1 /*****************************************************************************
4 ** Name: backprojectors.cpp Classes for backprojection
5 ** Programmer: Kevin Rosenberg
6 ** Date Started: June 2000
8 ** This is part of the CTSim program
9 ** Copyright (c) 1983-2001 Kevin Rosenberg
11 ** $Id: backprojectors.cpp,v 1.32 2001/03/18 18:08:25 kevin Exp $
13 ** This program is free software; you can redistribute it and/or modify
14 ** it under the terms of the GNU General Public License (version 2) as
15 ** published by the Free Software Foundation.
17 ** This program is distributed in the hope that it will be useful,
18 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
19 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 ** GNU General Public License for more details.
22 ** You should have received a copy of the GNU General Public License
23 ** along with this program; if not, write to the Free Software
24 ** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25 ******************************************************************************/
29 const int Backprojector::BPROJ_INVALID = -1;
30 const int Backprojector::BPROJ_TRIG = 0;
31 const int Backprojector::BPROJ_TABLE = 1;
32 const int Backprojector::BPROJ_DIFF = 2;
33 const int Backprojector::BPROJ_IDIFF = 3;
35 const char* const Backprojector::s_aszBackprojectName[] =
43 const char* const Backprojector::s_aszBackprojectTitle[] =
45 {"Direct Trigometric"},
46 {"Trigometric Table"},
47 {"Difference Iteration"},
48 {"Integer Difference Iteration"},
51 const int Backprojector::s_iBackprojectCount = sizeof(s_aszBackprojectName) / sizeof(const char*);
53 const int Backprojector::INTERP_INVALID = -1;
54 const int Backprojector::INTERP_NEAREST = 0;
55 const int Backprojector::INTERP_LINEAR = 1;
56 const int Backprojector::INTERP_CUBIC = 2;
57 const int Backprojector::INTERP_FREQ_PREINTERPOLATION = 3;
58 #if HAVE_BSPLINE_INTERP
59 const int Backprojector::INTERP_BSPLINE = 4;
60 const int Backprojector::INTERP_1BSPLINE = 5;
61 const int Backprojector::INTERP_2BSPLINE = 6;
62 const int Backprojector::INTERP_3BSPLINE = 7;
65 const char* const Backprojector::s_aszInterpName[] =
70 #if HAVE_FREQ_PREINTERP
71 {"freq_preinterpolationj"},
73 #if HAVE_BSPLINE_INTERP
81 const char* const Backprojector::s_aszInterpTitle[] =
86 #if HAVE_FREQ_PREINTERP
87 {"Frequency Preinterpolation"},
89 #if HAVE_BSPLINE_INTERP
91 {"B-Spline 1st Order"},
92 {"B-Spline 2nd Order"},
93 {"B-Spline 3rd Order"},
97 const int Backprojector::s_iInterpCount = sizeof(s_aszInterpName) / sizeof(const char*);
101 Backprojector::Backprojector (const Projections& proj, ImageFile& im, const char* const backprojName,
102 const char* const interpName, const int interpFactor, const ReconstructionROI* pROI)
105 m_pBackprojectImplem = NULL;
107 initBackprojector (proj, im, backprojName, interpName, interpFactor, pROI);
111 Backprojector::BackprojectView (const double* const viewData, const double viewAngle)
113 if (m_pBackprojectImplem != NULL)
114 m_pBackprojectImplem->BackprojectView (viewData, viewAngle);
118 Backprojector::PostProcessing()
120 if (m_pBackprojectImplem != NULL)
121 m_pBackprojectImplem->PostProcessing();
124 Backprojector::~Backprojector ()
126 delete m_pBackprojectImplem;
129 // FUNCTION IDENTIFICATION
130 // Backproject* projector = selectBackprojector (...)
