itkMeshTransform.h

/*
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// File         : itkMeshTransform.h
// Author       : Pavel A. Koshevoy
// Created      : 2009/05/06 20:13
// Copyright    : (C) 2009 University of Utah
// Description  : A discontinuous transform -- a Delaunay triangle mesh
//                mapped to an image. At each vertex, in addition to image
//                space coordinates a second set of coordinates is stored.
//                This is similar to texture mapped OpenGL triangle meshes,
//                where the texture coordinates correspond to the image space
//                vertex coordinates.

#ifndef __itkMeshTransform_h
#define __itkMeshTransform_h

// system includes:
#include <math.h>
#include <iostream>

// ITK includes:
#include <itkTransform.h>
#include <itkExceptionObject.h>
#include <itkIdentityTransform.h>
#include <itkMacro.h>
#include <itkImage.h>

// local includes:
#include <Core/ITKCommon/Transform/itkDiscontinuousTransform.h>


//----------------------------------------------------------------
// itk::MeshTransform
//
namespace itk
{

class MeshTransform : public Transform<double, 2, 2>
{
public:
  // standard typedefs:
  typedef MeshTransform Self;
  typedef SmartPointer<Self> Pointer;
  typedef SmartPointer<const Self> ConstPointer;

  typedef Transform<double, 2, 2> Superclass;

  typedef Superclass::InverseTransformBaseType InverseTransformBaseType;
  typedef InverseTransformBaseType::Pointer    InverseTransformBasePointer;
  
  // RTTI:
  itkTypeMacro(MeshTransform, Transform);

  // macro for instantiation through the object factory:
  itkNewMacro(Self);

  typedef double ScalarType;

  itkStaticConstMacro(InputSpaceDimension, unsigned int, 2);
  itkStaticConstMacro(OutputSpaceDimension, unsigned int, 2);

  // shortcuts:
  typedef Superclass::ParametersType ParametersType;
  typedef Superclass::JacobianType JacobianType;
  
  typedef Superclass::InputPointType InputPointType;
  typedef Superclass::OutputPointType OutputPointType;
  
  // virtual:
  virtual OutputPointType TransformPoint(const InputPointType & x) const
  {
    OutputPointType y;
    if ( transform_.grid_.cols_ == 0 || transform_.grid_.cols_ == 0 )
    {
      // No grid has been setup.  Use the identity.
      y[0] = x[0];
      y[1] = x[1];
    }
    else if (is_inverse())
    {
      pnt2d_t uv;
      uv[0] = (x[0] - transform_.tile_min_[0]) / transform_.tile_ext_[0];
      uv[1] = (x[1] - transform_.tile_min_[1]) / transform_.tile_ext_[1];
      transform_.transform_inv(uv, y);
    }
    else
    {
      transform_.transform(x, y);
      y[0] *= transform_.tile_ext_[0];
      y[1] *= transform_.tile_ext_[1];
      y[0] += transform_.tile_min_[0];
      y[1] += transform_.tile_min_[1];
    }
    
    // ITK is not forgiving to NaNs:
    if (y[0] != y[0])
    {
      y[0] = std::numeric_limits<double>::max();
      y[1] = y[0];
    }
    
    return y;
  }
  
  // Inverse transformations:
  // If y = Transform(x), then x = BackTransform(y);
  // if no mapping from y to x exists, then an exception is thrown.
  InputPointType BackTransformPoint(const OutputPointType & y) const
  {
    InputPointType x;
    if (is_inverse())
    {
      transform_.transform(y, x);
      x[0] *= transform_.tile_ext_[0];
      x[1] *= transform_.tile_ext_[1];
      x[0] += transform_.tile_min_[0];
      x[1] += transform_.tile_min_[1];
    }
    else
    {
      pnt2d_t uv;
      uv[0] = (y[0] - transform_.tile_min_[0]) / transform_.tile_ext_[0];
      uv[1] = (y[1] - transform_.tile_min_[1]) / transform_.tile_ext_[1];
      transform_.transform_inv(uv, x);
    }
    
