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/*
-----------------------------------------------------------------------
Copyright: 2010-2018, imec Vision Lab, University of Antwerp
2014-2018, CWI, Amsterdam
Contact: astra@astra-toolbox.com
Website: http://www.astra-toolbox.com/
This file is part of the ASTRA Toolbox.
The ASTRA Toolbox 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 3 of the License, or
(at your option) any later version.
The ASTRA Toolbox 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 the ASTRA Toolbox. If not, see <http://www.gnu.org/licenses/>.
-----------------------------------------------------------------------
*/
template <typename Policy>
void CParallelBeamStripKernelProjector2D::project(Policy& p)
{
projectBlock_internal(0, m_pProjectionGeometry->getProjectionAngleCount(),
0, m_pProjectionGeometry->getDetectorCount(), p);
}
template <typename Policy>
void CParallelBeamStripKernelProjector2D::projectSingleProjection(int _iProjection, Policy& p)
{
projectBlock_internal(_iProjection, _iProjection + 1,
0, m_pProjectionGeometry->getDetectorCount(), p);
}
template <typename Policy>
void CParallelBeamStripKernelProjector2D::projectSingleRay(int _iProjection, int _iDetector, Policy& p)
{
projectBlock_internal(_iProjection, _iProjection + 1,
_iDetector, _iDetector + 1, p);
}
//----------------------------------------------------------------------------------------
/* PROJECT BLOCK
Kernel limitations: isotropic pixels (PixelLengthX == PixelLengthY)
For each angle/detector pair:
Let DL=(DLx,DLy) denote the left of the detector (point) in volume coordinates, and
Let DR=(DRx,DRy) denote the right of the detector (point) in volume coordinates, and
let R=(Rx,Ry) denote the direction of the ray (vector).
For mainly vertical rays (|Rx|<=|Ry|),
let E=(Ex,Ey) denote the centre of the most upper left pixel:
E = (WindowMinX + PixelLengthX/2, WindowMaxY - PixelLengthY/2),
and let F=(Fx,Fy) denote a vector to the next pixel
F = (PixelLengthX, 0)
The intersection of the left edge of the strip (DL+aR) with the centre line of the upper row of pixels (E+bF) is
{ DLx + a*Rx = Ex + b*Fx
{ DLy + a*Ry = Ey + b*Fy
Solving for (a,b) results in:
a = (Ey + b*Fy - DLy)/Ry
= (Ey - DLy)/Ry
b = (DLx + a*Rx - Ex)/Fx
= (DLx + (Ey - DLy)*Rx/Ry - Ex)/Fx
Define cL as the x-value of the intersection of the left edge of the strip with the upper row in pixel coordinates.
cL = b
cR, the x-value of the intersection of the right edge of the strip with the upper row in pixel coordinates can be found similarly.
The intersection of the ray (DL+aR) with the left line of the second row of pixels (E'+bF) with
E'=(WindowMinX + PixelLengthX/2, WindowMaxY - 3*PixelLengthY/2)
expressed in x-value pixel coordinates is
cL' = (DLx + (Ey' - DLy)*Rx/Ry - Ex)/Fx.
And thus:
deltac = cL' - cL = (DLx + (Ey' - DLy)*Rx/Ry - Ex)/Fx - (DLx + (Ey - DLy)*Rx/Ry - Ex)/Fx
= [(Ey' - DLy)*Rx/Ry - (Ey - DLy)*Rx/Ry]/Fx
= [Ey' - Ey]*(Rx/Ry)/Fx
= [Ey' - Ey]*(Rx/Ry)/Fx
= -PixelLengthY*(Rx/Ry)/Fx.
The projection weight for a certain pixel is defined by the area between two points of
_____ LengthPerRow
/| | |\
/ | | | \
__/ | | | \__ 0
-T -S 0 S T
with S = 1/2 - 1/2*|Rx/Ry|, T = 1/2 + 1/2*|Rx/Ry|, and LengthPerRow = pixelLengthX * sqrt(Rx^2+Ry^2) / |Ry|
For a certain row, all columns that are 'hit' by this kernel lie in the interval
(col_left, col_right) = (floor(cL-1/2+S), floor(cR+3/2-S))
The offsets for both is
(offsetL, offsetR) = (cL - floor(col_left), cR - floor(col_left))
The projection weight is found by the difference between the integrated values of the kernel
offset <= -T Kernel = 0
-T < offset <= -S Kernel = PixelArea/2*(T+offset)^2/(T-S)
-S < offset <= S Kernel = PixelArea/2 + offset
S < offset <= T Kernel = PixelArea - PixelArea/2*(T-offset)^2/(T-S)
T <= offset: Kernel = PixelArea
*/
template <typename Policy>
void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p)
{
// get vector geometry
const CParallelVecProjectionGeometry2D* pVecProjectionGeometry;
if (dynamic_cast<CParallelProjectionGeometry2D*>(m_pProjectionGeometry)) {
pVecProjectionGeometry = dynamic_cast<CParallelProjectionGeometry2D*>(m_pProjectionGeometry)->toVectorGeometry();
} else {
pVecProjectionGeometry = dynamic_cast<CParallelVecProjectionGeometry2D*>(m_pProjectionGeometry);
}
// precomputations
const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX();
const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY();
const float32 pixelArea = pixelLengthX * pixelLengthY;
