Baseline.cc

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#include <list>
#include <cmath>
#include <cstdint>

#include "lsst/log/Log.h"
#include "lsst/meas/deblender/Baseline.h"
#include "lsst/pex/exceptions.h"
#include "lsst/afw/geom/Box.h"

using std::lround;

namespace image = lsst::afw::image;
namespace det = lsst::afw::detection;
namespace deblend = lsst::meas::deblender;
namespace geom = lsst::afw::geom;


static bool span_ptr_compare(PTR(det::Span) sp1, PTR(det::Span) sp2) {
    return (*sp1 < *sp2);
}

template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
void
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
medianFilter(ImageT const& img,
             ImageT & out,
             int halfsize) {
    int S = halfsize*2 + 1;
    int SS = S*S;
    typedef typename ImageT::xy_locator xy_loc;
    xy_loc pix = img.xy_at(halfsize,halfsize);
    std::vector<typename xy_loc::cached_location_t> locs;
    for (int i=0; i<S; ++i) {
        for (int j=0; j<S; ++j) {
            locs.push_back(pix.cache_location(j-halfsize, i-halfsize));
        }
    }
    int W = img.getWidth();
    int H = img.getHeight();
    ImagePixelT vals[S*S];
    for (int y=halfsize; y<H-halfsize; ++y) {
        xy_loc inpix = img.xy_at(halfsize, y), end = img.xy_at(W-halfsize, y);
        for (typename ImageT::x_iterator optr = out.row_begin(y) + halfsize;
             inpix != end; ++inpix.x(), ++optr) {
            for (int i=0; i<SS; ++i)
                vals[i] = inpix[locs[i]];
            std::nth_element(vals, vals+SS/2, vals+SS);
            *optr = vals[SS/2];
        }
    }

    // grumble grumble margins
    for (int y=0; y<2*halfsize; ++y) {
        int iy = y;
        if (y >= halfsize)
            iy = H - 1 - (y-halfsize);
        typename ImageT::x_iterator optr = out.row_begin(iy);
        typename ImageT::x_iterator iptr = img.row_begin(iy), end=img.row_end(iy);
        for (; iptr != end; ++iptr,++optr)
            *optr = *iptr;
    }
    for (int y=halfsize; y<H-halfsize; ++y) {
        typename ImageT::x_iterator optr = out.row_begin(y);
        typename ImageT::x_iterator iptr = img.row_begin(y), end=img.row_begin(y)+halfsize;
        for (; iptr != end; ++iptr,++optr)
            *optr = *iptr;
        iptr = img.row_begin(y) + ((W-1) - halfsize);
        end  = img.row_begin(y) + (W-1);
        optr = out.row_begin(y) + ((W-1) - halfsize);
        for (; iptr != end; ++iptr,++optr)
            *optr = *iptr;
    }

}

template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
void
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
makeMonotonic(
    ImageT & img,
    det::PeakRecord const& peak) {

    int cx = peak.getIx();
    int cy = peak.getIy();
    int ix0 = img.getX0();
    int iy0 = img.getY0();
    int iW = img.getWidth();
    int iH = img.getHeight();

    ImagePtrT shadowingImg = ImagePtrT(new ImageT(img, true));

    int DW = std::max(cx - img.getX0(), img.getX0() + img.getWidth() - cx);
    int DH = std::max(cy - img.getY0(), img.getY0() + img.getHeight() - cy);

    const int S = 5;

    // Work out from the peak in chunks of "S" pixels.
    int s;
    for (s = 0; s < std::max(DW,DH); s += S) {
        int p;
        for (p=0; p<S; p++) {
            // visit pixels with L_inf distance = s + p from the
            // center (ie, the s+p'th square ring of pixels)
            // L is the half-length of the ring (box).
            int L = s+p;
            int x = L, y = -L;
            int dx = 0, dy = 0; // initialized here to satisfy the
                                // compiler; initialized for real
                                // below (first time through loop)
            /*
            int i;
            int leg;
            for (i=0; i<(8*L); i++, x += dx, y += dy) {
                if (i % (2*L) == 0) {
                    leg = (i/(2*L));
                    dx = ( leg    % 2) * (-1 + 2*(leg/2));
                    dy = ((leg+1) % 2) * ( 1 - 2*(leg/2));
                }
             */