    // ITK does not handle NaNs well:
    if (x[0] != x[0])
    {
      x[0] = std::numeric_limits<double>::max();
      x[1] = x[0];
    }
    
    return x;
  }
  
  // virtual:
  virtual void SetFixedParameters(const ParametersType & params)
  { this->m_FixedParameters = params; }
  
  // virtual:
  const ParametersType & GetFixedParameters() const
  {
    ParametersType params = this->m_FixedParameters;

    // acceleration grid size:
    params[1] = transform_.grid_.rows_;
    params[2] = transform_.grid_.cols_;
    
    // bounding box if the image associated with this transform:
    params[3] = transform_.tile_min_[0];
    params[4] = transform_.tile_min_[1];
    params[5] = transform_.tile_ext_[0];
    params[6] = transform_.tile_ext_[1];
    
    // number of vertices in the Delaunay triangle mesh:
    params[7] = transform_.grid_.mesh_.size();
    
    // update the parameters vector:
    MeshTransform * fake = const_cast<MeshTransform *>(this);
    fake->m_FixedParameters = params;
    return this->m_FixedParameters;
  }

  // virtual:
  virtual void SetParameters(const ParametersType & params)
  {
    this->m_Parameters = params;
    
    std::size_t accel_grid_rows = std::size_t(this->m_FixedParameters[1]);
    std::size_t accel_grid_cols = std::size_t(this->m_FixedParameters[2]);

    pnt2d_t tile_min;
    tile_min[0] = this->m_FixedParameters[3];
    tile_min[1] = this->m_FixedParameters[4];

    pnt2d_t tile_max;
    tile_max[0] = tile_min[0] + this->m_FixedParameters[5];
    tile_max[1] = tile_min[1] + this->m_FixedParameters[6];

    const std::size_t num_points = std::size_t(this->m_FixedParameters[7]);
    std::vector<pnt2d_t> uv(num_points);
    std::vector<pnt2d_t> xy(num_points);

    for (unsigned int i = 0; i < num_points; i++)
    {
      const std::size_t idx = i * 4;
      
      uv[i][0] = params[idx + 0];
      uv[i][1] = params[idx + 1];
      xy[i][0] = params[idx + 2];
      xy[i][1] = params[idx + 3];
    }

    transform_.setup(tile_min,
                     tile_max,
                     uv,
                     xy,
                     accel_grid_rows,
                     accel_grid_cols);
  }

  // virtual:
  virtual const ParametersType & GetParameters() const
  {
    ParametersType params(GetNumberOfParameters());

    const std::size_t num_points = transform_.grid_.mesh_.size();
    for (std::size_t i = 0; i < num_points; i++)
    {
      const vertex_t & vx = transform_.grid_.mesh_[i];
      const std::size_t idx = i * 4;
      
      params[idx + 0] = vx.uv_[0];
      params[idx + 1] = vx.uv_[1];
      params[idx + 2] = vx.xy_[0];
      params[idx + 3] = vx.xy_[1];
    }

    // update the parameters vector:
    MeshTransform * fake = const_cast<MeshTransform *>(this);
    fake->m_Parameters = params;
    return this->m_Parameters;
  }

  // virtual:
  virtual NumberOfParametersType GetNumberOfParameters(void) const
  { return 4 * transform_.grid_.mesh_.size(); }

  // virtual: return an inverse of this transform.
  virtual InverseTransformBasePointer GetInverseTransform() const
  {
    MeshTransform::Pointer inv = MeshTransform::New();
    inv->setup(transform_, !is_inverse());
    return inv.GetPointer();
  }

  // setup the transform:
  void setup(const the_mesh_transform_t & transform,
             const bool & is_inverse = false)
  {
    transform_ = transform;
    GetParameters();
    GetFixedParameters();
//    this->m_Jacobian.SetSize(2, GetNumberOfParameters());
    this->m_FixedParameters[0] = is_inverse ? 1.0 : 0.0;
  }

