Jafar: Module bundle

Detailed Description

Version:: 0.1

Author:: martial.sanfourche@laas.fr

The bundle adjustment (BA) is a technique for simultaneously refining 3D structure and viewing parameters to obtain a reconstruction which is optimal in comparison with the noise affecting the observed image features (and other sources of information : like camera pose given by an odomertry sensor, like position of some 3D features in the World Frame). BA amounts to minimizing an non linear least squares criterion, non linear because the predictive model is non linear in terms of the sought parameters. For more information, I advise you to read the Bill Triggs's review.

In our implementation, we have introduced two additive terms permitting to add a priori on structure parameters and/or camera pose parameters. Then the global criterion is :

$C_{BA}\left( \left\{ \mathit{\mathbf{M}}_k \right\}_{1\leq k \leq K}, \left\{ \mathit{\mathbf{X}}_n \right\}_{1\leq n \leq N} \right) = \sum_{k} \sum_{n} \left|\left| \mathit{\mathbf{x}}_{k,n}^{obs} - \mathit{\mathbf{x}}_{k,n} \left(\mathit{\mathbf{M}}_k, \mathit{\mathbf{X}}_n \right) \right|\right|_{\Sigma_{2D}}^2 + \sum_{k} \left|\left| \mathit{\mathbf{M}}_k - \mathit{\mathbf{M}}_k^{obs} \right|\right|_{\Sigma_{MOT}}^2 + \sum_{n} \left|\left| \mathit{\mathbf{X}}_n - \mathit{\mathbf{X}}_n^{obs} \right|\right|_{\Sigma_{STR}}^2$

The bundle modules includes two algorithms :

a minimization process using Gauss-Newton Algorithm
a minimization process using Levenberg-Marquardt Algorithm (a damped Gauss-Newton method)

This implementation is widely inspired by the C implematation coded and documented by Manolis Lourakis. Another contributor is Gunter Winkler for his implementation of conjugated gradient method for solving linear system (much faster than LU decomposition method when the number of equation is high).

How to Use

To run our Bundle Adjustment implementation, the user need to fill an configuration file on the model of paramBA_default.bun (located in the doc directory of bundle jafar-module). This file gives information on :

the problem dimensions (number of cameras, number of image features, number of 3D object, ... )
where data-loading methods search input file
where output file are written Note that some fields of this configuration file are already filled.

Input file format

All data-loading functions wait for binary files. The format of files depends on the recorded data. Now, I'm going list the different files potentially needed by bundle adjustement.

2D observations (obligatory). For each image features, the loading method wait for the 4 numerical values in this given order: View index on the used image sequence (unsigned int), 3D structure object identifier index (unsigned int), column index (double ), row index (double ). Remember that the a priori precision on features extraction is given in a configuration file.

3D structure observations (facultative). For each 3D object, the loading method wait for (in the given order): its 3D structure object indentifier index (unsigned int), its position (3 double ) and the corresponding covariance matrix (9 double aligned in an row major matrix iterator).

Extrinsic parameters observations (facultative).For each known extrinsic parameters, the loading method wait for (in the given order) : its view index on the used image sequence (unsigned int), the 6 Euler extrinsic parameters (6 double ) and the corresponding covariance matrix (36 double aligned in an row major matrix iterator).

3D structure initial values (obligatory). One 3D structure initial values is the set composed by : an 3D structure object indentifier index (unsigned int) and an position vector (3 double ).

Extrinsic parameters intial values (obligatory). In order to initialize the extrinsic parameters, the loading method wait for each view for : one view index on the used image sequence (unsigned int) and the 6 Euler extrinsic parameters (6 double ).

Output file format

At the end of the optimization process, two files are generated : one to store position of the 3D structure elements in the format of the 3D structure initialization file and an other to store refined extrinsic parameters in the format of the motion initialization file.

History

0.1 (2006-08-03) - Initial version

Macro

Extra doc for macro can go here... (you can delete this section if not relevant)

Tcl interface (generated by swig)

The interface of the module is generated from the following files:

bundle.i defines the wrapped classes and functions,
bundleException.i defines the try { } catch block for this module.

Classes
class	jafar::bundle::observation
	Base class of observation object. More...
class	jafar::bundle::observationsContainer
	Container for all observations used by the BA algorithm. More...
class	jafar::bundle::bundleDimension
	Container for problem dimensions (Number of cameras, number of 3D points, ...) More...
class	jafar::bundle::BundleException
	Base class for all exceptions defined in the module bundle. More...
class	jafar::bundle::bundleParameters
	Container for bundle parameter storage. More...
class	jafar::bundle::bundleVariables< Sensor >
	Base class for parameters to refine during optimization process The class is templated in order to be generic with rapport to camera model. More...
class	jafar::bundle::bundleLinearSys
	Mathematical part of our Bundle Adjustment implementation. More...
class	jafar::bundle::SBAObservation
	class SBAObsevation Holds structure of observed point. More...
class	jafar::bundle::SBACamera
	class SBACamera Holds intrinsic and extrinsic camera parameters. More...
class	jafar::bundle::SparseBundleAdjustment
	class SparseBundleAdjustment It's an interface to Lourakis Sparse Bundle Adjustment I started recoding in cpp templated way but haven't time to finish it. More...
Functions
template<typename CamType >
void	jafar::bundle::computeResidual (observationsContainer &obs, bundleVariables< CamType > &variables)
	Update all residual vectors (2D, 3D structure and extrinsic parameters) from current variables estimation (variables) and from observations (obs)
template<typename CamType >
void	jafar::bundle::bundleGN (std::string paramFile)
	Bundle adjustment algorithm using the Gauss-Newton minimization algorithm.
template<typename CamType >
void	jafar::bundle::bundleLM (std::string paramFile)
	Bundle adjustment algorithm using the Levenberg Marquardt minimization algorithm.