            /*
             We visit pixels in a box of "radius" L, in this order:

             L=1:

             4 3 2
             5   1
             6 7 0

             L=2:

             8  7  6  5  4
             9           3
             10          2
             11          1
             12 13 14 15 0

             Note that the number of pixel visited is 8*L, and that we
             change "dx" or "dy" each "2*L" steps.
             */
            for (int i=0; i<(8*L); i++, x += dx, y += dy) {
                // time to change directions?  (Note that this runs
                // the first time through the loop, initializing dx,dy
                // appropriately.)
                if (i % (2*L) == 0) {
                    int leg = (i/(2*L));
                    // dx = [ 0, -1,  0, 1 ][leg]
                    dx = ( leg    % 2) * (-1 + 2*(leg/2));
                    // dy = [ 1,  0, -1, 0 ][leg]
                    dy = ((leg+1) % 2) * ( 1 - 2*(leg/2));
                }
                //printf("  i=%i, leg=%i, dx=%i, dy=%i, x=%i, y=%i\n", i, leg, dx, dy, x, y);
                int px = cx + x - ix0;
                int py = cy + y - iy0;
                // If the shadowing pixel is out of bounds, nothing to do.
                if (px < 0 || px >= iW || py < 0 || py >= iH)
                    continue;
                // The pixel casting the shadow
                ImagePixelT pix = (*shadowingImg)(px,py);

                // Cast this pixel's shadow S pixels long in a cone.
                // We compute the range of slopes (or inverse-slopes)
                // shadowed by the pixel, [ds0,ds1]
                double ds0, ds1;
                // Range of slopes shadowed
                const double A = 0.3;
                int shx, shy;
                int psx, psy;
                // Are we traversing a vertical edge of the box?
                if (dx == 0) {
                    // (if so, then "x" is +- L, so no div-by-zero)
                    ds0 = (double(y) / double(x)) - A;
                    ds1 = ds0 + 2.0 * A;
                    // cast the shadow on column x + sign(x)*shx
                    for (shx=1; shx<=S; shx++) {
                        int xsign = (x>0?1:-1);
                        // the column being shadowed
                        psx = cx + x + (xsign*shx) - ix0;
                        if (psx < 0 || psx >= iW)
                            continue;
                        // shadow covers a range of y values based on slope
                        for (shy  = lround(shx * ds0);
                             shy <= lround(shx * ds1); shy++) {
                            psy = cy + y + xsign*shy - iy0;
                            if (psy < 0 || psy >= iH)
                                continue;
                            img(psx, psy) = std::min(img(psx, psy), pix);
                        }
                    }

                } else {
                    // We're traversing a horizontal edge of the box; y = +-L
                    ds0 = (double(x) / double(y)) - A;
                    ds1 = ds0 + 2.0 * A;
                    // Cast shadow on row y + sign(y)*shy
                    for (shy=1; shy<=S; shy++) {
                        int ysign = (y>0?1:-1);
                        psy = cy + y + (ysign*shy) - iy0;
                        if (psy < 0 || psy >= iH)
                            continue;
                        // shadow covers a range of x vals based on slope
                        for (shx  = lround(shy * ds0);
                             shx <= lround(shy * ds1); shx++) {
                            psx = cx + x + ysign*shx - ix0;
                            if (psx < 0 || psx >= iW)
                                continue;
                            img(psx, psy) = std::min(img(psx, psy), pix);
                        }
                    }
                }
            }
        }
        shadowingImg->assign(img);
    }
}

static double _get_contrib_r_to_footprint(int x, int y,
                                          PTR(det::Footprint) tfoot) {
    typedef det::Footprint::SpanList SpanList;
    double minr2 = 1e12;
    SpanList const& tspans = tfoot->getSpans();
    for (SpanList::const_iterator ts = tspans.begin(); ts < tspans.end(); ++ts) {
        geom::Span* sp = ts->get();
        int mindx;
        // span is to right of pixel?
        int dx = sp->getX0() - x;
        if (dx >= 0) {
            mindx = dx;
        } else {
            // span is to left of pixel?
            dx = x - sp->getX1();
            if (dx >= 0) {
                mindx = dx;
            } else {
                // span contains pixel (in x direction)
                mindx = 0;
            }
        }
        int dy = sp->getY() - y;
        minr2 = std::min(minr2, (double)(mindx*mindx + dy*dy));
    }
    //printf("stray flux at (%i,%i): dist to t %i is %g\n", x, y, (int)i, sqrt(minr2));
    return 1. / (1. + minr2);
}