const float32 inv_pixelLengthX = 1.0f / pixelLengthX;
const float32 inv_pixelLengthY = 1.0f / pixelLengthY;
const int colCount = m_pVolumeGeometry->getGridColCount();
const int rowCount = m_pVolumeGeometry->getGridRowCount();
const int detCount = pVecProjectionGeometry->getDetectorCount();
// loop angles
for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) {
// variables
float32 DLx, DLy, DRx, DRy, Ex, Ey, S, T, deltac, deltar, offsetL, offsetR, invTminS;
float32 res, RxOverRy, RyOverRx, cL, cR, rL, rR;
int iVolumeIndex, iRayIndex, iDetector;
int row, row_top, row_bottom, col, col_left, col_right;
const SParProjection * proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle];
bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY);
if (vertical) {
RxOverRy = proj->fRayX/proj->fRayY;
deltac = -m_pVolumeGeometry->getPixelLengthY() * RxOverRy * inv_pixelLengthX;
S = 0.5f - 0.5f*fabs(RxOverRy);
T = 0.5f + 0.5f*fabs(RxOverRy);
invTminS = 1.0f / (T-S);
} else {
RyOverRx = proj->fRayY/proj->fRayX;
deltar = -m_pVolumeGeometry->getPixelLengthX() * RyOverRx * inv_pixelLengthY;
S = 0.5f - 0.5f*fabs(RyOverRx);
T = 0.5f + 0.5f*fabs(RyOverRx);
invTminS = 1.0f / (T-S);
}
Ex = m_pVolumeGeometry->getWindowMinX() + pixelLengthX*0.5f;
Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f;
// loop detectors
for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) {
iRayIndex = iAngle * detCount + iDetector;
// POLICY: RAY PRIOR
if (!p.rayPrior(iRayIndex)) continue;
DLx = proj->fDetSX + iDetector * proj->fDetUX;
DLy = proj->fDetSY + iDetector * proj->fDetUY;
DRx = DLx + proj->fDetUX;
DRy = DLy + proj->fDetUY;
// vertically
if (vertical) {
// calculate cL and cR for row 0
cL = (DLx + (Ey - DLy)*RxOverRy - Ex) * inv_pixelLengthX;
cR = (DRx + (Ey - DRy)*RxOverRy - Ex) * inv_pixelLengthX;
if (cR < cL) {
float32 tmp = cL;
cL = cR;
cR = tmp;
}
// loop rows
for (row = 0; row < rowCount; ++row, cL += deltac, cR += deltac) {
col_left = int(cL-0.5f+S);
col_right = int(cR+1.5-S);
if (col_left < 0) col_left = 0;
if (col_right > colCount-1) col_right = colCount-1;
float32 tmp = float32(col_left);
offsetL = cL - tmp;
offsetR = cR - tmp;
// loop columns
for (col = col_left; col <= col_right; ++col, offsetL -= 1.0f, offsetR -= 1.0f) {
iVolumeIndex = row * colCount + col;
// POLICY: PIXEL PRIOR + ADD + POSTERIOR
if (p.pixelPrior(iVolumeIndex)) {
// right ray edge
if (T <= offsetR) res = 1.0f;
else if (S < offsetR) res = 1.0f - 0.5f*(T-offsetR)*(T-offsetR)*invTminS;
else if (-S < offsetR) res = 0.5f + offsetR;
else if (-T < offsetR) res = 0.5f*(offsetR+T)*(offsetR+T)*invTminS;
else res = 0.0f;
// left ray edge
if (T <= offsetL) res -= 1.0f;
else if (S < offsetL) res -= 1.0f - 0.5f*(T-offsetL)*(T-offsetL)*invTminS;
else if (-S < offsetL) res -= 0.5f + offsetL;
else if (-T < offsetL) res -= 0.5f*(offsetL+T)*(offsetL+T)*invTminS;
p.addWeight(iRayIndex, iVolumeIndex, pixelArea*res);
p.pixelPosterior(iVolumeIndex);
}
}
}
}
// horizontally
else {
// calculate rL and rR for row 0
rL = -(DLy + (Ex - DLx)*RyOverRx - Ey) * inv_pixelLengthY;
rR = -(DRy + (Ex - DRx)*RyOverRx - Ey) * inv_pixelLengthY;
if (rR < rL) {
float32 tmp = rL;
rL = rR;
rR = tmp;
}
// loop columns
for (col = 0; col < colCount; ++col, rL += deltar, rR += deltar) {
row_top = int(rL-0.5f+S);
row_bottom = int(rR+1.5-S);
if (row_top < 0) row_top = 0;
if (row_bottom > rowCount-1) row_bottom = rowCount-1;
float32 tmp = float32(row_top);
offsetL = rL - tmp;
offsetR = rR - tmp;
// loop rows
for (row = row_top; row <= row_bottom; ++row, offsetL -= 1.0f, offsetR -= 1.0f) {
iVolumeIndex = row * colCount + col;
// POLICY: PIXEL PRIOR + ADD + POSTERIOR
if (p.pixelPrior(iVolumeIndex)) {
// right ray edge
if (T <= offsetR) res = 1.0f;
else if (S < offsetR) res = 1.0f - 0.5f*(T-offsetR)*(T-offsetR)*invTminS;
else if (-S < offsetR) res = 0.5f + offsetR;
else if (-T < offsetR) res = 0.5f*(offsetR+T)*(offsetR+T)*invTminS;
else res = 0.0f;
// left ray edge
if (T <= offsetL) res -= 1.0f;
else if (S < offsetL) res -= 1.0f - 0.5f*(T-offsetL)*(T-offsetL)*invTminS;
else if (-S < offsetL) res -= 0.5f + offsetL;
else if (-T < offsetL) res -= 0.5f*(offsetL+T)*(offsetL+T)*invTminS;
p.addWeight(iRayIndex, iVolumeIndex, pixelArea*res);
p.pixelPosterior(iVolumeIndex);
}
}
}
}
// POLICY: RAY POSTERIOR
p.rayPosterior(iRayIndex);
} // end loop detector
} // end loop angles
if (dynamic_cast<CParallelProjectionGeometry2D*>(m_pProjectionGeometry))
delete pVecProjectionGeometry;
}
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