/usr/include/relion-1.3/src/transformations.h is in librelion-dev-common 1.3+dfsg-2.
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*
* Author: "Sjors H.W. Scheres"
* MRC Laboratory of Molecular Biology
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* This complete copyright notice must be included in any revised version of the
* source code. Additional authorship citations may be added, but existing
* author citations must be preserved.
***************************************************************************/
/***************************************************************************
*
* Authors: Carlos Oscar S. Sorzano (coss@cnb.csic.es)
* Sjors H.W. Scheres
*
* Unidad de Bioinformatica of Centro Nacional de Biotecnologia , CSIC
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
* 02111-1307 USA
*
* All comments concerning this program package may be sent to the
* e-mail address 'xmipp@cnb.csic.es'
***************************************************************************/
#ifndef TRANSFORMATIONS_H
#define TRANSFORMATIONS_H
#include "src/multidim_array.h"
#include "src/euler.h"
#define IS_INV true
#define IS_NOT_INV false
#define DONT_WRAP false
#define WRAP true
#ifndef DBL_EPSILON
#define DBL_EPSILON 1e-50
#endif
/// @defgroup GeometricalTransformations Geometrical transformations
/// @ingroup DataLibrary
//@{
/** Creates a rotational matrix (3x3) for images
* @ingroup GeometricalTransformations
*
* The rotation angle is in degrees.
* m must have been already resized to 3x3
*
* @code
* rotation2DMatrix(60,m);
* @endcode
*/
void rotation2DMatrix(double ang, Matrix2D< double > &m, bool homogeneous=true);
/** Creates a translational matrix (3x3) for images
* @ingroup GeometricalTransformations
*
* The shift is given as a R2 vector (shift_X, shift_Y). An exception is thrown
* if the displacement is not a R2 vector.
*
* @code
* // Displacement of 1 pixel to the right
* m = translation2DMatrix(vectorR2(1, 0));
* @endcode
*/
void translation2DMatrix(const Matrix1D< double > &v, Matrix2D< double > &m);
/** Creates a rotational matrix (4x4) for volumes around system axis
* @ingroup GeometricalTransformations
*
* The rotation angle is in degrees, and the rotational axis is either 'X', 'Y'
* or 'Z'. An exception is thrown if the axis given is not one of these.
*
* The returned matrices are respectively alpha degrees around Z
*
* @code
* [ cos(A) -sin(A) 0 ]
* [ sin(A) cos(A) 0 ]
* [ 0 0 1 ]
* @endcode
*
* alpha degrees around Y
* @code
* [ cos(A) 0 -sin(A) ]
* [ 0 1 0 ]
* [ sin(A) 0 cos(A) ]
* @endcode
*
* alpha degrees around X
* @code
* [ 1 0 0 ]
* [ 0 cos(A) -sin(A) ]
* [ 0 sin(A) cos(A) ]
* @endcode
*
* @code
* m = rotation3DMatrix(60, 'X');
* @endcode
*/
void rotation3DMatrix(double ang, char axis, Matrix2D< double > &m,
bool homogeneous=true);
/** Creates a rotational matrix (4x4) for volumes around any axis
* @ingroup GeometricalTransformations
*
* The rotation angle is in degrees, and the rotational axis is given as a R3
* vector. An exception is thrown if the axis is not a R3 vector. The axis needs
* not to be unitary.
*
* @code
* m = rotation3DMatrix(60, vectorR3(1, 1, 1));
* @endcode
*/
void rotation3DMatrix(double ang, const Matrix1D< double >& axis, Matrix2D< double > &m,
bool homogeneous=true);
/** Matrix which transforms the given axis into Z
* @ingroup GeometricalTransformations
*
* A geometrical transformation matrix (4x4) is returned such that the given
* axis is rotated until it is aligned with the Z axis. This is very useful in
* order to produce rotational matrices, for instance, around any axis.
*
* @code
* Matrix2D< double > A = alignWithZ(axis);
* return A.transpose() * rotation3DMatrix(ang, 'Z') * A;
* @endcode
*
* The returned matrix is such that A*axis=Z, where Z and axis are column
* vectors.