template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
void
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
_find_stray_flux(det::Footprint const& foot,
                 ImagePtrT tsum,
                 MaskedImageT const& img,
                 int strayFluxOptions,
                 std::vector<PTR(det::Footprint)> tfoots,
                 std::vector<bool> const& ispsf,
                 std::vector<int>  const& pkx,
                 std::vector<int>  const& pky,
                 double clipStrayFluxFraction,
                 std::vector<std::shared_ptr<typename det::HeavyFootprint<ImagePixelT,MaskPixelT,VariancePixelT> > > & strays
                 ) {

    typedef typename det::Footprint::SpanList SpanList;
    typedef typename det::HeavyFootprint<ImagePixelT, MaskPixelT, VariancePixelT> HeavyFootprint;
    typedef typename std::shared_ptr< HeavyFootprint > HeavyFootprintPtrT;

    // when doing stray flux: the footprints and pixels, which we'll
    // combine into the return 'strays' HeavyFootprint at the end.
    std::vector<PTR(det::Footprint) > strayfoot;
    std::vector<std::vector<ImagePixelT> > straypix;
    std::vector<std::vector<MaskPixelT> > straymask;
    std::vector<std::vector<VariancePixelT> > strayvar;

    int ix0 = img.getX0();
    int iy0 = img.getY0();
    geom::Box2I sumbb = tsum->getBBox();
    int sumx0 = sumbb.getMinX();
    int sumy0 = sumbb.getMinY();

    for (size_t i=0; i<tfoots.size(); ++i) {
        strayfoot.push_back(PTR(det::Footprint)());
        straypix.push_back(std::vector<ImagePixelT>());
        straymask.push_back(std::vector<MaskPixelT>());
        strayvar.push_back(std::vector<VariancePixelT>());
    }

    bool always = (strayFluxOptions & STRAYFLUX_TO_POINT_SOURCES_ALWAYS);

    typedef std::uint16_t itype;
    PTR(image::Image<itype>) nearest;

    if (strayFluxOptions & STRAYFLUX_NEAREST_FOOTPRINT) {
        // Compute the map of which footprint is closest to each
        // pixel in the bbox.
        typedef std::uint16_t dtype;
        PTR(image::Image<dtype>) dist(new image::Image<dtype>(sumbb));
        nearest = PTR(image::Image<itype>)(new image::Image<itype>(sumbb));

        std::vector<PTR(det::Footprint)> templist;
        std::vector<PTR(det::Footprint)>* footlist = &tfoots;

        if (!always && ispsf.size()) {
            // create a temp list that has empty footprints in place
            // of all the point sources.
            PTR(det::Footprint) empty(new det::Footprint(foot.getPeaks().getSchema()));
            for (size_t i=0; i<tfoots.size(); ++i) {
                if (ispsf[i]) {
                    templist.push_back(empty);
                } else {
                    templist.push_back(tfoots[i]);
                }
            }
            footlist = &templist;
        }
        nearestFootprint(*footlist, nearest, dist);
    }

    // Go through the (parent) Footprint looking for stray flux:
    // pixels that are not claimed by any template, and positive.
    const SpanList& spans = foot.getSpans();
    for (SpanList::const_iterator s = spans.begin(); s < spans.end(); s++) {
        int y = (*s)->getY();
        int x0 = (*s)->getX0();
        int x1 = (*s)->getX1();
        typename ImageT::x_iterator tsum_it =
            tsum->row_begin(y - sumy0) + (x0 - sumx0);
        typename MaskedImageT::x_iterator in_it =
            img.row_begin(y - iy0) + (x0 - ix0);
        double contrib[tfoots.size()];

