
intrinsicInverse[2] = -cx / (tau*fy);
intrinsicInverse[3] = 0.0;
intrinsicInverse[4] = 1.0 / fy;
intrinsicInverse[5] = -cy / fy;
intrinsicInverse[6] = 0.0;
intrinsicInverse[7] = 0.0;
intrinsicInverse[8] = 1.0;
}
@stephanepechard

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commented Mar 5, 2012

Hi,
I don't get your multMat operation (I don't know ActionScript), is it:

R = U * vT

or something else?
Thanks

@inspirit

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Owner Author

commented Mar 18, 2012

yeah it is just simple matrix multiplication.
the latest source and all methods available at my google code: http://code.google.com/p/in-spirit/

@greydon

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commented Aug 20, 2013

Hi,can i compute homography using rotation and translation?

@Ziyou1987

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commented Sep 8, 2014

Hi, do you know how to decompose the homography matrix to get the surface normal ? Thanks

@wutangyibo

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commented Oct 29, 2017

Hi, I don't understand principle about the code. Is there any document for the code.

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