Decompose Homography into Rotation matrix & Translation vector

HomographyDecomposition.as

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;
}

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

R = U * vT

or something else?
Thanks

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/

Hi,can i compute homography using rotation and translation?

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

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