        for (int x = x0; x <= x1; ++x, ++tsum_it, ++in_it) {
            // Skip pixels that are covered by at least one
            // template (*tsum_it > 0) or the input is not
            // positive (*in_it <= 0).
            if ((*tsum_it > 0) || (*in_it).image() <= 0) {
                continue;
            }

            if (strayFluxOptions & STRAYFLUX_R_TO_FOOTPRINT) {
                // we'll compute these just-in-time
                for (size_t i=0; i<tfoots.size(); ++i) {
                    contrib[i] = -1.0;
                }
            } else if (strayFluxOptions & STRAYFLUX_NEAREST_FOOTPRINT) {
                for (size_t i=0; i<tfoots.size(); ++i) {
                    contrib[i] = 0.0;
                }
                int i = nearest->get0(x, y);
                contrib[i] = 1.0;
            } else {
                // R_TO_PEAK
                for (size_t i=0; i<tfoots.size(); ++i) {
                    // Split the stray flux by 1/(1+r^2) to peaks
                    int dx, dy;
                    dx = pkx[i] - x;
                    dy = pky[i] - y;
                    contrib[i] = 1. / (1. + dx*dx + dy*dy);
                }
            }

            // Round 1: skip point sources unless STRAYFLUX_TO_POINT_SOURCES_ALWAYS
            // are we going to assign stray flux to ptsrcs?
            bool ptsrcs = always;
            double csum = 0.;
            for (size_t i=0; i<tfoots.size(); ++i) {
                // if we're skipping point sources and this is a point source...
                if ((!ptsrcs) && ispsf.size() && ispsf[i]) {
                    continue;
                }
                if (contrib[i] == -1.0) {
                    contrib[i] = _get_contrib_r_to_footprint(x, y, tfoots[i]);
                }
                csum += contrib[i];
            }
            if ((csum == 0.) &&
                (strayFluxOptions &
                 STRAYFLUX_TO_POINT_SOURCES_WHEN_NECESSARY)) {
                // No extended sources -- assign to pt sources
                //LOGL_DEBUG(_log, "necessary to assign stray flux to point sources");
                ptsrcs = true;
                for (size_t i=0; i<tfoots.size(); ++i) {
                    if (contrib[i] == -1.0) {
                        contrib[i] = _get_contrib_r_to_footprint(x, y, tfoots[i]);
                    }
                    csum += contrib[i];
                }
            }

            // Drop small contributions...
            double strayclip = (clipStrayFluxFraction * csum);
            csum = 0.;
            for (size_t i=0; i<tfoots.size(); ++i) {
                // skip ptsrcs?
                if ((!ptsrcs) && ispsf.size() && ispsf[i]) {
                    contrib[i] = 0.;
                    continue;
                }
                // skip small contributions
                if (contrib[i] < strayclip) {
                    contrib[i] = 0.;
                    continue;
                }
                csum += contrib[i];
            }

            for (size_t i=0; i<tfoots.size(); ++i) {
                if (contrib[i] == 0.) {
                    continue;
                }
                // the stray flux to give to template i
                double p = (contrib[i] / csum) * (*in_it).image();
                if (!strayfoot[i]) {
                    strayfoot[i] = PTR(det::Footprint)(new det::Footprint(foot.getPeaks().getSchema()));
                }
                strayfoot[i]->addSpanInSeries(y, x, x); // XXX this may be rather heavy in memory use
                straypix[i].push_back(p);
                straymask[i].push_back((*in_it).mask());
                strayvar[i].push_back((*in_it).variance());
            }
        }
    }

    // Store the stray flux in HeavyFootprints
    for (size_t i=0; i<tfoots.size(); ++i) {
        if (!strayfoot[i]) {
            strays.push_back(HeavyFootprintPtrT());
        } else {
            HeavyFootprintPtrT heavy(new HeavyFootprint(*strayfoot[i]));
            ndarray::Array<ImagePixelT,1,1> himg = heavy->getImageArray();
            typename std::vector<ImagePixelT>::const_iterator spix;
            typename std::vector<MaskPixelT>::const_iterator smask;
            typename std::vector<VariancePixelT>::const_iterator svar;
            typename ndarray::Array<ImagePixelT,1,1>::Iterator hpix;
            typename ndarray::Array<MaskPixelT,1,1>::Iterator mpix;
            typename ndarray::Array<VariancePixelT,1,1>::Iterator vpix;

