diff options
Diffstat (limited to 'include/astra/ParallelBeamLinearKernelProjector2D.inl')
| -rw-r--r-- | include/astra/ParallelBeamLinearKernelProjector2D.inl | 151 |
1 files changed, 75 insertions, 76 deletions
diff --git a/include/astra/ParallelBeamLinearKernelProjector2D.inl b/include/astra/ParallelBeamLinearKernelProjector2D.inl index d2c529f..61e4973 100644 --- a/include/astra/ParallelBeamLinearKernelProjector2D.inl +++ b/include/astra/ParallelBeamLinearKernelProjector2D.inl @@ -51,80 +51,80 @@ 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 -// +/* 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 <typename Policy> void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p) { @@ -143,13 +143,12 @@ void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom, 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 Dx, Dy, Ex, Ey, x, y, c, r, deltac, deltar, offset; + float32 Dx, Dy, Ex, Ey, c, r, deltac, deltar, offset; float32 RxOverRy, RyOverRx, lengthPerRow, lengthPerCol; int iVolumeIndex, iRayIndex, row, col, iDetector; |