From 1ff4a270a7df1edb54dd91fe653d6a936b959b3a Mon Sep 17 00:00:00 2001 From: Wim van Aarle Date: Wed, 27 May 2015 15:48:48 +0200 Subject: some marginal gains + added documentation --- include/astra/FanFlatBeamLineKernelProjector2D.inl | 156 ++++++--------- .../astra/ParallelBeamBlobKernelProjector2D.inl | 119 ++++++++---- .../astra/ParallelBeamLineKernelProjector2D.inl | 209 ++++++++++++++------- .../astra/ParallelBeamLinearKernelProjector2D.inl | 153 ++++++++++----- .../astra/ParallelBeamStripKernelProjector2D.inl | 166 +++++++++++----- 5 files changed, 509 insertions(+), 294 deletions(-) diff --git a/include/astra/FanFlatBeamLineKernelProjector2D.inl b/include/astra/FanFlatBeamLineKernelProjector2D.inl index 1676cb1..23438fb 100644 --- a/include/astra/FanFlatBeamLineKernelProjector2D.inl +++ b/include/astra/FanFlatBeamLineKernelProjector2D.inl @@ -25,9 +25,7 @@ along with the ASTRA Toolbox. If not, see . ----------------------------------------------------------------------- $Id$ */ - - -using namespace astra; +#define policy_weight(p,rayindex,volindex,weight) if (p.pixelPrior(volindex)) { p.addWeight(rayindex, volindex, weight); p.pixelPosterior(volindex); } template void CFanFlatBeamLineKernelProjector2D::project(Policy& p) @@ -55,12 +53,6 @@ void CFanFlatBeamLineKernelProjector2D::projectSingleRay(int _iProjection, int _ template void CFanFlatBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p) { - // variables - float32 detX, detY, S, T, I, x, y, c, r, update_c, update_r, offset; - float32 lengthPerRow, lengthPerCol, inv_pixelLengthX, inv_pixelLengthY, invTminSTimesLengthPerRow, invTminSTimesLengthPerCol; - int iVolumeIndex, iRayIndex, row, col, iAngle, iDetector, colCount, rowCount, detCount; - const SFanProjection * proj = 0; - // get vector geometry const CFanFlatVecProjectionGeometry2D* pVecProjectionGeometry; if (dynamic_cast(m_pProjectionGeometry)) { @@ -70,16 +62,26 @@ void CFanFlatBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, in } // precomputations - inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX(); - inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY(); - colCount = m_pVolumeGeometry->getGridColCount(); - rowCount = m_pVolumeGeometry->getGridRowCount(); - detCount = pVecProjectionGeometry->getDetectorCount(); + const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX(); + const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY(); + 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(); + const float32 Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f; + const float32 Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f; // loop angles - for (iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) { + #pragma omp parallel for + for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) { + + // variables + float32 Dx, Dy, Rx, Ry, S, T, weight, c, r, deltac, deltar, offset, RxOverRy, RyOverRx; + float32 lengthPerRow, lengthPerCol, invTminSTimesLengthPerRow, invTminSTimesLengthPerCol; + int iVolumeIndex, iRayIndex, row, col, iDetector; - proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle]; + const SFanProjection * proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle]; // loop detectors for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) { @@ -89,156 +91,116 @@ void CFanFlatBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, in // POLICY: RAY PRIOR if (!p.rayPrior(iRayIndex)) continue; - detX = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX; - detY = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY; + Dx = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX; + Dy = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY; - float32 fRayX = proj->fSrcX - detX; - float32 fRayY = proj->fSrcY - detY; + Rx = proj->fSrcX - Dx; + Ry = proj->fSrcY - Dy; - bool vertical = fabs(fRayX) < fabs(fRayY); + bool vertical = fabs(Rx) < fabs(Ry); if (vertical) { - lengthPerRow = m_pVolumeGeometry->getPixelLengthX() * sqrt(fRayY*fRayY + fRayX*fRayX) / abs(fRayY); - update_c = -m_pVolumeGeometry->getPixelLengthY() * (fRayX/fRayY) * inv_pixelLengthX; - S = 0.5f - 