            assert((size_t)strayfoot[i]->getNpix() == straypix[i].size());

            for (spix = straypix[i].begin(),
                     smask = straymask[i].begin(),
                     svar  = strayvar [i].begin(),
                     hpix = himg.begin(),
                     mpix = heavy->getMaskArray().begin(),
                     vpix = heavy->getVarianceArray().begin();
                 spix != straypix[i].end();
                 ++spix, ++smask, ++svar, ++hpix, ++mpix, ++vpix) {
                *hpix = *spix;
                *mpix = *smask;
                *vpix = *svar;
            }
            strays.push_back(heavy);
        }
    }
}

template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
void
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
_sum_templates(std::vector<ImagePtrT> timgs,
               ImagePtrT tsum) {
    geom::Box2I sumbb = tsum->getBBox();
    int sumx0 = sumbb.getMinX();
    int sumy0 = sumbb.getMinY();

    // Compute  tsum = the sum of templates
    for (size_t i=0; i<timgs.size(); ++i) {
        ImagePtrT timg = timgs[i];
        geom::Box2I tbb = timg->getBBox();
        int tx0 = tbb.getMinX();
        int ty0 = tbb.getMinY();
        // To handle "ramped" templates that can extend outside the
        // parent, clip the bbox.  Note that we saved tx0,ty0 BEFORE
        // doing this!
        tbb.clip(sumbb);
        int copyx0 = tbb.getMinX();
        // Here we iterate over the template bbox -- we could instead
        // iterate over the "tfoot"s.
        for (int y=tbb.getMinY(); y<=tbb.getMaxY(); ++y) {
            typename ImageT::x_iterator in_it = timg->row_begin(y - ty0) + (copyx0 - tx0);
            typename ImageT::x_iterator inend = in_it + tbb.getWidth();
            typename ImageT::x_iterator tsum_it =
                tsum->row_begin(y - sumy0) + (copyx0 - sumx0);
            for (; in_it != inend; ++in_it, ++tsum_it) {
                *tsum_it += std::max((ImagePixelT)0., static_cast<ImagePixelT>(*in_it));
            }
        }
    }

}

template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
std::vector<typename PTR(image::MaskedImage<ImagePixelT, MaskPixelT, VariancePixelT>)>
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
apportionFlux(MaskedImageT const& img,
              det::Footprint const& foot,
              std::vector<ImagePtrT> timgs,
              std::vector<PTR(det::Footprint)> tfoots,
              ImagePtrT tsum,
              std::vector<bool> const& ispsf,
              std::vector<int>  const& pkx,
              std::vector<int>  const& pky,
              std::vector<std::shared_ptr<typename det::HeavyFootprint<ImagePixelT,MaskPixelT,VariancePixelT> > > & strays,
              int strayFluxOptions,
              double clipStrayFluxFraction
    ) {
    typedef typename det::Footprint::SpanList SpanList;

    if (timgs.size() != tfoots.size()) {
        throw LSST_EXCEPT(lsst::pex::exceptions::LengthError,
            (boost::format("Template images must be the same length as template footprints (%d vs %d)")
                % timgs.size() % tfoots.size()).str());
    }

    for (size_t i=0; i<timgs.size(); ++i) {
        if (!timgs[i]->getBBox().contains(tfoots[i]->getBBox())) {
            throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                              "Template image MUST contain template footprint");
        }
        if (!img.getBBox().contains(foot.getBBox())) {
            throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                              "Image bbox MUST contain parent footprint");
        }
        // template bounding-boxes *can* extend outside the parent
        // footprint if we are ramping templates with significant flux
        // at the edges.  We handle this below.
    }

    // the apportioned flux return value
    std::vector<MaskedImagePtrT> portions;