133 // Selects a backprojector based on BackprojType
134 // and initializes the backprojector
137 Backprojector::initBackprojector (const Projections& proj, ImageFile& im, const char* const backprojName,
138 const char* const interpName, const int interpFactor, const ReconstructionROI* pROI)
140 m_nameBackproject = backprojName;
141 m_nameInterpolation = interpName;
142 m_pBackprojectImplem = NULL;
143 m_idBackproject = convertBackprojectNameToID (backprojName);
144 if (m_idBackproject == BPROJ_INVALID) {
146 m_failMessage = "Invalid backprojection name ";
147 m_failMessage += backprojName;
149 m_idInterpolation = convertInterpNameToID (interpName);
150 if (m_idInterpolation == INTERP_INVALID) {
152 m_failMessage = "Invalid interpolation name ";
153 m_failMessage += interpName;
156 if (m_fail || m_idBackproject == BPROJ_INVALID || m_idInterpolation == INTERP_INVALID) {
161 if (proj.geometry() == Scanner::GEOMETRY_EQUILINEAR)
162 m_pBackprojectImplem = static_cast<Backproject*>(new BackprojectEquilinear(proj, im, m_idInterpolation, interpFactor, pROI));
163 else if (proj.geometry() == Scanner::GEOMETRY_EQUIANGULAR)
164 m_pBackprojectImplem = static_cast<Backproject*>(new BackprojectEquiangular(proj, im, m_idInterpolation, interpFactor, pROI));
165 else if (proj.geometry() == Scanner::GEOMETRY_PARALLEL) {
166 if (m_idBackproject == BPROJ_TRIG)
167 m_pBackprojectImplem = static_cast<Backproject*>(new BackprojectTrig (proj, im, m_idInterpolation, interpFactor, pROI));
168 else if (m_idBackproject == BPROJ_TABLE)
169 m_pBackprojectImplem = static_cast<Backproject*>(new BackprojectTable (proj, im, m_idInterpolation, interpFactor, pROI));
170 else if (m_idBackproject == BPROJ_DIFF)
171 m_pBackprojectImplem = static_cast<Backproject*>(new BackprojectDiff (proj, im, m_idInterpolation, interpFactor, pROI));
172 else if (m_idBackproject == BPROJ_IDIFF)
173 m_pBackprojectImplem = static_cast<Backproject*>(new BackprojectIntDiff (proj, im, m_idInterpolation, interpFactor, pROI));
176 m_failMessage = "Unable to select a backprojection method [Backprojector::initBackprojector]";
185 Backprojector::convertBackprojectNameToID (const char* const backprojName)
187 int backprojID = BPROJ_INVALID;
189 for (int i = 0; i < s_iBackprojectCount; i++)
190 if (strcasecmp (backprojName, s_aszBackprojectName[i]) == 0) {
199 Backprojector::convertBackprojectIDToName (int bprojID)
201 static const char *bprojName = "";
203 if (bprojID >= 0 && bprojID < s_iBackprojectCount)
204 return (s_aszBackprojectName[bprojID]);
210 Backprojector::convertBackprojectIDToTitle (const int bprojID)
212 static const char *bprojTitle = "";
214 if (bprojID >= 0 && bprojID < s_iBackprojectCount)
215 return (s_aszBackprojectTitle[bprojID]);
222 Backprojector::convertInterpNameToID (const char* const interpName)
224 int interpID = INTERP_INVALID;
226 for (int i = 0; i < s_iInterpCount; i++)
227 if (strcasecmp (interpName, s_aszInterpName[i]) == 0) {
236 Backprojector::convertInterpIDToName (const int interpID)
238 static const char *interpName = "";
240 if (interpID >= 0 && interpID < s_iInterpCount)
241 return (s_aszInterpName[interpID]);
247 Backprojector::convertInterpIDToTitle (const int interpID)
249 static const char *interpTitle = "";
251 if (interpID >= 0 && interpID < s_iInterpCount)
252 return (s_aszInterpTitle[interpID]);
254 return (interpTitle);
259 // CLASS IDENTICATION
263 // Pure virtual base class for all backprojectors.
