Why does the Jacobian always have onl 6 columns?

Diego Coelho

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Jun 15, 2016, 5:01:00 PM6/15/16

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Hi All

I am studying and trying to modify some Ceres linear system solver routines for bundle adjustment problems. During my investigation, I noticed that every time I call ceres with SPARSE_NORMAL_CHOLESKY option, the Jacobian have only six columns. Why that is happening? The Jacobian is supposed to have as much columns as the number of parameters of the associated minimization problem (usually way more than 6). But it is not clear to me why it is just 6 (both Jacobian columns and parameters).

But if I ran with other option, for example, DENSE_SCHUR, the number of parameters is way more than 6.

Best,

D.

Sameer Agarwal

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Jun 15, 2016, 5:02:58 PM6/15/16

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check to see how many parameters are constant and how many are variable.

This information should be visible in the output of Summary::FullReport.

Guessing from the fact that you are seeing six parameters, I think you are seeing some camera pose estimation problems being solved. OpenMVG solves a number of different optimization problems of different sizes when doing 3d reconstruction. Large bundle adjustment is just one of them.

Sameer

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Diego Coelho

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Jun 15, 2016, 5:23:40 PM6/15/16

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Hi Sameer,

Many thanks. I checked full report. I noticed that every time that ceres execute with SPARSE_NORMAL_CHOLESKY the number of reduced parameters is always 6. For example, in one of the executions I have 5958 parameters, which are reduced to 6. Is it always the case for BA problems with SPARSE_NORMAL_CHOLESKY? See one copy of a part of full report below.

Solver Summary (v 1.12.0-eigen-(3.2.8)-lapack-suitesparse-(4.4.6)-openmp)

Original Reduced

Parameter blocks 1984 1

Parameters 5958 6

Residual blocks 1982 1982

Residual 3964 3964

Minimizer TRUST_REGION

Sparse linear algebra library SUITE_SPARSE

Trust region strategy LEVENBERG_MARQUARDT

Given Used

Linear solver SPARSE_NORMAL_CHOLESKY SPARSE_NORMAL_CHOLESKY

Threads 4 4

Linear solver threads 4 4

Cost:

Initial 1.856405e+04

Final 1.203406e+04

Change 6.529985e+03

Minimizer iterations 3

Successful steps 3

Unsuccessful steps 0

Time (in seconds):

Preprocessor 0.0008

Residual evaluation 0.0067

Jacobian evaluation 0.0052

Linear solver 0.0821

Minimizer 0.0978

Postprocessor 0.0001

Total 0.0987

Termination: CONVERGENCE (Function tolerance reached. |cost_change|/cost: 5.108553e-09 <= 1.000000e-06)

Sameer Agarwal

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Jun 15, 2016, 5:25:02 PM6/15/16

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It is most likely that all these parameter blocks are in the problem but they are constant.

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Diego Coelho

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Jun 15, 2016, 7:15:35 PM6/15/16

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Hi Sameer,

You are right. I made an experiment changing from SPARSE_NORMAL_CHOLESKY to SPARSE_SCHUR and I got the same number of reduced parameters.