    LOG_LOGGER _log = LOG_GET("meas.deblender.apportionFlux");
    bool findStrayFlux = (strayFluxOptions & ASSIGN_STRAYFLUX);

    int ix0 = img.getX0();
    int iy0 = img.getY0();
    geom::Box2I fbb = foot.getBBox();

    if (!tsum) {
        tsum = ImagePtrT(new ImageT(fbb.getDimensions()));
        tsum->setXY0(fbb.getMinX(), fbb.getMinY());
    }

    if (!tsum->getBBox().contains(foot.getBBox())) {
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Template sum image MUST contain parent footprint");
    }

    geom::Box2I sumbb = tsum->getBBox();
    int sumx0 = sumbb.getMinX();
    int sumy0 = sumbb.getMinY();

    _sum_templates(timgs, tsum);

    // Compute flux portions
    for (size_t i=0; i<timgs.size(); ++i) {
        ImagePtrT timg = timgs[i];
        // Initialize return value:
        MaskedImagePtrT port(new MaskedImageT(timg->getDimensions()));
        port->setXY0(timg->getXY0());
        portions.push_back(port);

        // Split flux = image * template / tsum
        geom::Box2I tbb = timg->getBBox();
        int tx0 = tbb.getMinX();
        int ty0 = tbb.getMinY();
        // As above
        tbb.clip(sumbb);
        int copyx0 = tbb.getMinX();
        for (int y=tbb.getMinY(); y<=tbb.getMaxY(); ++y) {
            typename MaskedImageT::x_iterator in_it =
                img.row_begin(y - iy0) + (copyx0 - ix0);
            typename ImageT::x_iterator tptr =
                timg->row_begin(y - ty0) + (copyx0 - tx0);
            typename ImageT::x_iterator tend = tptr + tbb.getWidth();
            typename ImageT::x_iterator tsum_it =
                tsum->row_begin(y - sumy0) + (copyx0 - sumx0);
            typename MaskedImageT::x_iterator out_it =
                port->row_begin(y - ty0) + (copyx0 - tx0);
            for (; tptr != tend; ++tptr, ++in_it, ++out_it, ++tsum_it) {
                if (*tsum_it == 0) {
                    continue;
                }
                double frac = std::max((ImagePixelT)0., static_cast<ImagePixelT>(*tptr)) / (*tsum_it);
                //if (frac == 0) {
                // treat mask planes differently?
                // }
                out_it.mask()     = (*in_it).mask();
                out_it.variance() = (*in_it).variance();
                out_it.image()    = (*in_it).image() * frac;
            }
        }
    }

    if (findStrayFlux) {
        if ((ispsf.size() > 0) && (ispsf.size() != timgs.size())) {
            throw LSST_EXCEPT(lsst::pex::exceptions::LengthError,
                (boost::format("'ispsf' must be the same length as templates (%d vs %d)")
                     % ispsf.size() % timgs.size()).str());
        }
        if ((pkx.size() != timgs.size()) || (pky.size() != timgs.size())) {
            throw LSST_EXCEPT(lsst::pex::exceptions::LengthError,
                (boost::format("'pkx' and 'pky' must be the same length as templates (%d,%d vs %d)")
                    % pkx.size() % pky.size() % timgs.size()).str());
        }
        _find_stray_flux(foot, tsum, img, strayFluxOptions, tfoots,
                         ispsf, pkx, pky, clipStrayFluxFraction, strays);
    }
    return portions;
}


class RelativeSpanIterator {
public:
    typedef det::Footprint::SpanList SpanList;

    RelativeSpanIterator() {}

    RelativeSpanIterator(SpanList::const_iterator const& real,
                         SpanList const& arr,
                         int cx, int cy, bool forward=true) 
        : _real(real), _cx(cx), _cy(cy), _forward(forward)
        {
            if (_forward) {
                _end = arr.end();
            } else {
                _end = arr.begin();
            }
        }

    bool operator==(const SpanList::const_iterator & other) {
        return _real == other;
    }
    bool operator!=(const SpanList::const_iterator & other) {
        return _real != other;
    }
    bool operator<=(const SpanList::const_iterator & other) {
        return _real <= other;
    }
    bool operator<(const SpanList::const_iterator & other) {
        return _real < other;
    }
    bool operator>=(const SpanList::const_iterator & other) {
        return _real >= other;
    }
    bool operator>(const SpanList::const_iterator & other) {
        return _real > other;
    }

    bool operator==(RelativeSpanIterator & other) {
        return (_real == other._real) &&
            (_cx == other._cx) && (_cy == other._cy) &&
            (_forward == other._forward);
    }
    bool operator!=(RelativeSpanIterator & other) {
        return !(*this == other);
    }