  // inverse transform flag check:
  inline bool is_inverse() const
  { return this->m_FixedParameters[0] != 0.0; }

//  // virtual:
//  virtual
//  const JacobianType &
//  GetJacobian(const InputPointType & point) const
//  {
//    // FIXME: 20061227 -- this function was written and not tested:
//
//    // these scales are necessary to account for the fact that
//    // the_mesh_transform_t expects uv in the [0,1]x[0,1] range,
//    // where as we remap it into the image tile physical coordinates
//    // according to tile_min_ and tile_ext_:
//    double Su = transform_.tile_ext_[0];
//    double Sv = transform_.tile_ext_[1];
//
//    unsigned int idx[3];
//    double jac[12];
//    this->m_Jacobian.SetSize(2, GetNumberOfParameters());
//    this->m_Jacobian.Fill(0.0);
//    if (transform_.jacobian(point, idx, jac))
//    {
//      for (unsigned int i = 0; i < 3; i++)
//      {
//        unsigned int addr = idx[i] * 2;
//        this->m_Jacobian(0, addr) = Su * jac[i * 2];
//        this->m_Jacobian(0, addr + 1) = Su * jac[i * 2 + 1];
//        this->m_Jacobian(1, addr) = Sv * jac[i * 2 + 6];
//        this->m_Jacobian(1, addr + 1) = Sv * jac[i * 2 + 7];
//      }
//    }
//
//    return this->m_Jacobian;
//  }

  virtual
  void
  ComputeJacobianWithRespectToParameters( const InputPointType &point, JacobianType &jacobian ) const
  {
    // FIXME: 20061227 -- this function was written and not tested:
    
    // these scales are necessary to account for the fact that
    // the_mesh_transform_t expects uv in the [0,1]x[0,1] range,
    // where as we remap it into the image tile physical coordinates
    // according to tile_min_ and tile_ext_:
    double Su = transform_.tile_ext_[0];
    double Sv = transform_.tile_ext_[1];
    
    unsigned int idx[3];
    double jac[12];
    jacobian.SetSize(2, GetNumberOfParameters());
    jacobian.Fill(0.0);
    if (transform_.jacobian(point, idx, jac))
    {
      for (unsigned int i = 0; i < 3; i++)
      {
        unsigned int addr = idx[i] * 2;
        jacobian(0, addr) = Su * jac[i * 2];
        jacobian(0, addr + 1) = Su * jac[i * 2 + 1];
        jacobian(1, addr) = Sv * jac[i * 2 + 6];
        jacobian(1, addr + 1) = Sv * jac[i * 2 + 7];
      }
    }
  }
  
protected:
  MeshTransform():
//    Superclass(2, 0)
    Superclass(0)
  {
    this->m_FixedParameters.SetSize(8);

    // initialize the inverse flag:
    this->m_FixedParameters[0] = 0.0;

    // acceleration grid size:
    this->m_FixedParameters[1] = 0.0;
    this->m_FixedParameters[2] = 0.0;

    // bounding box if the image associated with this transform:
    this->m_FixedParameters[3] = std::numeric_limits<double>::max();
    this->m_FixedParameters[4] = this->m_FixedParameters[3];
    this->m_FixedParameters[5] = -(this->m_FixedParameters[3]);
    this->m_FixedParameters[6] = -(this->m_FixedParameters[3]);

    // number of vertices in the Delaunay triangle mesh:
    this->m_FixedParameters[7] = 0.0;
  }

private:
  // disable default copy constructor and assignment operator:
  MeshTransform(const Self & other);
  const Self & operator = (const Self & t);

public:
  // the actual transform:
  the_mesh_transform_t transform_;

}; // class MeshTransform

} // namespace itk


#endif //  __itkMeshTransform_h