*/
void alignWithZ(const Matrix1D< double >& axis, Matrix2D< double > &m, bool homogeneous=true);
/** Creates a translational matrix (4x4) for volumes
* @ingroup GeometricalTransformations
*
* The shift is given as a R3 vector (shift_X, shift_Y, shift_Z). An exception
* is thrown if the displacement is not a R3 vector.
*
* @code
* // Displacement of 2 pixels down
* m = translation3DMatrix(vectorR3(0, 0, 2));
* @endcode
*/
void translation3DMatrix(const Matrix1D< double >& v, Matrix2D< double > &m);
/** Creates a scaling matrix (4x4) for volumes
* @ingroup GeometricalTransformations
*
* The scaling factors for the different axis must be given as a vector. So
* that, XX(sc)=scale for X axis, YY(sc)=...
*/
void scale3DMatrix(const Matrix1D< double >& sc, Matrix2D< double > &m,
bool homogeneous=true);
/** Applies a geometrical transformation.
* @ingroup GeometricalTransformations
*
* Any geometrical transformation defined by the matrix A (double (4x4)!!
* ie, in homogeneous R3 coordinates) is applied to the volume V1.
* The result is stored in V2 (it cannot be the same as the input volume).
* An exception is thrown if the transformation matrix is not 4x4.
*
* Structure of the transformation matrix: It should have the following
* components
*
* r11 r12 r13 x
* r21 r22 r23 y
* r31 r32 r33 z
* 0 0 0 1
*
* where (x,y,z) is the translation desired, and Rij are the components of
* the rotation matrix R. If you want to apply a scaling factor to the
* transformation, then multiply r11, r22 and r33 by it.
*
* The result volume (with ndim=1) is resized to the same
* dimensions as V1 if V2 is empty (0x0) at the beginning, if it
* is not, ie, if V2 has got some size then only those values in
* the volume are filled, this is very useful for resizing the
* volume, then you manually resize the output volume to the
* desired size and then call this routine.
*
* The relationship between the output coordinates and the input ones are
*
* @code
* out = A * in
* (x, y, z) = A * (x', y', z')
* @endcode
*
* This function works independently from the logical indexing of each
* matrix, it sets the logical center and the physical center of the image
* and work with these 2 coordinate spaces. At the end the original logical
* indexing of each matrix is kept.
*
* The procedure followed goes from coordinates in the output volume
* to the ones in the input one, so the inverse of the A matrix is
* needed. There is a flag telling if the given matrix is already
* the inverse one or the normal one. If it is the normal one internally
* the matrix is inversed. If you are to do many "rotations" then
* some time is spent in inverting the matrix. Normally the matrix is the
* normal one.
*
* There is something else to tell about the geometrical tranformation.
* The value of the voxel in the output volume is computed via
* bilinear interpolation in the input volume. If any of the voxels
* participating in the interpolation falls outside the input volume,
* then automatically the corresponding output voxel is set to 0, unless
* that the wrap flag has been set to 1. In this case if the voxel
* falls out by the right hand then it is "wrapped" and the corresponding
* voxel in the left hand is used. The same is appliable to top-bottom.
* Usually wrap mode is off. Wrap mode is interesting for translations
* but not for rotations, for example.
*
* The inverse mode and wrapping mode should be taken by default by the
* routine, g++ seems to have problems with template functions outside
* a class with default parameters. So, I'm sorry, you will have to
* put them always. The usual combination is
*
* applyGeometry(..., IS_NOT_INV, DONT_WRAP).
*
* Although you can also use the constants IS_INV, or WRAP.