265 Backproject::Backproject (const Projections& proj, ImageFile& im, int interpType, const int interpFactor,
266 const ReconstructionROI* pROI)
267 : proj(proj), im(im), interpType(interpType), m_interpFactor(interpFactor), m_bPostProcessingDone(false)
269 detInc = proj.detInc();
271 iDetCenter = (nDet - 1) / 2; // index refering to L=0 projection
272 rotScale = proj.rotInc();
274 if (proj.geometry() == Scanner::GEOMETRY_PARALLEL)
275 rotScale /= (proj.nView() * proj.rotInc() / PI); // scale by number of PI rotations
276 else if (proj.geometry() == Scanner::GEOMETRY_EQUIANGULAR || proj.geometry() == Scanner::GEOMETRY_EQUILINEAR)
277 rotScale /= (proj.nView() * proj.rotInc() / (2 * PI)); // scale by number of 2PI rotations
279 sys_error (ERR_SEVERE, "Invalid geometry type %d [Backproject::Backproject]", proj.geometry());
286 xMin = -proj.phmLen() / 2; // Retangular coords of phantom
287 xMax = xMin + proj.phmLen();
288 yMin = -proj.phmLen() / 2;
289 yMax = yMin + proj.phmLen();
292 if (pROI->m_dXMin > xMin)
293 xMin = pROI->m_dXMin;
294 if (pROI->m_dXMax < xMax)
295 xMax = pROI->m_dXMax;
296 if (pROI->m_dYMin > yMin)
297 yMin = pROI->m_dYMin;
298 if (pROI->m_dYMax < yMax)
299 yMax = pROI->m_dYMax;
313 xInc = (xMax - xMin) / nx; // size of cells
314 yInc = (yMax - yMin) / ny;
316 im.setAxisIncrement (xInc, yInc);
317 im.setAxisExtent (xMin, xMax, yMin, yMax);
319 m_dFocalLength = proj.focalLength();
320 m_dSourceDetectorLength = proj.sourceDetectorLength();
323 Backproject::~Backproject ()
327 Backproject::PostProcessing()
329 m_bPostProcessingDone = true;
333 Backproject::ScaleImageByRotIncrement ()
335 for (int ix = 0; ix < nx; ix++)
336 for (int iy = 0; iy < ny; iy++)
337 v[ix][iy] *= rotScale;
340 void Backproject::errorIndexOutsideDetector (int ix, int iy, double theta, double r, double phi, double L, int iDetPos)
342 sys_error (ERR_WARNING, "r=%f, phi=%f", r, phi);
343 errorIndexOutsideDetector (ix, iy, theta, L, iDetPos);
346 void Backproject::errorIndexOutsideDetector (int ix, int iy, double theta, double L, int iDetPos)
349 std::ostringstream os;
350 os << "ix=" << ix << ", iy=" << iy << ", theta=" << theta << ", L=" << L << ", detinc=" << detInc << "\n";
351 os << "ndet=" << nDet << ", detInc=" << detInc << ", iDetCenter=" << iDetCenter << "\n";
352 os << "xMin=" << xMin << ", xMax=" << xMax << ", xInc=" << xInc << "\n";
353 os << "yMin=" << yMin << ", yMax=" << yMax << ", yInc=" << yInc << "\n";
354 os << "iDetPos index outside bounds: " << iDetPos << " [backprojector]";;
356 sys_error (ERR_WARNING, os.str().c_str());
361 // CLASS IDENTICATION
365 // Uses trigometric functions at each point in image for backprojection.
368 BackprojectTrig::BackprojectView (const double* const filteredProj, const double view_angle)
370 double theta = view_angle;
372 CubicPolyInterpolator* pCubicInterp = NULL;
373 if (interpType == Backprojector::INTERP_CUBIC)
374 pCubicInterp = new CubicPolyInterpolator (filteredProj, nDet);
376 double x = xMin + xInc / 2; // Rectang coords of center of pixel
377 for (int ix = 0; ix < nx; x += xInc, ix++) {
378 double y = yMin + yInc / 2;
379 for (int iy = 0; iy < ny; y += yInc, iy++) {
380 double r = sqrt (x * x + y * y); // distance of cell from center
381 double phi = atan2 (y, x); // angle of cell from center
382 double L = r * cos (theta - phi); // position on detector
384 if (interpType == Backprojector::INTERP_NEAREST) {
385 int iDetPos = iDetCenter + nearest<int> (L / detInc); // calc'd index in the filter raysum array
387 if (iDetPos >= 0 && iDetPos < nDet)
388 v[ix][iy] += rotScale * filteredProj[iDetPos];
389 } else if (interpType == Backprojector::INTERP_LINEAR) {
390 double p = L / detInc; // position along detector
391 double pFloor = floor (p);
392 int iDetPos = iDetCenter + static_cast<int>(pFloor);
393 double frac = p - pFloor; // fraction distance from det
394 if (iDetPos >= 0 && iDetPos < nDet - 1)
395 v[ix][iy] += rotScale * ((1-frac) * filteredProj[iDetPos] + frac * filteredProj[iDetPos+1]);
396 } else if (interpType == Backprojector::INTERP_CUBIC) {
397 double p = iDetCenter + (L / detInc); // position along detector
398 if (p >= 0 && p < nDet)
399 v[ix][iy] += rotScale * pCubicInterp->interpolate (p);
404 if (interpType == Backprojector::INTERP_CUBIC)
409 // CLASS IDENTICATION
413 // Precalculates trigometric function value for each point in image for backprojection.
