volume calibration process.txt

Volume & camera calibration.
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Build 2D markers.
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- Undistort with pre calibrated K, D(k1, k2, p1, p2).
- Clip to view bounds. (Maybe not required? - depends on distortion issues).


Phase 1 - Build rough extrinsic parameters.
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- For each camera & root camera pair:
	- Find corresponding points.
		- Look for frames that have a single 2D marker across all cameras and assume a match. 
			(Closest point match should remove outliers)	
	- Find fundamental matrix using Levenberg-Marquardt.
	- Epiline errors may be useful to minimize sync video error.
	- Essential matrix = Kt * fMat * K.
	- Recover R,t for second camera in pair relative to first.
		- Uses faux focal length and principal point.
		- t is unit vector, needs to be scaled.
	- Calculate camera matrices.
	- Pairwise triangulate 3D markers.
	- Build scale value by comparing 3D markers to root pair markers.
	- Scale t by scale value.
	- Calculate camera matrices.

- Output:  Need R, t - relative to world 0,0,0 (Root camera).


Phase 2 - Create refined extrinsic & intrinsic parameters.
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- Inputs: K, R, t, D(k1, k2, p1, p2)
- Bundle adjust.
- Outputs: K', R', t', D(k1, k2, p1, p2)'


Calculate camera matrices.
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- Inputs: K, R, t

Cw (Camera world matrix) = [R|(-Rt * t)]
Pu (Camera unit projection matrix) = [R|t]
P (Camera projection matrix) = K[R|t]


Build 3D markers.
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Assumes no distortion.

- Inputs: K, W

- Build 2D marker rays in world space.
	- CSR(camera space ray direction) = Kinv[vec3(undistorted point pixel coords,1)]
	- WSR(world space ray direction) = W * vec4(CSR,0)
	- WSO(world space ray origin) = W * vec4(0,0,0,1)

- Find corresponding rays.
	- A: Match 2D marker rays in undistorted camera space using pixel distance.
		- Project ray into camera space. P projects world to undistorted camspace.
	- B: Match 2D marker rays in world space using world unit distance.

- Find closest point between corresponding rays.