*
* @code
* Matrix2D< double > A(4,4);
* A.initIdentity;
* applyGeometry(V2, A, V1);
* @endcode
*/
template<typename T>
void applyGeometry(const MultidimArray<T>& V1,
MultidimArray<T>& V2,
const Matrix2D< double > A,
bool inv,
bool wrap,
T outside = 0)
{
if (&V1 == &V2)
REPORT_ERROR("ApplyGeometry: Input array cannot be the same as output array");
if ( V1.getDim()==2 && ((MAT_XSIZE(A) != 3) || (MAT_YSIZE(A) != 3)) )
REPORT_ERROR("ApplyGeometry: 2D transformation matrix is not 3x3");
if ( V1.getDim()==3 && ((MAT_XSIZE(A) != 4) || (MAT_YSIZE(A) != 4)) )
REPORT_ERROR("ApplyGeometry: 3D transformation matrix is not 4x4");
if (A.isIdentity())
{
V2=V1;
return;
}
if (XSIZE(V1) == 0)
{
V2.clear();
return;
}
Matrix2D<double> Ainv;
const Matrix2D<double> * Aptr=&A;
if (!inv)
{
Ainv = A.inv();
Aptr=&Ainv;
}
const Matrix2D<double> &Aref=*Aptr;
// For scalings the output matrix is resized outside to the final
// size instead of being resized inside the routine with the
// same size as the input matrix
if (XSIZE(V2) == 0)
V2.resize(V1);
if (V1.getDim() == 2)
{
// 2D transformation
int m1, n1, m2, n2;
double x, y, xp, yp;
double minxp, minyp, maxxp, maxyp;
int cen_x, cen_y, cen_xp, cen_yp;
double wx, wy;
int Xdim, Ydim;
// Find center and limits of image
cen_y = (int)(YSIZE(V2) / 2);
cen_x = (int)(XSIZE(V2) / 2);
cen_yp = (int)(YSIZE(V1) / 2);
cen_xp = (int)(XSIZE(V1) / 2);
minxp = -cen_xp;
minyp = -cen_yp;
maxxp = XSIZE(V1) - cen_xp - 1;
maxyp = YSIZE(V1) - cen_yp - 1;
Xdim = XSIZE(V1);
Ydim = YSIZE(V1);
// Now we go from the output image to the input image, ie, for any pixel
// in the output image we calculate which are the corresponding ones in
// the original image, make an interpolation with them and put this value
// at the output pixel
#ifdef DEBUG_APPLYGEO
std::cout << "A\n" << Aref << std::endl
<< "(cen_x ,cen_y )=(" << cen_x << "," << cen_y << ")\n"
<< "(cen_xp,cen_yp)=(" << cen_xp << "," << cen_yp << ")\n"
<< "(min_xp,min_yp)=(" << minxp << "," << minyp << ")\n"
<< "(max_xp,max_yp)=(" << maxxp << "," << maxyp << ")\n";
#endif
for (int i = 0; i < YSIZE(V2); i++)
{
// Calculate position of the beginning of the row in the output image
x = -cen_x;
y = i - cen_y;
// Calculate this position in the input image according to the
// geometrical transformation
// they are related by
// coords_output(=x,y) = A * coords_input (=xp,yp)
xp = x * Aref(0, 0) + y * Aref(0, 1) + Aref(0, 2);
yp = x * Aref(1, 0) + y * Aref(1, 1) + Aref(1, 2);
for (int j = 0; j < XSIZE(V2); j++)
{
bool interp;
T tmp;
#ifdef DEBUG_APPLYGEO
std::cout << "Computing (" << i << "," << j << ")\n";
std::cout << " (y, x) =(" << y << "," << x << ")\n"
<< " before wrapping (y',x')=(" << yp << "," << xp << ") "
<< std::endl;
#endif
// If the point is outside the image, apply a periodic extension
// of the image, what exits by one side enters by the other
interp = true;
if (wrap)
{
if (xp < minxp - XMIPP_EQUAL_ACCURACY ||
xp > maxxp + XMIPP_EQUAL_ACCURACY)
xp = realWRAP(xp, minxp - 0.5, maxxp + 0.5);
if (yp < minyp - XMIPP_EQUAL_ACCURACY ||
yp > maxyp + XMIPP_EQUAL_ACCURACY)
yp = realWRAP(yp, minyp - 0.5, maxyp + 0.5);
}
else
{
if (xp < minxp - XMIPP_EQUAL_ACCURACY ||
xp > maxxp + XMIPP_EQUAL_ACCURACY)
interp = false;
if (yp < minyp - XMIPP_EQUAL_ACCURACY ||
yp > maxyp + XMIPP_EQUAL_ACCURACY)
interp = false;
}
#ifdef DEBUG_APPLYGEO
std::cout << " after wrapping (y',x')=(" << yp << "," << xp << ") "
<< std::endl;
std::cout << " Interp = " << interp << std::endl;
// The following line sounds dangerous...