415 BackprojectTable::BackprojectTable (const Projections& proj, ImageFile& im, int interpType,
416 const int interpFactor, const ReconstructionROI* pROI)
417 : Backproject (proj, im, interpType, interpFactor, pROI)
419 arrayR.initSetSize (im.nx(), im.ny());
420 arrayPhi.initSetSize (im.nx(), im.ny());
421 r = arrayR.getArray();
422 phi = arrayPhi.getArray();
424 double x, y; // Rectang coords of center of pixel
426 for (x = xMin + xInc / 2, ix = 0; ix < nx; x += xInc, ix++)
427 for (y = yMin + yInc / 2, iy = 0; iy < ny; y += yInc, iy++) {
428 r[ix][iy] = sqrt (x * x + y * y);
429 phi[ix][iy] = atan2 (y, x);
433 BackprojectTable::~BackprojectTable ()
438 BackprojectTable::PostProcessing()
440 if (! m_bPostProcessingDone) {
441 ScaleImageByRotIncrement();
442 m_bPostProcessingDone = true;
447 BackprojectTable::BackprojectView (const double* const filteredProj, const double view_angle)
449 double theta = view_angle;
451 CubicPolyInterpolator* pCubicInterp = NULL;
452 if (interpType == Backprojector::INTERP_CUBIC)
453 pCubicInterp = new CubicPolyInterpolator (filteredProj, nDet);
455 for (int ix = 0; ix < nx; ix++) {
456 ImageFileColumn pImCol = v[ix];
458 for (int iy = 0; iy < ny; iy++) {
459 double L = r[ix][iy] * cos (theta - phi[ix][iy]);
461 if (interpType == Backprojector::INTERP_NEAREST) {
462 int iDetPos = iDetCenter + nearest<int>(L / detInc); // calc index in the filtered raysum vector
464 if (iDetPos >= 0 && iDetPos < nDet)
465 pImCol[iy] += filteredProj[iDetPos];
466 } else if (interpType == Backprojector::INTERP_LINEAR) {
467 double dPos = L / detInc; // position along detector
468 double dPosFloor = floor (dPos);
469 int iDetPos = iDetCenter + static_cast<int>(dPosFloor);
470 double frac = dPos - dPosFloor; // fraction distance from det
471 if (iDetPos >= 0 && iDetPos < nDet - 1)
472 pImCol[iy] += ((1-frac) * filteredProj[iDetPos] + frac * filteredProj[iDetPos+1]);
473 } else if (interpType == Backprojector::INTERP_CUBIC) {
474 double p = iDetCenter + (L / detInc); // position along detector
475 if (p >= 0 && p < nDet)
476 pImCol[iy] += pCubicInterp->interpolate (p);
481 if (interpType == Backprojector::INTERP_CUBIC)
486 // CLASS IDENTICATION
490 // Backprojects by precalculating the change in L position for each x & y step in the image.
491 // Iterates in x & y direction by adding difference in L position
493 BackprojectDiff::BackprojectDiff (const Projections& proj, ImageFile& im, int interpType,
494 const int interpFactor, const ReconstructionROI* pROI)
495 : Backproject (proj, im, interpType, interpFactor, pROI)
497 // calculate center of first pixel v[0][0]
498 double x = xMin + xInc / 2;
499 double y = yMin + yInc / 2;
500 start_r = sqrt (x * x + y * y);
501 start_phi = atan2 (y, x);
506 BackprojectDiff::~BackprojectDiff ()
511 BackprojectDiff::PostProcessing()
513 if (! m_bPostProcessingDone) {
514 ScaleImageByRotIncrement();
515 m_bPostProcessingDone = true;
520 BackprojectDiff::BackprojectView (const double* const filteredProj, const double view_angle)
522 double theta = view_angle;
524 // Distance between detectors for an angle given in units of detectors
525 double det_dx = xInc * cos (theta) / detInc;
526 double det_dy = yInc * sin (theta) / detInc;
528 // calculate detPosition for first point in image (ix=0, iy=0)
529 double detPosColStart = start_r * cos (theta - start_phi) / detInc;
531 CubicPolyInterpolator* pCubicInterp = NULL;
532 if (interpType == Backprojector::INTERP_CUBIC)
533 pCubicInterp = new CubicPolyInterpolator (filteredProj, nDet);
535 for (int ix = 0; ix < nx; ix++, detPosColStart += det_dx) {