0.5f*fabs(fRayX/fRayY); - T = 0.5f + 0.5f*fabs(fRayX/fRayY); + RxOverRy = Rx/Ry; + lengthPerRow = pixelLengthX * sqrt(Rx*Rx + Ry*Ry) / abs(Ry); + deltac = -pixelLengthY * RxOverRy * inv_pixelLengthX; + S = 0.5f - 0.5f*fabs(RxOverRy); + T = 0.5f + 0.5f*fabs(RxOverRy); invTminSTimesLengthPerRow = lengthPerRow / (T - S); } else { - lengthPerCol = m_pVolumeGeometry->getPixelLengthY() * sqrt(fRayY*fRayY + fRayX*fRayX) / abs(fRayX); - update_r = -m_pVolumeGeometry->getPixelLengthX() * (fRayY/fRayX) * inv_pixelLengthY; - S = 0.5f - 0.5f*fabs(fRayY/fRayX); - T = 0.5f + 0.5f*fabs(fRayY/fRayX); + RyOverRx = Ry/Rx; + lengthPerCol = pixelLengthY * sqrt(Rx*Rx + Ry*Ry) / abs(Rx); + deltar = -pixelLengthX * RyOverRx * inv_pixelLengthY; + S = 0.5f - 0.5f*fabs(RyOverRx); + T = 0.5f + 0.5f*fabs(RyOverRx); invTminSTimesLengthPerCol = lengthPerCol / (T - S); } + bool isin = false; + // vertically if (vertical) { - // calculate x for row 0 - x = detX + (fRayX/fRayY)*(m_pVolumeGeometry->pixelRowToCenterY(0)-detY); - c = (x - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f; + // calculate c for row 0 + c = (Dx + (Ey - Dy)*RxOverRy - Ex) * inv_pixelLengthX; // for each row - for (row = 0; row < rowCount; ++row, c += update_c) { + for (row = 0; row < rowCount; ++row, c += deltac) { col = int(c+0.5f); + if (col <= 0 || col >= colCount-1) { if (!isin) continue; else break; } offset = c - float32(col); - if (col <= 0 || col >= colCount-1) continue; - // left if (offset < -S) { - I = (offset + T) * invTminSTimesLengthPerRow; + weight = (offset + T) * invTminSTimesLengthPerRow; iVolumeIndex = row * colCount + col - 1; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerRow-weight) iVolumeIndex++; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, weight) } // right else if (S < offset) { - I = (offset - S) * invTminSTimesLengthPerRow; + weight = (offset - S) * invTminSTimesLengthPerRow; iVolumeIndex = row * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerRow-weight) iVolumeIndex++; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, weight) } // centre else { iVolumeIndex = row * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerRow) } - + isin = true; } } // horizontally else { - // calculate y for col 0 - y = detY + (fRayY/fRayX)*(m_pVolumeGeometry->pixelColToCenterX(0)-detX); - r = (m_pVolumeGeometry->getWindowMaxY() - y) * inv_pixelLengthY - 0.5f; + // calculate r for col 0 + r = -(Dy + (Ex - Dx)*RyOverRx - Ey) * inv_pixelLengthY; // for each col - for (col = 0; col < colCount; ++col, r += update_r) { + for (col = 0; col < colCount; ++col, r += deltar) { int row = int(r+0.5f); + if (row <= 0 || row >= rowCount-1) { if (!isin) continue; else break; } offset = r - float32(row); - if (row <= 0 || row >= rowCount-1) continue; - // up if (offset < -S) { - I = (offset + T) * invTminSTimesLengthPerCol; + weight = (offset + T) * invTminSTimesLengthPerCol; iVolumeIndex = (row-1) * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol-I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol-weight) iVolumeIndex += colCount; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, weight) } // down else if (S < offset) { - I = (offset - S) * invTminSTimesLengthPerCol; + weight = (offset - S) * invTminSTimesLengthPerCol; iVolumeIndex = row * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol-I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol-weight) iVolumeIndex += colCount; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, weight) } // centre else { iVolumeIndex = row * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol) } - + isin = true; } } diff --git a/include/astra/ParallelBeamBlobKernelProjector2D.inl b/include/astra/ParallelBeamBlobKernelProjector2D.inl index 1945cdd..c2aa193 100644 --- a/include/astra/ParallelBeamBlobKernelProjector2D.inl +++ b/include/astra/ParallelBeamBlobKernelProjector2D.inl @@ -50,6 +50,63 @@ void CParallelBeamBlobKernelProjector2D::projectSingleRay(int _iProjection, int //---------------------------------------------------------------------------------------- // PROJECT BLOCK - vector projection geometry +// +// Kernel