//x++;
#endif
if (interp)
{
// Linear interpolation
// Calculate the integer position in input image, be careful
// that it is not the nearest but the one at the top left corner
// of the interpolation square. Ie, (0.7,0.7) would give (0,0)
// Calculate also weights for point m1+1,n1+1
wx = xp + cen_xp;
m1 = (int) wx;
wx = wx - m1;
m2 = m1 + 1;
wy = yp + cen_yp;
n1 = (int) wy;
wy = wy - n1;
n2 = n1 + 1;
// m2 and n2 can be out by 1 so wrap must be check here
if (wrap)
{
if (m2 >= Xdim)
m2 = 0;
if (n2 >= Ydim)
n2 = 0;
}
#ifdef DEBUG_APPLYGEO
std::cout << " From (" << n1 << "," << m1 << ") and ("
<< n2 << "," << m2 << ")\n";
std::cout << " wx= " << wx << " wy= " << wy << std::endl;
#endif
// Perform interpolation
// if wx == 0 means that the rightest point is useless for this
// interpolation, and even it might not be defined if m1=xdim-1
// The same can be said for wy.
tmp = (T)((1 - wy) * (1 - wx) * DIRECT_A2D_ELEM(V1, n1, m1));
if (wx != 0 && m2 < V1.xdim)
tmp += (T)((1 - wy) * wx * DIRECT_A2D_ELEM(V1, n1, m2));
if (wy != 0 && n2 < V1.ydim)
{
tmp += (T)(wy * (1 - wx) * DIRECT_A2D_ELEM(V1, n2, m1));
if (wx != 0 && m2 < V1.xdim)
tmp += (T)(wy * wx * DIRECT_A2D_ELEM(V1, n2, m2));
}
dAij(V2, i, j) = tmp;
#ifdef DEBUG_APPYGEO
std::cout << " val= " << dAij(V2, i, j) << std::endl;
#endif
} // if interp
else
dAij(V2, i, j) = outside;
// Compute new point inside input image
xp += Aref(0, 0);
yp += Aref(1, 0);
}
}
}
else
{
// 3D transformation
int m1, n1, o1, m2, n2, o2;
double x, y, z, xp, yp, zp;
double minxp, minyp, maxxp, maxyp, minzp, maxzp;
int cen_x, cen_y, cen_z, cen_xp, cen_yp, cen_zp;
double wx, wy, wz;
// Find center of MultidimArray
cen_z = (int)(V2.zdim / 2);
cen_y = (int)(V2.ydim / 2);
cen_x = (int)(V2.xdim / 2);
cen_zp = (int)(V1.zdim / 2);
cen_yp = (int)(V1.ydim / 2);
cen_xp = (int)(V1.xdim / 2);
minxp = -cen_xp;
minyp = -cen_yp;
minzp = -cen_zp;
maxxp = V1.xdim - cen_xp - 1;
maxyp = V1.ydim - cen_yp - 1;
maxzp = V1.zdim - cen_zp - 1;
#ifdef DEBUG
std::cout << "Geometry 2 center=("
<< cen_z << "," << cen_y << "," << cen_x << ")\n"
<< "Geometry 1 center=("
<< cen_zp << "," << cen_yp << "," << cen_xp << ")\n"
<< " min=("
<< minzp << "," << minyp << "," << minxp << ")\n"
<< " max=("
<< maxzp << "," << maxyp << "," << maxxp << ")\n"
;
#endif
// Now we go from the output MultidimArray to the input MultidimArray, ie, for any
// voxel in the output MultidimArray we calculate which are the corresponding
// ones in the original MultidimArray, make an interpolation with them and put
// this value at the output voxel
// V2 is not initialised to 0 because all its pixels are rewritten
for (int k = 0; k < V2.zdim; k++)