536 double curDetPos = detPosColStart;
537 ImageFileColumn pImCol = v[ix];
539 for (int iy = 0; iy < ny; iy++, curDetPos += det_dy) {
540 if (interpType == Backprojector::INTERP_NEAREST) {
541 int iDetPos = iDetCenter + nearest<int> (curDetPos); // calc index in the filtered raysum vector
543 if (iDetPos >= 0 && iDetPos < nDet)
544 *pImCol++ += filteredProj[iDetPos];
545 } else if (interpType == Backprojector::INTERP_LINEAR) {
546 double detPosFloor = floor (curDetPos);
547 int iDetPos = iDetCenter + static_cast<int>(detPosFloor);
548 double frac = curDetPos - detPosFloor; // fraction distance from det
549 if (iDetPos > 0 && iDetPos < nDet - 1)
550 *pImCol++ += filteredProj[iDetPos] + (frac * (filteredProj[iDetPos+1] - filteredProj[iDetPos]));
551 } else if (interpType == Backprojector::INTERP_CUBIC) {
552 double p = iDetCenter + curDetPos; // position along detector
553 if (p >= 0 && p < nDet)
554 *pImCol++ += pCubicInterp->interpolate (p);
559 if (interpType == Backprojector::INTERP_CUBIC)
564 // CLASS IDENTICATION
565 // BackprojectIntDiff
568 // Highly optimized and integer version of BackprojectDiff
571 BackprojectIntDiff::BackprojectView (const double* const filteredProj, const double view_angle)
573 double theta = view_angle; // add half PI to view angle to get perpendicular theta angle
574 static const int scaleShift = 16;
575 static const kint32 scale = (1 << scaleShift);
576 static const kint32 scaleBitmask = scale - 1;
577 static const kint32 halfScale = scale / 2;
578 static const double dInvScale = 1. / scale;
580 const kint32 det_dx = nearest<kint32> (xInc * cos (theta) / detInc * scale);
581 const kint32 det_dy = nearest<kint32> (yInc * sin (theta) / detInc * scale);
583 // calculate L for first point in image (0, 0)
584 kint32 detPosColStart = nearest<kint32> ((start_r * cos (theta - start_phi) / detInc + iDetCenter) * scale);
586 double* deltaFilteredProj = NULL;
587 CubicPolyInterpolator* pCubicInterp = NULL;
588 if (interpType == Backprojector::INTERP_LINEAR) {
589 // precalculate scaled difference for linear interpolation
590 deltaFilteredProj = new double [nDet];
591 for (int i = 0; i < nDet - 1; i++)
592 deltaFilteredProj[i] = (filteredProj[i+1] - filteredProj[i]) * dInvScale;
593 deltaFilteredProj[nDet - 1] = 0; // last detector
594 } else if (interpType == Backprojector::INTERP_CUBIC) {
595 pCubicInterp = new CubicPolyInterpolator (filteredProj, nDet);
598 int iLastDet = nDet - 1;
599 for (int ix = 0; ix < nx; ix++, detPosColStart += det_dx) {
600 kint32 curDetPos = detPosColStart;
601 ImageFileColumn pImCol = v[ix];
603 if (interpType == Backprojector::INTERP_NEAREST) {
604 for (int iy = 0; iy < ny; iy++, curDetPos += det_dy) {
605 const int iDetPos = (curDetPos + halfScale) >> 16;
606 if (iDetPos >= 0 && iDetPos <= iLastDet)
607 *pImCol++ += filteredProj[iDetPos];
609 } else if (interpType == Backprojector::INTERP_FREQ_PREINTERPOLATION) {
610 for (int iy = 0; iy < ny; iy++, curDetPos += det_dy) {
611 const int iDetPos = ((curDetPos + halfScale) >> 16) * m_interpFactor;
612 if (iDetPos >= 0 && iDetPos <= iLastDet)
613 *pImCol++ += filteredProj[iDetPos];
615 } else if (interpType == Backprojector::INTERP_LINEAR) {
616 for (int iy = 0; iy < ny; iy++, curDetPos += det_dy) {
617 const kint32 iDetPos = curDetPos >> scaleShift;
618 const kint32 detRemainder = curDetPos & scaleBitmask;
619 if (iDetPos >= 0 && iDetPos <= iLastDet)
620 *pImCol++ += filteredProj[iDetPos] + (detRemainder * deltaFilteredProj[iDetPos]);
622 } else if (interpType == Backprojector::INTERP_CUBIC) {
623 for (int iy = 0; iy < ny; iy++, curDetPos += det_dy) {