limitations: isotropic pixels (PixelLengthX == PixelLengthY) +// +// For each angle/detector pair: +// +// Let D=(Dx,Dy) denote the centre 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 ray (D+aR) with the centre line of the upper row of pixels (E+bF) is +// { Dx + a*Rx = Ex + b*Fx +// { Dy + a*Ry = Ey + b*Fy +// Solving for (a,b) results in: +// a = (Ey + b*Fy - Dy)/Ry +// = (Ey - Dy)/Ry +// b = (Dx + a*Rx - Ex)/Fx +// = (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx +// +// Define c as the x-value of the intersection of the ray with the upper row in pixel coordinates. +// c = b +// +// The intersection of the ray (D+aR) with the centre 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 +// c' = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx. +// And thus: +// deltac = c' - c = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx - (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx +// = [(Ey' - Dy)*Rx/Ry - (Ey - Dy)*Rx/Ry]/Fx +// = [Ey' - Ey]*(Rx/Ry)/Fx +// = [Ey' - Ey]*(Rx/Ry)/Fx +// = -PixelLengthY*(Rx/Ry)/Fx. +// +// Given c on a certain row, its pixel directly on its left (col), and the distance (offset) to it, can be found: +// col = floor(c) +// offset = c - col +// +// The index of this pixel is +// volumeIndex = row * colCount + col +// +// +// Mainly horizontal rays (|Rx|<=|Ry|) are handled in a similar fashion: +// +// E = (WindowMinX + PixelLengthX/2, WindowMaxY - PixelLengthY/2), +// F = (0, -PixelLengthX) +// +// a = (Ex + b*Fx - Dx)/Rx = (Ex - Dx)/Rx +// b = (Dy + a*Ry - Ey)/Fy = (Dy + (Ex - Dx)*Ry/Rx - Ey)/Fy +// r = b +// deltar = PixelLengthX*(Ry/Rx)/Fy. +// row = floor(r+1/2) +// offset = r - row +// template void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p) { @@ -62,6 +119,8 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i } // precomputations + const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX(); + const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY(); const float32 inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX(); const float32 inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY(); const int colCount = m_pVolumeGeometry->getGridColCount(); @@ -73,7 +132,7 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) { // variables - float32 detX, detY, x, y, c, r, update_c, update_r, offset, invBlobExtent, weight, d; + float32 Dx, Dy, Ex, Ey, c, r, deltac, deltar, offset, invBlobExtent, RxOverRy, RyOverRx; int iVolumeIndex, iRayIndex, row, col, iDetector; int col_left, col_right, row_top, row_bottom, index; @@ -81,15 +140,18 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY); if (vertical) { - update_c = -m_pVolumeGeometry->getPixelLengthY() * (proj->fRayX/proj->fRayY) * inv_pixelLengthX; - float32 normR = sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX); - invBlobExtent = m_pVolumeGeometry->getPixelLengthY() / abs(m_fBlobSize * normR / proj->fRayY); + RxOverRy = proj->fRayX/proj->fRayY; + deltac = -m_pVolumeGeometry->getPixelLengthY() * (proj->fRayX/proj->fRayY) * inv_pixelLengthX; + invBlobExtent = m_pVolumeGeometry->getPixelLengthY() / abs(m_fBlobSize * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / proj->fRayY); } else { - update_r = -m_pVolumeGeometry->getPixelLengthX() * (proj->fRayY/proj->fRayX) * inv_pixelLengthY; - float32 normR = sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX); - invBlobExtent = m_pVolumeGeometry->getPixelLengthX() / abs(m_fBlobSize * normR / proj->fRayX); + RyOverRx = proj->fRayY/proj->fRayX; + deltar = -m_pVolumeGeometry->getPixelLengthX() * (proj->fRayY/proj->fRayX) * inv_pixelLengthY; + invBlobExtent = m_pVolumeGeometry->getPixelLengthX() / abs(m_fBlobSize * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / proj->fRayX); } + Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f; + Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f; + // loop detectors for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) { @@ -98,18 +160,17 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i // POLICY: RAY PRIOR if (!p.rayPrior(iRayIndex)) continue; - detX = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX; - detY = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY; + Dx = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX; + Dy = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY; // vertically if (vertical) { - // calculate x for row 0 - x = detX + (proj->fRayX/proj->fRayY)*(m_pVolumeGeometry->pixelRowToCenterY(0)-detY); - c = (x - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f; + // calculate c for row 0 + c = (Dx + (Ey - Dy)*RxOverRy - Ex) * inv_pixelLengthX; - // for each row - for (row = 0; row < rowCount; ++row, c += update_c) { + // loop rows + for (row = 0; row < rowCount; ++row, c += deltac) { col_left = int(c - 0.5f - m_fBlobSize); col_right = int(c + 0.5f + m_fBlobSize); @@ -117,17 +178,15 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i if (col_left < 0) col_left = 0; if (col_right > colCount-1) col_right = colCount-1; - // for each column + // loop columns for (col = col_left; col <= col_right; ++col) { - offset = abs(c - float32(col)) * invBlobExtent; - index = (int)(offset*m_iBlobSampleCount+0.5f); - weight = m_pfBlobValues[min(index,m_iBlobSampleCount-1)]; - iVolumeIndex = row * colCount + col; // POLICY: PIXEL PRIOR + ADD + POSTERIOR if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, weight); + offset = abs(c - float32(col)) * invBlobExtent; + index = (int)(offset*m_iBlobSampleCount+0.5f); + p.addWeight(iRayIndex, iVolumeIndex, m_pfBlobValues[min(index,m_iBlobSampleCount-1)]); p.pixelPosterior(iVolumeIndex); } } @@ -137,12 +196,11 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i // horizontally else { - // calculate y for col 0 - y = detY + (proj->fRayY/proj->fRayX)*(m_pVolumeGeometry->pixelColToCenterX(0)-detX); - r = (m_pVolumeGeometry->getWindowMaxY() - y) * inv_pixelLengthY - 0.5f; + // calculate r for col 0 + r = -(Dy + (Ex - Dx)*RyOverRx - Ey) * inv_pixelLengthY; - // for each col - for (col = 0; col < colCount; ++col, r += update_r) { + // loop columns + for (col = 0; col < colCount; ++col, r += deltar) { row_top = int(r - 0.5f - m_fBlobSize); row_bottom = int(r + 0.5f + m_fBlobSize); @@ -150,21 +208,18 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i if (row_top < 0) row_top = 0; if (row_bottom > rowCount-1) row_bottom = rowCount-1; - // for each column + // loop rows for (row = row_top; row <= row_bottom; ++row) { - offset = abs(r - float32(row)) * invBlobExtent; - index = (int)(offset*m_iBlobSampleCount+0.5f); - weight = m_pfBlobValues[min(index,m_iBlobSampleCount-1)]; - iVolumeIndex = row * colCount + col; // POLICY: PIXEL PRIOR + ADD + POSTERIOR if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, weight); + offset = abs(r - float32(row)) * invBlobExtent; + index = (int)(offset*m_iBlobSampleCount+0.5f); + p.addWeight(iRayIndex, iVolumeIndex, m_pfBlobValues[min(index,m_iBlobSampleCount-1)]); p.pixelPosterior(iVolumeIndex); } } - } } diff --git a/include/astra/ParallelBeamLineKernelProjector2D.inl b/include/astra/ParallelBeamLineKernelProjector2D.inl index 9c58d60..199cfd7 100644 --- a/include/astra/ParallelBeamLineKernelProjector2D.inl +++ b/include/astra/ParallelBeamLineKernelProjector2D.inl @@ -25,6 +25,7 @@ along with the ASTRA Toolbox. If not, see . ----------------------------------------------------------------------- $Id$ */ +#define policy_weight(p,rayindex,volindex,weight) if (p.pixelPrior(volindex)) { p.addWeight(rayindex, volindex, weight); p.pixelPosterior(volindex); } template void CParallelBeamLineKernelProjector2D::project(Policy& p) @@ -48,10 +49,95 @@ void CParallelBeamLineKernelProjector2D::projectSingleRay(int _iProjection, int } - - //---------------------------------------------------------------------------------------- // PROJECT BLOCK - vector projection geometry +// +// Kernel limitations: isotropic pixels (PixelLengthX == PixelLengthY) +// +// For each angle/detector pair: +// +// Let D=(Dx,Dy) denote the centre 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 ray (D+aR) with the centre line of the upper row of pixels (E+bF) is +// { Dx + a*Rx = Ex + b*Fx +// { Dy + a*Ry = Ey + b*Fy +// Solving for (a,b) results