for (int i = 0; i < V2.ydim; i++)
{
// Calculate position of the beginning of the row in the output
// MultidimArray
x = -cen_x;
y = i - cen_y;
z = k - cen_z;
// Calculate this position in the input image according to the
// geometrical transformation they are related by
// coords_output(=x,y) = A * coords_input (=xp,yp)
xp = x * Aref(0, 0) + y * Aref(0, 1) + z * Aref(0, 2) + Aref(0, 3);
yp = x * Aref(1, 0) + y * Aref(1, 1) + z * Aref(1, 2) + Aref(1, 3);
zp = x * Aref(2, 0) + y * Aref(2, 1) + z * Aref(2, 2) + Aref(2, 3);
for (int j = 0; j < V2.xdim; j++)
{
bool interp;
T tmp;
#ifdef DEBUG
bool show_debug = false;
if ((i == 0 && j == 0 && k == 0) ||
(i == V2.ydim - 1 && j == V2.xdim - 1 && k == V2.zdim - 1))
show_debug = true;
if (show_debug)
std::cout << "(x,y,z)-->(xp,yp,zp)= "
<< "(" << x << "," << y << "," << z << ") "
<< "(" << xp << "," << yp << "," << zp << ")\n";
#endif
// If the point is outside the volume, apply a periodic
// extension of the volume, what exits by one side enters by
// the other
interp = true;
if (wrap)
{
if (xp < minxp - XMIPP_EQUAL_ACCURACY ||
xp > maxxp + XMIPP_EQUAL_ACCURACY)
xp = realWRAP(xp, minxp - 0.5, maxxp + 0.5);
if (yp < minyp - XMIPP_EQUAL_ACCURACY ||
yp > maxyp + XMIPP_EQUAL_ACCURACY)
yp = realWRAP(yp, minyp - 0.5, maxyp + 0.5);
if (zp < minzp - XMIPP_EQUAL_ACCURACY ||
zp > maxzp + XMIPP_EQUAL_ACCURACY)
zp = realWRAP(zp, minzp - 0.5, maxzp + 0.5);
}
else
{
if (xp < minxp - XMIPP_EQUAL_ACCURACY ||
xp > maxxp + XMIPP_EQUAL_ACCURACY)
interp = false;
if (yp < minyp - XMIPP_EQUAL_ACCURACY ||
yp > maxyp + XMIPP_EQUAL_ACCURACY)
interp = false;
if (zp < minzp - XMIPP_EQUAL_ACCURACY ||
zp > maxzp + XMIPP_EQUAL_ACCURACY)
interp = false;
}
if (interp)
{
// Linear interpolation
// Calculate the integer position in input volume, be
// careful that it is not the nearest but the one at the
// top left corner of the interpolation square. Ie,
// (0.7,0.7) would give (0,0)
// Calculate also weights for point m1+1,n1+1
wx = xp + cen_xp;
m1 = (int) wx;
wx = wx - m1;
m2 = m1 + 1;
wy = yp + cen_yp;
n1 = (int) wy;
wy = wy - n1;
n2 = n1 + 1;
wz = zp + cen_zp;
o1 = (int) wz;
wz = wz - o1;
o2 = o1 + 1;
#ifdef DEBUG
if (show_debug)
{
std::cout << "After wrapping(xp,yp,zp)= "
<< "(" << xp << "," << yp << "," << zp << ")\n";
std::cout << "(m1,n1,o1)-->(m2,n2,o2)="
<< "(" << m1 << "," << n1 << "," << o1 << ") "
<< "(" << m2 << "," << n2 << "," << o2 << ")\n";
std::cout << "(wx,wy,wz)="
<< "(" << wx << "," << wy << "," << wz << ")\n";
}
#endif
// Perform interpolation
// if wx == 0 means that the rightest point is useless for
// this interpolation, and even it might not be defined if
// m1=xdim-1
// The same can be said for wy.
