LSQRRecipes

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This repository contains implementations of algorithms for least squares estimation of various parametric objects. In addition, a generic implementation of the RANdom SAmple Consensus (RANSAC) is provided. This adds the ability to perform robust estimation without integrating the associated logic into the least squares logic.

The context within which these algorithms were used is image-guided interventions.

Example and testing programs are provided.

The parametric objects include:

1. hypersphere (2D - circle, 3D - sphere, kD - sphere).
2. hyperplane (2D - line, 3D - plane, kD - plane).
3. intersection point of 3D rays.
4. US calibration matrix via (a) crosswire phantom (b) calibrated pointer (c) plane phantom.
5. absolute orientation, rigid transformation, relating corresponding point pairs in two coordinate systems [unit quaternion solution due to B.K.P. Horn].
6. kD line (line in any dimension).
7. 2D line - doesn't require the VNL library and can be easily incorporated into an existing project using a minimal subset of the LSQRRecipes library (see details below).
8. solution to a set of linear equations.
9. translations obtained via pivot calibration.

Requirements:

Configuration is done via the Cmake tool (http://www.cmake.org).

The VNL subcomponent from the VXL (http://vxl.sourceforge.net/) toolkit is required for linear algebra and nonlinear estimation methods. This set of libraries is also available as part of ITK (http://www.itk.org/). The LSQRRecipes library can be configured to use either of these distributions through a Cmake flag (USING_ITK_VNL)

2D line

If all you need is a robust estimation of a 2D line and you don't want to use a linear algebra package for computing eigenvectors you can directly copy the following files into your project: 0. copyright.h

1. ParametersEstimator.h
2. Line2DParametersEstimator.{h,cxx}
3. RANSAC.{h,hxx}

You will need a 2D point class which has the square bracket operator to access the point elements (Point2D.h). Either you already have such a class or you can use the following minimal implementation, just copy paste:

#ifndef POINT2D_H #define POINT2D_H

#include "copyright.h"

namespace lsqrRecipes {

class Point2D { public: Point2D(double x=0.0, double y=0.0) {this->data[0] = x; this->data[1] = y;} const double & operator[](int index) const {return this->data[index];}

private: double data[2]; };

} //namespace lsqrRecipes

#endif //POINT2D_H