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-rw-r--r--include/astra/ParallelBeamStripKernelProjector2D.inl166
1 files changed, 114 insertions, 52 deletions
diff --git a/include/astra/ParallelBeamStripKernelProjector2D.inl b/include/astra/ParallelBeamStripKernelProjector2D.inl
index 85faaa3..f0203f2 100644
--- a/include/astra/ParallelBeamStripKernelProjector2D.inl
+++ b/include/astra/ParallelBeamStripKernelProjector2D.inl
@@ -49,6 +49,68 @@ void CParallelBeamStripKernelProjector2D::projectSingleRay(int _iProjection, int
//----------------------------------------------------------------------------------------
// 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)
{
@@ -61,9 +123,11 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
}
// precomputations
- const float32 inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX();
- const float32 inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY();
- const float32 pixelArea = m_pVolumeGeometry->getPixelLengthX() * m_pVolumeGeometry->getPixelLengthY();
+ 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();
@@ -73,8 +137,8 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) {
// variables
- float32 detLX, detLY, detRX, detRY, S, T, update_c, update_r, offsetL, offsetR, invTminS;
- float32 res, fRxOverRy, fRyOverRx;
+ 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;
@@ -82,19 +146,22 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY);
if (vertical) {
- fRxOverRy = proj->fRayX/proj->fRayY;
- update_c = -m_pVolumeGeometry->getPixelLengthY() * fRxOverRy * inv_pixelLengthX;
- S = 0.5f - 0.5f*fabs(fRxOverRy);
- T = 0.5f + 0.5f*fabs(fRxOverRy);
+ 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 {
- fRyOverRx = proj->fRayY/proj->fRayX;
- update_r = -m_pVolumeGeometry->getPixelLengthX() * fRyOverRx * inv_pixelLengthY;
- S = 0.5f - 0.5f*fabs(fRyOverRx);
- T = 0.5f + 0.5f*fabs(fRyOverRx);
+ 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->getWindowMinY() + pixelLengthX*0.5f;
+ Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f;
+
// loop detectors
for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) {
@@ -103,19 +170,17 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
// POLICY: RAY PRIOR
if (!p.rayPrior(iRayIndex)) continue;
- detLX = proj->fDetSX + iDetector * proj->fDetUX;
- detLY = proj->fDetSY + iDetector * proj->fDetUY;
- detRX = detLX + proj->fDetUX;
- detRY = detLY + proj->fDetUY;
+ 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
- float32 xL = detLX + fRxOverRy*(m_pVolumeGeometry->pixelRowToCenterY(0)-detLY);
- float32 cL = (xL - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f;
- float32 xR = detRX + fRxOverRy*(m_pVolumeGeometry->pixelRowToCenterY(0)-detRY);
- float32 cR = (xR - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f;
+ cL = (DLx + (Ey - DLy)*RxOverRy - Ex) * inv_pixelLengthX;
+ cR = (DRx + (Ey - DRy)*RxOverRy - Ex) * inv_pixelLengthX;
if (cR < cL) {
float32 tmp = cL;
@@ -123,8 +188,8 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
cR = tmp;
}
- // for each row
- for (row = 0; row < rowCount; ++row, cL += update_c, cR += update_c) {
+ // 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);
@@ -132,27 +197,27 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
if (col_left < 0) col_left = 0;
if (col_right > colCount-1) col_right = colCount-1;
- offsetL = cL - float32(col_left);
- offsetR = cR - float32(col_left);
+ float32 tmp = float32(col_left);
+ offsetL = cL - tmp;
+ offsetR = cR - tmp;
- // for each column
+ // 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;
+ 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;
+ 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;
@@ -167,10 +232,8 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
else {
// calculate rL and rR for row 0
- float32 yL = detLY + fRyOverRx*(m_pVolumeGeometry->pixelColToCenterX(0)-detLX);
- float32 rL = (m_pVolumeGeometry->getWindowMaxY() - yL) * inv_pixelLengthY - 0.5f;
- float32 yR = detRY + fRyOverRx*(m_pVolumeGeometry->pixelColToCenterX(0)-detRX);
- float32 rR = (m_pVolumeGeometry->getWindowMaxY() - yR) * inv_pixelLengthY - 0.5f;
+ rL = -(DLy + (Ex - DLx)*RyOverRx - Ey) * inv_pixelLengthY;
+ rR = -(DRy + (Ex - DRx)*RyOverRx - Ey) * inv_pixelLengthY;
if (rR < rL) {
float32 tmp = rL;
@@ -178,8 +241,8 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
rR = tmp;
}
- // for each column
- for (col = 0; col < colCount; ++col, rL += update_r, rR += update_r) {
+ // 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);
@@ -187,31 +250,30 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
if (row_top < 0) row_top = 0;
if (row_bottom > rowCount-1) row_bottom = rowCount-1;
- offsetL = rL - float32(row_top);
- offsetR = rR - float32(row_top);
+ float32 tmp = float32(row_top);
+ offsetL = rL - tmp;
+ offsetR = rR - tmp;
- // for each row
+ // 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;
+ 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;
+ 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);
}
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