tmp = (T)((1 - wz) * (1 - wy) * (1 - wx) * DIRECT_A3D_ELEM(V1, o1, n1, m1));
if (wx != 0 && m2 < V1.xdim)
tmp += (T)((1 - wz) * (1 - wy) * wx * DIRECT_A3D_ELEM(V1, o1, n1, m2));
if (wy != 0 && n2 < V1.ydim)
{
tmp += (T)((1 - wz) * wy * (1 - wx) * DIRECT_A3D_ELEM(V1, o1, n2, m1));
if (wx != 0 && m2 < V1.xdim)
tmp += (T)((1 - wz) * wy * wx * DIRECT_A3D_ELEM(V1, o1, n2, m2));
}
if (wz != 0 && o2 < V1.zdim)
{
tmp += (T)(wz * (1 - wy) * (1 - wx) * DIRECT_A3D_ELEM(V1, o2, n1, m1));
if (wx != 0 && m2 < V1.xdim)
tmp += (T)(wz * (1 - wy) * wx * DIRECT_A3D_ELEM(V1, o2, n1, m2));
if (wy != 0 && n2 < V1.ydim)
{
tmp += (T)(wz * wy * (1 - wx) * DIRECT_A3D_ELEM(V1, o2, n2, m1));
if (wx != 0 && m2 < V1.xdim)
tmp += (T)(wz * wy * wx * DIRECT_A3D_ELEM(V1, o2, n2, m2));
}
}
#ifdef DEBUG
if (show_debug)
std::cout <<
"tmp1=" << DIRECT_A3D_ELEM(V1, o1, n1, m1) << " "
<< (T)((1 - wz) *(1 - wy) *(1 - wx) * DIRECT_A3D_ELEM(V1, o1, n1, m1))
<< std::endl <<
"tmp2=" << DIRECT_A3D_ELEM(V1, o1, n1, m2) << " "
<< (T)((1 - wz) *(1 - wy) * wx * DIRECT_A3D_ELEM(V1, o1, n1, m2))
<< std::endl <<
"tmp3=" << DIRECT_A3D_ELEM(V1, o1, n2, m1) << " "
<< (T)((1 - wz) * wy *(1 - wx) * DIRECT_A3D_ELEM(V1, o1, n2, m1))
<< std::endl <<
"tmp4=" << DIRECT_A3D_ELEM(V1, o1, n2, m2) << " "
<< (T)((1 - wz) * wy * wx * DIRECT_A3D_ELEM(V1, o2, n1, m1))
<< std::endl <<
"tmp6=" << DIRECT_A3D_ELEM(V1, o2, n1, m2) << " "
<< (T)(wz * (1 - wy) * wx * DIRECT_A3D_ELEM(V1, o2, n1, m2))
<< std::endl <<
"tmp7=" << DIRECT_A3D_ELEM(V1, o2, n2, m1) << " "
<< (T)(wz * wy *(1 - wx) * DIRECT_A3D_ELEM(V1, o2, n2, m1))
<< std::endl <<
"tmp8=" << DIRECT_A3D_ELEM(V1, o2, n2, m2) << " "
<< (T)(wz * wy * wx * DIRECT_A3D_ELEM(V1, o2, n2, m2))
<< std::endl <<
"tmp= " << tmp << std::endl;
#endif
dAkij(V2 , k, i, j) = tmp;
}
else
dAkij(V2, k, i, j) = outside;
// Compute new point inside input image
xp += Aref(0, 0);
yp += Aref(1, 0);
zp += Aref(2, 0);
}
}
}
}
/** Applies a geometrical transformation and overwrites the input matrix.
* @ingroup GeometricalTransformations
*
* The same as the previous function, but input array is overwritten
*/
template<typename T>
void selfApplyGeometry(MultidimArray<T>& V1,
const Matrix2D< double > A, bool inv,
bool wrap, T outside = 0)
{
MultidimArray<T> aux = V1;
V1.initZeros();
applyGeometry(aux, V1, A, inv, wrap, outside);
}
/** Rotate an array around a given system axis.
* @ingroup GeometricalTransformations
*
* The rotation angle is in degrees, and the rotational axis is either
* 'X', 'Y' or 'Z' for 3D arrays and only 'Z' for 2D arrays. An
* exception is thrown if the axis given is not one of these.