in: +// a = (Ey + b*Fy - Dy)/Ry +// = (Ey - Dy)/Ry +// b = (Dx + a*Rx - Ex)/Fx +// = (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx +// +// Define c as the x-value of the intersection of the ray with the upper row in pixel coordinates. +// c = b +// +// The intersection of the ray (D+aR) with the centre 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 +// c' = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx. +// And thus: +// deltac = c' - c = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx - (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx +// = [(Ey' - Dy)*Rx/Ry - (Ey - Dy)*Rx/Ry]/Fx +// = [Ey' - Ey]*(Rx/Ry)/Fx +// = [Ey' - Ey]*(Rx/Ry)/Fx +// = -PixelLengthY*(Rx/Ry)/Fx. +// +// Given c on a certain row, its closest pixel (col), and the distance (offset) to it, can be found: +// col = floor(c+1/2) +// offset = c - col +// +// The index of this pixel is +// volumeIndex = row * colCount + col +// +// The projection kernel is defined by +// +// _____ 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| +// +// And thus +// { (offset+T)/(T-S) * LengthPerRow if -T <= offset < S +// W_(rayIndex,volIndex) = { LengthPerRow if -S <= offset <= S +// { (offset-S)/(T-S) * LengthPerRow if S < offset <= T +// +// If -T <= offset < S, the weight for the pixel directly to the left is +// W_(rayIndex,volIndex-1) = LengthPerRow - (offset+T)/(T-S) * LengthPerRow, +// and if S < offset <= T, the weight for the pixel directly to the right is +// W_(rayIndex,volIndex+1) = LengthPerRow - (offset-S)/(T-S) * LengthPerRow. +// +// +// Mainly horizontal rays (|Rx|<=|Ry|) are handled in a similar fashion: +// +// E = (WindowMinX + PixelLengthX/2, WindowMaxY - PixelLengthY/2), +// F = (0, -PixelLengthX) +// +// a = (Ex + b*Fx - Dx)/Rx = (Ex - Dx)/Rx +// b = (Dy + a*Ry - Ey)/Fy = (Dy + (Ex - Dx)*Ry/Rx - Ey)/Fy +// r = b +// deltar = PixelLengthX*(Ry/Rx)/Fy. +// row = floor(r+1/2) +// offset = r - row +// S = 1/2 - 1/2*|Ry/Rx| +// T = 1/2 + 1/2*|Ry/Rx| +// LengthPerCol = pixelLengthY * sqrt(Rx^2+Ry^2) / |Rx| +// +// { (offset+T)/(T-S) * LengthPerCol if -T <= offset < S +// W_(rayIndex,volIndex) = { LengthPerCol if -S <= offset <= S +// { (offset-S)/(T-S) * LengthPerCol if S < offset <= T +// +// W_(rayIndex,volIndex-colcount) = LengthPerCol - (offset+T)/(T-S) * LengthPerCol +// W_(rayIndex,volIndex+colcount) = LengthPerCol - (offset-S)/(T-S) * LengthPerCol +// template void CParallelBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p) { @@ -64,8 +150,10 @@ void CParallelBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, i } // precomputations - const float32 inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX(); - const float32 inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY(); + const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX(); + const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY(); + 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(); @@ -75,87 +163,92 @@ void CParallelBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, i for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) { // variables - float32 detX, detY, S, T, I, x, y, c, r, update_c, update_r, offset; - float32 lengthPerRow, lengthPerCol, invTminSTimesLengthPerRow, invTminSTimesLengthPerCol; + float32 Dx, Dy, Ex, Ey, S, T, weight, c, r, deltac, deltar, offset; + float32 RxOverRy, RyOverRx, lengthPerRow, lengthPerCol, invTminSTimesLengthPerRow, invTminSTimesLengthPerCol; int iVolumeIndex, iRayIndex, row, col, iDetector; const SParProjection * proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle]; bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY); if (vertical) { - lengthPerRow = m_pVolumeGeometry->getPixelLengthX() * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayY); - update_c = -m_pVolumeGeometry->getPixelLengthY() * (proj->fRayX/proj->fRayY) * inv_pixelLengthX; - S = 0.5f - 0.5f*fabs(proj->fRayX/proj->fRayY); - T = 0.5f + 0.5f*fabs(proj->fRayX/proj->fRayY); + RxOverRy = proj->fRayX/proj->fRayY; + lengthPerRow = pixelLengthX * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayY); + deltac = -pixelLengthY * RxOverRy * inv_pixelLengthX; + S = 0.5f - 0.5f*fabs(RxOverRy); + T = 0.5f + 0.5f*fabs(RxOverRy); invTminSTimesLengthPerRow = lengthPerRow / (T - S); } else { - lengthPerCol = m_pVolumeGeometry->getPixelLengthY() * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayX); - update_r = -m_pVolumeGeometry->getPixelLengthX() * (proj->fRayY/proj->fRayX) * inv_pixelLengthY; - S = 0.5f - 0.5f*fabs(proj->fRayY/proj->fRayX); - T = 0.5f + 0.5f*fabs(proj->fRayY/proj->fRayX); + RyOverRx = proj->fRayY/proj->fRayX; + lengthPerCol = pixelLengthY * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayX); + deltar = -pixelLengthX * RyOverRx * inv_pixelLengthY; + S = 0.5f - 0.5f*fabs(RyOverRx); + T = 0.5f + 0.5f*fabs(RyOverRx); invTminSTimesLengthPerCol = lengthPerCol / (T - S); } + Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f; + Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f; + // loop detectors - for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) { - + for (int iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) { + iRayIndex = iAngle * m_pProjectionGeometry->getDetectorCount() + iDetector; // POLICY: RAY PRIOR if (!p.rayPrior(iRayIndex)) continue; - - detX = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX; - detY = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY; + Dx = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX; + Dy = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY; + + bool isin = false; + // vertically if (vertical) { - // calculate x for row 0 - x = detX + (proj->fRayX/proj->fRayY)*(m_pVolumeGeometry->pixelRowToCenterY(0)-detY); - c = (x - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f; + // calculate c for row 0 + c = (Dx + (Ey - Dy)*RxOverRy - Ex) * inv_pixelLengthX; - // for each row - for (row = 0; row < rowCount; ++row, c += update_c) { + // loop rows + for (row = 0; row < rowCount; ++row, c += deltac) { col = int(c+0.5f); + if (col <= 0 || col >= colCount-1) { if (!isin) continue; else break; } offset = c - float32(col); - if (col <= 0 || col >= colCount-1) continue; - // left if (offset < -S) { - I = (offset + T) * invTminSTimesLengthPerRow; + weight = (offset + T) * invTminSTimesLengthPerRow; iVolumeIndex = row * colCount + col - 1; // POLICY: PIXEL PRIOR + ADD + POSTERIOR if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-I); + p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-weight); p.pixelPosterior(iVolumeIndex); } iVolumeIndex++; // POLICY: PIXEL PRIOR + ADD + POSTERIOR if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, I); + p.addWeight(iRayIndex, iVolumeIndex, weight); p.pixelPosterior(iVolumeIndex); } } // right else if (S < offset) { - I = (offset - S) * invTminSTimesLengthPerRow; + weight = (offset - S) * invTminSTimesLengthPerRow; iVolumeIndex = row * colCount + col; // POLICY: PIXEL PRIOR + ADD + POSTERIOR if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-I); + p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-weight); p.pixelPosterior(iVolumeIndex); } iVolumeIndex++; // POLICY: PIXEL PRIOR + ADD + POSTERIOR if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, I); + p.addWeight(iRayIndex, iVolumeIndex, weight); p.pixelPosterior(iVolumeIndex); } } @@ -169,73 +262,51 @@ void CParallelBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, i p.pixelPosterior(iVolumeIndex); } } - + isin = true; } } // horizontally else { - // calculate y for col 0 - y = detY + (proj->fRayY/proj->fRayX)*(m_pVolumeGeometry->pixelColToCenterX(0)-detX); - r = (m_pVolumeGeometry->getWindowMaxY() - y) * inv_pixelLengthY - 0.5f; + // calculate r for col 0 + r = -(Dy + (Ex - Dx)*RyOverRx - Ey) * inv_pixelLengthY; - // for each col - for (col = 0; col < colCount; ++col, r += update_r) { + // loop columns + for (col = 0; col < colCount; ++col, r += deltar) { - int row = int(r+0.5f); + row = int(r+0.5f); + if (row <= 0 || row >= rowCount-1) { if (!isin) continue; else break; } offset = r - float32(row); - if (row <= 0 || row >= rowCount-1) continue; - // up if (offset < -S) { - I = (offset + T) * invTminSTimesLengthPerCol; + weight = (offset + T) * invTminSTimesLengthPerCol; iVolumeIndex = (row-1) * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol-I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol-weight) iVolumeIndex += colCount; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, weight) } // down else if (S < offset) { - I = (offset - S) * invTminSTimesLengthPerCol; + weight = (offset - S) * invTminSTimesLengthPerCol; iVolumeIndex = row * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol-I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol-weight) iVolumeIndex += colCount; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, I); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, weight) } // centre else { iVolumeIndex = row * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol) } - + isin = true; } } diff --git a/include/astra/ParallelBeamLinearKernelProjector2D.inl b/include/astra/ParallelBeamLinearKernelProjector2D.inl index 79b82d4..ecbdeb3 100644 --- a/include/astra/ParallelBeamLinearKernelProjector2D.inl +++ b/include/astra/ParallelBeamLinearKernelProjector2D.inl @@ -25,6 +25,7 @@ along with the ASTRA Toolbox. If not, see . ----------------------------------------------------------------------- $Id$ */ +#define policy_weight(p,rayindex,volindex,weight) if (p.pixelPrior(volindex)) { p.addWeight(rayindex, volindex, weight); p.pixelPosterior(volindex); } template void CParallelBeamLinearKernelProjector2D::project(Policy& p) @@ -51,6 +52,79 @@ void CParallelBeamLinearKernelProjector2D::projectSingleRay(int _iProjection, in //---------------------------------------------------------------------------------------- // PROJECT BLOCK - vector projection geometry +// +// Kernel limitations: isotropic pixels (PixelLengthX == PixelLengthY) +// +// For each angle/detector pair: +// +// Let D=(Dx,Dy) denote the centre 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 ray (D+aR) with the centre line of the upper row of pixels (E+bF) is +// { Dx + a*Rx = Ex + b*Fx +// { Dy + a*Ry = Ey + b*Fy +// Solving for (a,b) results in: +// a = (Ey + b*Fy - Dy)/Ry +// = (Ey - Dy)/Ry +// b = (Dx + a*Rx - Ex)/Fx +// = (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx +// +// Define c as the x-value of the intersection of the ray with the upper row in pixel coordinates. +// c = b +// +// The intersection of the ray (D+aR) with the centre 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 +// c' = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx. +// And thus: +// deltac = c' - c = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx - (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx +// = [(Ey' - Dy)*Rx/Ry - (Ey - Dy)*Rx/Ry]/Fx +// = [Ey' - Ey]*(Rx/Ry)/Fx +// = [Ey' - Ey]*(Rx/Ry)/Fx +// = -PixelLengthY*(Rx/Ry)/Fx. +// +// Given c on a certain row, its pixel directly on its left (col), and the distance (offset) to it, can be found: +// col = floor(c) +// offset = c - col +// +// The index of this pixel is +// volumeIndex = row * colCount + col +// +// The projection kernel is defined by +// +// LengthPerRow +// /|\ +// / | \ +// __/ | \__ 0 +// p0 p1 p2 +// +// And thus +// W_(rayIndex,volIndex) = (1 - offset) * lengthPerRow +// W_(rayIndex,volIndex+1) = offset * lengthPerRow +// +// +// Mainly horizontal rays (|Rx|<=|Ry|) are handled in a similar fashion: +// +// E = (WindowMinX + PixelLengthX/2, WindowMaxY - PixelLengthY/2), +// F = (0, -PixelLengthX) +// +// a = (Ex + b*Fx - Dx)/Rx = (Ex - Dx)/Rx +// b = (Dy + a*Ry - Ey)/Fy = (Dy + (Ex - Dx)*Ry/Rx - Ey)/Fy +// r = b +// deltar = PixelLengthX*(Ry/Rx)/Fy. +// row = floor(r+1/2) +// offset = r - row +// LengthPerCol = pixelLengthY * sqrt(Rx^2+Ry^2) / |Rx| +// +// W_(rayIndex,volIndex) = (1 - offset) * lengthPerCol +// W_(rayIndex,volIndex+colcount) = offset * lengthPerCol +// template void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p) { @@ -63,8 +137,10 @@ void CParallelBeamLinearKernelProjector2D::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 pixelLengthX = m_pVolumeGeometry->getPixelLengthX(); + const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY(); + 