diff options
Diffstat (limited to 'include/astra/ParallelBeamStripKernelProjector2D.inl')
| -rw-r--r-- | include/astra/ParallelBeamStripKernelProjector2D.inl | 467 |
1 files changed, 230 insertions, 237 deletions
diff --git a/include/astra/ParallelBeamStripKernelProjector2D.inl b/include/astra/ParallelBeamStripKernelProjector2D.inl index e8e3739..fdfcd90 100644 --- a/include/astra/ParallelBeamStripKernelProjector2D.inl +++ b/include/astra/ParallelBeamStripKernelProjector2D.inl @@ -29,7 +29,7 @@ template <typename Policy> void CParallelBeamStripKernelProjector2D::project(Policy& p) { projectBlock_internal(0, m_pProjectionGeometry->getProjectionAngleCount(), - 0, m_pProjectionGeometry->getDetectorCount(), p); + 0, m_pProjectionGeometry->getDetectorCount(), p); } template <typename Policy> @@ -47,251 +47,244 @@ void CParallelBeamStripKernelProjector2D::projectSingleRay(int _iProjection, int } //---------------------------------------------------------------------------------------- -// PROJECT BLOCK +/* 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) { - ASTRA_ASSERT(m_bIsInitialized); - - // Some variables - float32 theta, t; - int row, col; - int iAngle; - int iDetector; - float32 res; - float32 PL, PLimitL, PLimitR; - float32 xL, xR, XLimitL, XLimitR; - int x1L,x1R; - float32 x2L, x2R, updateX; - int iVolumeIndex, iRayIndex; - - float32 sin_theta, cos_theta, inv_sin_theta, inv_cos_theta; - float32 fabs_sin_theta, fabs_cos_theta, fabs_inv_sin_theta, fabs_inv_cos_theta; - float32 PW, PH, DW, inv_PW, inv_PH; - float32 S, T, U, V, inv_4T; + // 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 (iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) { - - // get values - theta = m_pProjectionGeometry->getProjectionAngle(iAngle); - bool switch_t = false; - if (theta >= 7*PIdiv4) theta -= 2*PI; - if (theta >= 3*PIdiv4) { - theta -= PI; - switch_t = true; - } - - // Precalculate sin, cos, 1/cos - sin_theta = sin(theta); - cos_theta = cos(theta); - inv_cos_theta = 1.0f / cos_theta; - inv_sin_theta = 1.0f / sin_theta; - - fabs_sin_theta = (sin_theta < 0.0f) ? -sin_theta : sin_theta; - fabs_cos_theta = (cos_theta < 0.0f) ? -cos_theta : cos_theta; - fabs_inv_cos_theta = (inv_cos_theta < 0.0f) ? -inv_cos_theta : inv_cos_theta; - fabs_inv_sin_theta = (inv_sin_theta < 0.0f) ? -inv_sin_theta : inv_sin_theta; - - // Other precalculations - PW = m_pVolumeGeometry->getPixelLengthX(); - PH = m_pVolumeGeometry->getPixelLengthY(); - DW = m_pProjectionGeometry->getDetectorWidth(); - inv_PW = 1.0f / PW; - inv_PH = 1.0f / PH; - - // [-45?,45?] and [135?,225?] - if (theta < PIdiv4) { - - // Precalculate kernel limits - S = -0.5f * fabs_sin_theta * fabs_inv_cos_theta; - T = -S; - U = 1.0f + S; - V = 1.0f - S; - inv_4T = 0.25f / T; - - updateX = sin_theta * inv_cos_theta; - - // loop detectors - for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) { - - iRayIndex = iAngle * m_pProjectionGeometry->getDetectorCount() + iDetector; - - // POLICY: RAY PRIOR - if (!p.rayPrior(iRayIndex)) continue; - - // get t - t = m_pProjectionGeometry->indexToDetectorOffset(iDetector); - if (switch_t) t = -t; - - // calculate left strip extremes (volume coordinates) - PL = (t - sin_theta * m_pVolumeGeometry->pixelRowToCenterY(0) - DW*0.5f) * inv_cos_theta; - PLimitL = PL - 0.5f * fabs_sin_theta * fabs_inv_cos_theta * PH; - PLimitR = PLimitL + DW * inv_cos_theta + PH * fabs_sin_theta * fabs_inv_cos_theta; - - // calculate strip extremes (pixel coordinates) - XLimitL = (PLimitL - m_pVolumeGeometry->getWindowMinX()) * inv_PW; - XLimitR = (PLimitR - m_pVolumeGeometry->getWindowMinX()) * inv_PW; - xL = (PL - m_pVolumeGeometry->getWindowMinX()) * inv_PW; - xR = xL + (DW * inv_cos_theta) * inv_PW; - - // for each row - for (row = 0; row < m_pVolumeGeometry->getGridRowCount(); ++row) { - - // get strip extremes in column indices - x1L = int((XLimitL > 0.0f) ? XLimitL : XLimitL-1.0f); - x1R = int((XLimitR > 0.0f) ? XLimitR : XLimitR-1.0f); - - // get coords w.r.t leftmost column hit by strip - x2L = xL - x1L; - x2R = xR - x1L; - - // update strip extremes for the next row - XLimitL += updateX; - XLimitR += updateX; - xL += updateX; - xR += updateX; - - // for each affected col - for (col = x1L; col <= x1R; ++col) { - - if (col < 0 || col >= m_pVolumeGeometry->getGridColCount()) { x2L -= 1.0f; x2R -= 1.0f; continue; } - - iVolumeIndex = m_pVolumeGeometry->pixelRowColToIndex(row, col); - // POLICY: PIXEL PRIOR - if (!p.pixelPrior(iVolumeIndex)) { x2L -= 1.0f; x2R -= 1.0f; continue; } - - // right - if (x2R >= V) res = 1.0f; - else if (x2R > U) res = x2R - (x2R-U)*(x2R-U)*inv_4T; - else if (x2R >= T) res = x2R; - else if (x2R > S) res = (x2R-S)*(x2R-S) * inv_4T; - else { x2L -= 1.0f; x2R -= 1.0f; continue; } - - // left - if (x2L <= S) {} // - 0.0f - else if (x2L < T) res -= (x2L-S)*(x2L-S) * inv_4T; - else if (x2L <= U) res -= x2L; - else if (x2L < V) res -= x2L - (x2L-U)*(x2L-U)*inv_4T; - else { x2L -= 1.0f; x2R -= 1.0f; continue; } - - // POLICY: ADD - p.addWeight(iRayIndex, iVolumeIndex, PW*PH * res); - - // POLICY: PIXEL POSTERIOR - p.pixelPosterior(iVolumeIndex); - - x2L -= 1.0f; - x2R -= 1.0f; - - } // end col loop - - } // end row loop - - // POLICY: RAY POSTERIOR - p.rayPosterior(iRayIndex); - - } // end detector loop - - // [45?,135?] and [225?,315?] - // horizontaly + 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); + } - // Precalculate kernel limits - S = -0.5f * fabs_cos_theta * fabs_inv_sin_theta; - T = -S; - U = 1.0f + S; - V = 1.0f - S; - inv_4T = 0.25f / T; - - updateX = cos_theta * inv_sin_theta; - - // loop detectors - for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) { - - iRayIndex = iAngle * m_pProjectionGeometry->getDetectorCount() + iDetector; - - // POLICY: RAY PRIOR - if (!p.rayPrior(iRayIndex)) continue; + Ex = m_pVolumeGeometry->getWindowMinX() + pixelLengthX*0.5f; + Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f; - // get t - t = m_pProjectionGeometry->indexToDetectorOffset(iDetector); - if (switch_t) t = -t; + // loop detectors + for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) { - // calculate left strip extremes (volume coordinates) - PL = (t - cos_theta * m_pVolumeGeometry->pixelColToCenterX(0) + DW*0.5f) * inv_sin_theta; - PLimitL = PL + 0.5f * fabs_cos_theta * fabs_inv_sin_theta * PW; - PLimitR = PLimitL - DW * inv_sin_theta - PH * fabs_cos_theta * fabs_inv_sin_theta; - - // calculate strip extremes (pixel coordinates) - XLimitL = (m_pVolumeGeometry->getWindowMaxY() - PLimitL) * inv_PH; - XLimitR = (m_pVolumeGeometry->getWindowMaxY() - PLimitR) * inv_PH; - xL = (m_pVolumeGeometry->getWindowMaxY() - PL) * inv_PH; - xR = xL + (DW * fabs_inv_sin_theta) * inv_PH; - - // for each col - for (col = 0; col < m_pVolumeGeometry->getGridColCount(); ++col) { - - // get strip extremes in column indices - x1L = int((XLimitL > 0.0f) ? XLimitL : XLimitL-1.0f); - x1R = int((XLimitR > 0.0f) ? XLimitR : XLimitR-1.0f); - - // get coords w.r.t leftmost column hit by strip - x2L = xL - x1L; - x2R = xR - x1L; - - // update strip extremes for the next row - XLimitL += updateX; - XLimitR += updateX; - xL += updateX; - xR += updateX; + iRayIndex = iAngle * detCount + iDetector; - // for each affected col - for (row = x1L; row <= x1R; ++row) { - - if (row < 0 || row >= m_pVolumeGeometry->getGridRowCount()) { x2L -= 1.0f; x2R -= 1.0f; continue; } - - iVolumeIndex = m_pVolumeGeometry->pixelRowColToIndex(row, col); - - // POLICY: PIXEL PRIOR - if (!p.pixelPrior(iVolumeIndex)) { x2L -= 1.0f; x2R -= 1.0f; continue; } - - // right - if (x2R >= V) res = 1.0f; - else if (x2R > U) res = x2R - (x2R-U)*(x2R-U)*inv_4T; - else if (x2R >= T) res = x2R; - else if (x2R > S) res = (x2R-S)*(x2R-S) * inv_4T; - else { x2L -= 1.0f; x2R -= 1.0f; continue; } - - // left - if (x2L <= S) {} // - 0.0f - else if (x2L < T) res -= (x2L-S)*(x2L-S) * inv_4T; - else if (x2L <= U) res -= x2L; - else if (x2L < V) res -= x2L - (x2L-U)*(x2L-U)*inv_4T; - else { x2L -= 1.0f; x2R -= 1.0f; continue; } - - // POLICY: ADD - p.addWeight(iRayIndex, iVolumeIndex, PW*PH * res); - - // POLICY: PIXEL POSTERIOR - p.pixelPosterior(iVolumeIndex); - - x2L -= 1.0f; - x2R -= 1.0f; - - } // end row loop - - } // end col loop - - // POLICY: RAY POSTERIOR - p.rayPosterior(iRayIndex); - - } // end detector loop - - - } // end theta switch + // 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 - } // end angle loop + if (dynamic_cast<CParallelProjectionGeometry2D*>(m_pProjectionGeometry)) + delete pVecProjectionGeometry; } - - |