    RelativeSpanIterator operator++() {
        if (_forward) {
            _real++;
        } else {
            _real--;
        }
        return *this;
    }
    RelativeSpanIterator operator++(int dummy) {
        RelativeSpanIterator result = *this;
        ++(*this);
        return result;
    }

    bool notDone() {
        if (_forward) {
            return _real < _end;
        } else {
            return _real >= _end;
        }
    }

    int dxlo() {
        if (_forward) {
            return (*_real)->getX0() - _cx;
        } else {
            return _cx - (*_real)->getX1();
        }
    }
    int dxhi() {
        if (_forward) {
            return (*_real)->getX1() - _cx;
        } else {
            return _cx - (*_real)->getX0();
        }
    }
    int dy() {
        return std::abs((*_real)->getY() - _cy);
    }
    int x0() {
        return (*_real)->getX0();
    }
    int x1() {
        return (*_real)->getX1();
    }
    int y() {
        return (*_real)->getY();
    }

private:
    SpanList::const_iterator _real;
    SpanList::const_iterator _end;
    int _cx;
    int _cy;
    bool _forward;
};


/*
 // Check symmetrizeFootprint by computing truth naively.
     // compute correct answer dumbly
     det::Footprint truefoot;
     geom::Box2I bbox = foot.getBBox();
     for (int y=bbox.getMinY(); y<=bbox.getMaxY(); y++) {
     for (int x=bbox.getMinX(); x<=bbox.getMaxX(); x++) {
     int dy = y - cy;
     int dx = x - cx;
     int x2 = cx - dx;
     int y2 = cy - dy;
     if (foot.contains(geom::Point2I(x,  y)) &&
     foot.contains(geom::Point2I(x2, y2))) {
     truefoot.addSpan(y, x, x);
     }
     }
     }
     truefoot.normalize();

     SpanList sp1 = truefoot.getSpans();
     SpanList sp2 = sfoot->getSpans();
     for (SpanList::const_iterator spit1 = sp1.begin(),
     spit2 = sp2.begin();
     spit1 != sp1.end() && spit2 != sp2.end();
     spit1++, spit2++) {
     //printf("\n");
     printf(" true   y %i, x [%i, %i]\n", (*spit1)->getY(), (*spit1)->getX0(), (*spit1)->getX1());
     printf(" sfoot  y %i, x [%i, %i]\n", (*spit2)->getY(), (*spit2)->getX0(), (*spit2)->getX1());
     if (((*spit1)->getY()  != (*spit2)->getY()) ||
     ((*spit1)->getX0() != (*spit2)->getX0()) ||
     ((*spit1)->getX1() != (*spit2)->getX1())) {
     printf("*******************************************\n");
     }
     }
     assert(sp1.size() == sp2.size());
     for (SpanList::const_iterator spit1 = sp1.begin(),
     spit2 = sp2.begin();
     spit1 != sp1.end() && spit2 != sp2.end();
     spit1++, spit2++) {
     assert((*spit1)->getY()  == (*spit2)->getY());
     assert((*spit1)->getX0() == (*spit2)->getX0());
     assert((*spit1)->getX1() == (*spit2)->getX1());
     }
 */

template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
PTR(lsst::afw::detection::Footprint)
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
symmetrizeFootprint(
    det::Footprint const& foot,
    int cx, int cy) {

    typedef typename det::Footprint::SpanList SpanList;

    PTR(det::Footprint) sfoot(new det::Footprint(foot.getPeaks().getSchema()));
    const SpanList spans = foot.getSpans();
    assert(foot.isNormalized());

    LOG_LOGGER _log = LOG_GET("meas.deblender.symmetrizeFootprint");

