Photogrammetric approach

[Björn Piltz]

Hi,

First of all, thank you for a beautiful piece of software. I'm using ceres for classical BA with calibrated cameras supported by GPS/INS and GCPs and have a couple of questions:

I have modeled the following cost functions, returning their residuals as mahalanobis distances.

* A reprojection error relating a camera position, camera orientation and 3D point to an image observation.

* A GPS error relating a camera position to a GPS observation (pos and stddev)

* A GCP error relating a 3D point to a ground control point.

Now, when I throw this into ceres I get sensible results with good performance, but I have the following questions:

1. I additionally want to add a cost function relating the camera orientation to the INS reading (angles and stddev), but I can't think of a way to formulate a differentiable function.

2. How can I measure the quality of the result(beyond reprojection error)? Since I have the standard deviation of all measurements  going in, I would ideally like to have the standard deviation(xyz or covariances) of all results - i.e. camera positions, orientations and reconstructed points. Is there a standard way to propagate covariances?

I am thankful for any answer pointing me in the right direction

Regards,

Björn

[Sameer Agarwal]

Hi Bjorn,

 

Now, when I throw this into ceres I get sensible results with good performance, but I have the following questions:

1. I additionally want to add a cost function relating the camera orientation to the INS reading (angles and stddev), but I can't think of a way to formulate a differentiable function.

I am not sure I understand the barrier here. If you can do it for the position using GPS, why can't you do it for the orientation?

 

2. How can I measure the quality of the result(beyond reprojection error)? Since I have the standard deviation of all measurements  going in, I would ideally like to have the standard deviation(xyz or covariances) of all results - i.e. camera positions, orientations and reconstructed points. Is there a standard way to propagate covariances?

Yes you can estimate the covariance of the solution

http://homes.cs.washington.edu/~sagarwal/ceres-solver/dev/solving.html#covariance-estimation

Sameer

 

I am thankful for any answer pointing me in the right direction

Regards,

Björn

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[Björn Piltz]

2014-03-26 13:45 GMT+01:00 Sameer Agarwal <sameer...@google.com>:

I am not sure I understand the barrier here. If you can do it for the position using GPS, why can't you do it for the orientation? 

 Because right now, I'm using euler angles, and I need to perform a modulo on the difference. I'm also not quite sure how it would work for quaternions.

Thanks

[Sameer Agarwal]

Don't use euler angles:). They are a pain in the butt. Use a quaternion/angle-axis representation for your rotations.

Sameer

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[Björn Piltz]

Hi Sameer,

I'm having moderate success using the Covariance interface. It works well enough for small problems, but when I try a real size problem then calculating of the covariance takes much much longer than the actual bundle adjustment.(6 seconds vs more than half an hour).

This is the scope of the problem:

2.000 images

15.000 3D points

200.000 image points

When I try to retrieve the covariances for the 3D points I call Compute() with:

15.000 covariance blocks (out of 19.000)

Jacobian(400.000x60.000)

nnz 150.000

The time consuming part is that cholmod_solve2() gets called 60.000 times.(QR doesn't seem much faster)

Is this as it should be, or do I seem to be doing something wrong?

Björn

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[Sameer Agarwal]

Hi Bjorn,

Are you using OpenMP/threading?

half an hour seems excessive.

Sameer

[Björn Piltz]

I didn't time it exactly, but yes, even with 8 openMP threads and my laptop melting it's somewhere in that range. It's not a show stopper for me, but I was a bit surprised that that would be the bottleneck.

I was hoping to tweak it somehow. 

Björn

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[Sameer Agarwal]

So cholmod_solve2 calls are made to get one row of the covariance matrix at a time.

I am guessing you are solving for homogenous 3d points? which is why you are making 60k calls to cholmod_solve2.

I'd like the performance of the covariance estimator to be better. Please file a bug against me on the bug tracker, I will look into this. 

Sameer

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[Björn Piltz]

So cholmod_solve2 calls are made to get one row of the covariance matrix at a time.

Yes. 

I am guessing you are solving for homogenous 3d points? which is why you are making 60k calls to cholmod_solve2.

No, I'm using Cartesian coordinates. 

I'd like the performance of the covariance estimator to be better. Please file a bug against me on the bug tracker, I will look into this. 

I will. Thanks!

Björn

On Tue, Apr 1, 2014 at 8:43 AM, Björn Piltz <bjorn...@blikken.de> wrote:

I didn't time it exactly, but yes, even with 8 openMP threads and my laptop melting it's somewhere in that range. It's not a show stopper for me, but I was a bit surprised that that would be the bottleneck.

I was hoping to tweak it somehow. 

Björn

2014-04-01 17:27 GMT+02:00 Sameer Agarwal <sameer...@google.com>:

Hi Bjorn,

Are you using OpenMP/threading?

half an hour seems excessive.

Sameer

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[Sameer Agarwal]

hmm, can you show me your calling code then.

Sameer

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