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(); @@ -74,21 +150,26 @@ void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom, for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) { // variables - float32 detX, detY, x, y, c, r, update_c, update_r, offset; - float32 lengthPerRow, lengthPerCol; + float32 Dx, Dy, Ex, Ey, x, y, c, r, deltac, deltar, offset; + float32 RxOverRy, RyOverRx, lengthPerRow, lengthPerCol; int iVolumeIndex, iRayIndex, row, col, iDetector; const SParProjection * proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle]; bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY); if (vertical) { + RxOverRy = proj->fRayX/proj->fRayY; lengthPerRow = m_pVolumeGeometry->getPixelLengthX() * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayY); - update_c = -m_pVolumeGeometry->getPixelLengthY() * (proj->fRayX/proj->fRayY) * inv_pixelLengthX; + deltac = -pixelLengthY * RxOverRy * inv_pixelLengthX; } else { + RyOverRx = proj->fRayY/proj->fRayX; lengthPerCol = m_pVolumeGeometry->getPixelLengthY() * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayX); - update_r = -m_pVolumeGeometry->getPixelLengthX() * (proj->fRayY/proj->fRayX) * inv_pixelLengthY; + deltar = -pixelLengthX * RyOverRx * inv_pixelLengthY; } + Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f; + Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f; + // loop detectors for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) { @@ -97,70 +178,54 @@ void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom, // POLICY: RAY PRIOR if (!p.rayPrior(iRayIndex)) continue; - detX = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX; - detY = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY; + Dx = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX; + Dy = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY; + + bool isin = false; // vertically if (vertical) { - // calculate x for row 0 - x = detX + (proj->fRayX/proj->fRayY)*(m_pVolumeGeometry->pixelRowToCenterY(0)-detY); - c = (x - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f; + // calculate c for row 0 + c = (Dx + (Ey - Dy)*RxOverRy - Ex) * inv_pixelLengthX; - // for each row - for (row = 0; row < rowCount; ++row, c += update_c) { + // loop rows + for (row = 0; row < rowCount; ++row, c += deltac) { col = int(c); + if (col <= 0 || col >= colCount-1) { if (!isin) continue; else break; } offset = c - float32(col); - if (col <= 0 || col >= colCount-1) continue; - iVolumeIndex = row * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, (1.0f - offset) * lengthPerRow); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, (1.0f - offset) * lengthPerRow) iVolumeIndex++; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, offset * lengthPerRow); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, offset * lengthPerRow) + isin = true; } } // horizontally else { - // calculate y for col 0 - y = detY + (proj->fRayY/proj->fRayX)*(m_pVolumeGeometry->pixelColToCenterX(0)-detX); - r = (m_pVolumeGeometry->getWindowMaxY() - y) * inv_pixelLengthY - 0.5f; + // calculate r for col 0 + r = -(Dy + (Ex - Dx)*RyOverRx - Ey) * inv_pixelLengthY; - // for each col - for (col = 0; col < colCount; ++col, r += update_r) { + // loop columns + for (col = 0; col < colCount; ++col, r += deltar) { - int row = int(r); + row = int(r); + if (row <= 0 || row >= rowCount-1) { if (!isin) continue; else break; } offset = r - float32(row); - if (row <= 0 || row >= rowCount-1) continue; - iVolumeIndex = row * colCount + col; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, (1.0f - offset) * lengthPerCol); - p.pixelPosterior(iVolumeIndex); - } + policy_weight(p, iRayIndex, iVolumeIndex, (1.0f - offset) * lengthPerCol) iVolumeIndex += colCount; - // POLICY: PIXEL PRIOR + ADD + POSTERIOR - if (p.pixelPrior(iVolumeIndex)) { - p.addWeight(iRayIndex, iVolumeIndex, offset * lengthPerCol); - p.pixelPosterior(iVolumeIndex); - } - + policy_weight(p, iRayIndex, iVolumeIndex, offset * lengthPerCol) + + isin = true; } } 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 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); } -- cgit v1.2.3