*
* @code
* rotate(Vin, Vout, 60);
* @endcode
*/
template<typename T>
void rotate(const MultidimArray<T>& V1,
MultidimArray<T>& V2,
double ang, char axis = 'Z',
bool wrap = DONT_WRAP, T outside = 0)
{
Matrix2D< double > tmp;
if (V1.getDim()==2)
{
rotation2DMatrix(ang,tmp);
}
else if (V1.getDim()==3)
{
rotation3DMatrix(ang, axis, tmp);
}
else
REPORT_ERROR("rotate ERROR: rotate only valid for 2D or 3D arrays");
applyGeometry(V1, V2, tmp, IS_NOT_INV, wrap, outside);
}
/** Rotate an array around a given system axis.
* @ingroup GeometricalTransformations
*
* The same as the previous function, but input array is overwritten
*/
template<typename T>
void selfRotate(MultidimArray<T>& V1,
double ang, char axis = 'Z',
bool wrap = DONT_WRAP, T outside = 0)
{
MultidimArray<T> aux = V1;
rotate(aux, V1, ang, axis, wrap, outside);
}
/** Translate a array.
* @ingroup GeometricalTransformations
*
* The shift is given as a R2 or R3 vector (shift_X, shift_Y, shift_Z) for 2D and 3D arrays, respectively.
* An exception is thrown if the displacement is not a R3 vector.
*
* @code
* // Displacement of 2 pixels down
* V2 = V1.translate(vectorR3(0, 0, 2));
* @endcode
*/
template<typename T>
void translate(const MultidimArray<T> &V1,
MultidimArray<T> &V2,
const Matrix1D< double >& v,
bool wrap = WRAP, T outside = 0)
{
Matrix2D< double > tmp;
if (V1.getDim()==2)
translation2DMatrix(v, tmp);
else if (V1.getDim()==3)
translation3DMatrix(v, tmp);
else
REPORT_ERROR("translate ERROR: translate only valid for 2D or 3D arrays");
applyGeometry(V1, V2, tmp, IS_NOT_INV, wrap, outside);
}
/** Translate an array.
* @ingroup GeometricalTransformations
*
* The same as the previous function, but input array is overwritten
*/
template<typename T>
void selfTranslate(MultidimArray<T>& V1,
const Matrix1D< double >& v,
bool wrap = WRAP, T outside = 0)
{
MultidimArray<T> aux = V1;
translate(aux, V1, v, wrap, outside);
}
/** Translate center of mass to center
* @ingroup GeometricalTransformations
*
* If the input has very high values, it is better to rescale it to be
* between 0 and 1.
*/
template<typename T>
void translateCenterOfMassToCenter(const MultidimArray<T> &V1,
MultidimArray<T> &V2,
bool wrap = WRAP)
{
V2 = V1;
V2.setXmippOrigin();
Matrix1D< double > center;
V2.centerOfMass(center);
center *= -1;
translate(V1, V2, center, wrap, 0.);
}
/** Translate center of mass to center
* @ingroup GeometricalTransformations
*
* The same as the previous function, but input array is overwritten
*/
template<typename T>
void selfTranslateCenterOfMassToCenter(MultidimArray<T> &V1,
bool wrap = WRAP)
{
MultidimArray<T> aux = V1;
translateCenterOfMassToCenter(aux, V1, wrap);
}
/** Scales to a new size.
* @ingroup GeometricalTransformations
*
* The volume is scaled (resampled) to fill a new size. It is not the
* same as "window" in this same class. The size can be larger or smaller
* than the actual one.
*
* @code
* scaleToSize(Vin, Vout, 128, 128, 128);
* @endcode
*/
template<typename T>
void scaleToSize(const MultidimArray<T> &V1,
MultidimArray<T> &V2,
int Xdim, int Ydim, int Zdim = 1)
{
Matrix2D< double > tmp;
if (V1.getDim()==2)
{
tmp.initIdentity(3);
tmp(0, 0) = (double) Xdim / (double) XSIZE(V1);
tmp(1, 1) = (double) Ydim / (double) YSIZE(V1);
V2.resize(1, 1, Ydim, Xdim);
}
else if (V1.getDim()==3)
{
tmp.initIdentity(4);
tmp(0, 0) = (double) Xdim / (double) XSIZE(V1);
tmp(1, 1) = (double) Ydim / (double) YSIZE(V1);
tmp(2, 2) = (double) Zdim / (double) ZSIZE(V1);
V2.resize(1, Zdim, Ydim, Xdim);
}
else
REPORT_ERROR("scaleToSize ERROR: scaleToSize only valid for 2D or 3D arrays");
applyGeometry(V1, V2, tmp, IS_NOT_INV, WRAP, (T)0);
}
/** Scales to a new size.