624 *pImCol++ += pCubicInterp->interpolate (static_cast<double>(curDetPos) / 65536);
629 if (interpType == Backprojector::INTERP_LINEAR)
630 delete deltaFilteredProj;
631 else if (interpType == Backprojector::INTERP_CUBIC)
637 BackprojectEquiangular::BackprojectView (const double* const filteredProj, const double view_angle)
639 double beta = view_angle;
641 CubicPolyInterpolator* pCubicInterp = NULL;
642 if (interpType == Backprojector::INTERP_CUBIC)
643 pCubicInterp = new CubicPolyInterpolator (filteredProj, nDet);
645 for (int ix = 0; ix < nx; ix++) {
646 ImageFileColumn pImCol = v[ix];
648 for (int iy = 0; iy < ny; iy++) {
649 double dAngleDiff = beta - phi[ix][iy];
650 double rcos_t = r[ix][iy] * cos (dAngleDiff);
651 double rsin_t = r[ix][iy] * sin (dAngleDiff);
652 double dFLPlusSin = m_dFocalLength + rsin_t;
653 double gamma = atan (rcos_t / dFLPlusSin);
654 double dPos = gamma / detInc; // position along detector
655 double dL2 = dFLPlusSin * dFLPlusSin + (rcos_t * rcos_t);
657 if (interpType == Backprojector::INTERP_NEAREST) {
658 int iDetPos = iDetCenter + nearest<int>(dPos); // calc index in the filtered raysum vector
659 if (iDetPos >= 0 && iDetPos < nDet)
660 pImCol[iy] += filteredProj[iDetPos] / dL2;
661 } else if (interpType == Backprojector::INTERP_LINEAR) {
662 double dPosFloor = floor (dPos);
663 int iDetPos = iDetCenter + static_cast<int>(dPosFloor);
664 double frac = dPos - dPosFloor; // fraction distance from det
665 if (iDetPos >= 0 && iDetPos < nDet - 1)
666 pImCol[iy] += (filteredProj[iDetPos] + frac * (filteredProj[iDetPos+1] - filteredProj[iDetPos])) / dL2;
667 } else if (interpType == Backprojector::INTERP_CUBIC) {
668 double d = iDetCenter + dPos; // position along detector
669 if (d >= 0 && d < nDet)
670 pImCol[iy] += pCubicInterp->interpolate (d) / dL2;
675 if (interpType == Backprojector::INTERP_CUBIC)
680 BackprojectEquilinear::BackprojectView (const double* const filteredProj, const double view_angle)
682 double beta = view_angle;
684 CubicPolyInterpolator* pCubicInterp = NULL;
685 if (interpType == Backprojector::INTERP_CUBIC)
686 pCubicInterp = new CubicPolyInterpolator (filteredProj, nDet);
688 for (int ix = 0; ix < nx; ix++) {
689 ImageFileColumn pImCol = v[ix];
691 for (int iy = 0; iy < ny; iy++) {
692 double dAngleDiff = beta - phi[ix][iy];
693 double rcos_t = r[ix][iy] * cos (dAngleDiff);
694 double rsin_t = r[ix][iy] * sin (dAngleDiff);
696 double dU = (m_dFocalLength + rsin_t) / m_dFocalLength;
697 double dDetPos = rcos_t / dU;
698 // Scale for imaginary detector that passes through origin of phantom, see Kak-Slaney Figure 3.22.
699 dDetPos *= m_dSourceDetectorLength / m_dFocalLength;
700 double dPos = dDetPos / detInc; // position along detector array
702 if (interpType == Backprojector::INTERP_NEAREST) {
703 int iDetPos = iDetCenter + nearest<int>(dPos); // calc index in the filtered raysum vector
704 if (iDetPos >= 0 && iDetPos < nDet)
705 pImCol[iy] += (filteredProj[iDetPos] / (dU * dU));
706 } else if (interpType == Backprojector::INTERP_LINEAR) {
707 double dPosFloor = floor (dPos);
708 int iDetPos = iDetCenter + static_cast<int>(dPosFloor);
709 double frac = dPos - dPosFloor; // fraction distance from det
710 if (iDetPos >= 0 && iDetPos < nDet - 1)
711 pImCol[iy] += (filteredProj[iDetPos] + frac * (filteredProj[iDetPos+1] - filteredProj[iDetPos]))
713 } else if (interpType == Backprojector::INTERP_CUBIC) {
714 double d = iDetCenter + dPos; // position along detector
715 if (d >= 0 && d < nDet)
716 pImCol[iy] += pCubicInterp->interpolate (d) / (dU * dU);
721 if (interpType == Backprojector::INTERP_CUBIC)