* @ingroup GeometricalTransformations
*
* The same as the previous function, but input array is overwritten
*/
template<typename T>
void selfScaleToSize(MultidimArray<T> &V1,
int Xdim, int Ydim, int Zdim = 1)
{
MultidimArray<T> aux = V1;
scaleToSize(aux, V1, Xdim, Ydim, Zdim);
}
/** Does a radial average of a 2D/3D image, around the voxel where is the origin.
* @ingroup GeometricalTransformations
*
* A vector radial_mean is returned where:
* - the first element is the mean of the voxels whose
* distance to the origin is (0-1),
* - the second element is the mean of the voxels
* whose distance to the origin is (1-2)
* - and so on.
*
* A second vector radial_count is returned containing the number of voxels
* over which each radial average was calculated.
*
* Sjors nov2003: if rounding=true, element=round(distance);
* - so the first element is the mean of the voxels whose distance to the
* origin is (0.5-1.5),
* - the second element is the mean of the voxels whose distance to the origin
* is (1.5-2.5)
* - and so on.
*/
template<typename T>
void radialAverage(const MultidimArray< T >& m,
Matrix1D< int >& center_of_rot,
MultidimArray< T >& radial_mean,
MultidimArray< int >& radial_count,
const bool& rounding = false)
{
Matrix1D< double > idx(3);
// If center_of_rot was written for 2D image
if (center_of_rot.size() < 3)
center_of_rot.resize(3);
// First determine the maximum distance that one should expect, to set the
// dimension of the radial average vector
MultidimArray< int > distances(8);
double z = STARTINGZ(m) - ZZ(center_of_rot);
double y = STARTINGY(m) - YY(center_of_rot);
double x = STARTINGX(m) - XX(center_of_rot);
distances(0) = (int) floor(sqrt(x * x + y * y + z * z));
x = FINISHINGX(m) - XX(center_of_rot);
distances(1) = (int) floor(sqrt(x * x + y * y + z * z));
y = FINISHINGY(m) - YY(center_of_rot);
distances(2) = (int) floor(sqrt(x * x + y * y + z * z));
x = STARTINGX(m) - XX(center_of_rot);
distances(3) = (int) floor(sqrt(x * x + y * y + z * z));
z = FINISHINGZ(m) - ZZ(center_of_rot);
distances(4) = (int) floor(sqrt(x * x + y * y + z * z));
x = FINISHINGX(m) - XX(center_of_rot);
distances(5) = (int) floor(sqrt(x * x + y * y + z * z));
y = STARTINGY(m) - YY(center_of_rot);
distances(6) = (int) floor(sqrt(x * x + y * y + z * z));
x = STARTINGX(m) - XX(center_of_rot);
distances(7) = (int) floor(sqrt(x * x + y * y + z * z));
int dim = (int) CEIL(distances.computeMax()) + 1;
if (rounding)
dim++;
// Define the vectors
radial_mean.resize(dim);
radial_mean.initZeros();
radial_count.resize(dim);
radial_count.initZeros();
// Perform the radial sum and count pixels that contribute to every
// distance
FOR_ALL_ELEMENTS_IN_ARRAY3D(m)
{
ZZ(idx) = k - ZZ(center_of_rot);
YY(idx) = i - YY(center_of_rot);
XX(idx) = j - XX(center_of_rot);
// Determine distance to the center
int distance;
if (rounding)
distance = (int) ROUND(idx.module());
else
distance = (int) floor(idx.module());
// Sum te value to the pixels with the same distance
radial_mean(distance) += A3D_ELEM(m, k, i, j);
// Count the pixel
radial_count(distance)++;
}
// Perform the mean
FOR_ALL_ELEMENTS_IN_ARRAY1D(radial_mean)
radial_mean(i) /= (T) radial_count(i);
}
//@}
#endif
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