    // Find the Span containing the peak.
    PTR(det::Span) target(new det::Span(cy, cx, cx));
    SpanList::const_iterator peakspan =
        std::upper_bound(spans.begin(), spans.end(), target, span_ptr_compare);
    // upper_bound returns the last position where "target" could be inserted;
    // ie, the first Span larger than "target".  The Span containing "target"
    // should be peakspan-1 or (if the peak is on the first pixel in the span,
    // peakspan.
    PTR(det::Span) sp;
    if (peakspan == spans.begin()) {
        sp = *peakspan;
        if (!sp->contains(cx, cy)) {
            LOGL_WARN(_log,
                "Failed to find span containing (%i,%i): before the beginning of this footprint", cx, cy);
            return PTR(det::Footprint)();
        }
    } else {
        --peakspan;
        sp = *peakspan;

        if (!sp->contains(cx, cy)) {
            ++peakspan;
            sp = *peakspan;
            if (!sp->contains(cx, cy)) {
                geom::Box2I fbb = foot.getBBox();
                LOGL_WARN(_log, "Failed to find span containing (%i,%i): nearest is %i, [%i,%i].  "
                          "Footprint bbox is [%i,%i],[%i,%i]",
                          cx, cy, sp->getY(), sp->getX0(), sp->getX1(),
                          fbb.getMinX(), fbb.getMaxX(), fbb.getMinY(), fbb.getMaxY());
                return PTR(det::Footprint)();
            }
        }
    }
    LOGL_DEBUG(_log, "Span containing (%i,%i): (x=[%i,%i], y=%i)",
               cx, cy, sp->getX0(), sp->getX1(), sp->getY());

    // The symmetric templates are essentially an AND of the footprint
    // pixels and its 180-degree-rotated self, rotated around the
    // peak (cx,cy).
    //
    // We iterate forward and backward simultaneously, starting from
    // the span containing the peak and moving out, row by row.
    // 
    // In the loop below, we search for the next pair of Spans that
    // overlap (in "dx" from the center), output the overlapping
    // portion of the Spans, and advance either the "fwd" or "back"
    // iterator.  When we fail to find an overlapping pair of Spans,
    // we move on to the next row.
    //
    // [The following paragraph is somewhat obsoleted by the
    // RelativeSpanIterator class, which performs some of the renaming
    // and the dx,dy coords.]
    //
    // '''In reading the code, "forward", "advancing", etc, are all
    // from the perspective of the "fwd" iterator (the one going
    // forward through the Span list, from low to high Y and then low
    // to high X).  It will help to imagine making a copy of the
    // footprint and rotating it around the center pixel by 180
    // degrees, so that "fwd" and "back" are both iterating the same
    // direction; we're then just finding the AND of those two
    // iterators, except we have to work in dx,dy coordinates rather
    // than original x,y coords, and the accessors for "back" are
    // opposite.'''

    RelativeSpanIterator fwd (peakspan, spans, cx, cy, true);
    RelativeSpanIterator back(peakspan, spans, cx, cy, false);

    int dy = 0;
    while (fwd.notDone() && back.notDone()) {
        // forward and backward "y"; just symmetric around cy
        int fy = cy + dy;
        int by = cy - dy;
        // delta-x of the beginnings of the spans, for "fwd" and "back"
        int fdxlo =  fwd.dxlo();
        int bdxlo = back.dxlo();

        // First find:
        //    fend -- first span in the next row, or end(); ie,
        //            the end of this row in the forward direction
        //    bend -- the end of this row in the backward direction
        RelativeSpanIterator fend, bend;
        for (fend = fwd; fend.notDone(); ++fend) {
            if (fend.dy() != dy)
                break;
        }
        for (bend = back; bend.notDone(); ++bend) {
            if (bend.dy() != dy)
                break;
        }

        LOGL_DEBUG(_log, "dy=%i, fy=%i, fx=[%i, %i],   by=%i, fx=[%i, %i],  fdx=%i, bdx=%i",
                   dy, fy, fwd.x0(), fwd.x1(), by, back.x0(), back.x1(),
                   fdxlo, bdxlo);

        // Find possibly-overlapping span
        if (bdxlo > fdxlo) {
            LOGL_DEBUG(_log, "Advancing forward.");
            // While the "forward" span is entirely to the "left" of the "backward" span,
            // (in dx coords), ie, |---fwd---X   X---back---|
            // and we are comparing the edges marked X
            while ((fwd != fend) && (fwd.dxhi() < bdxlo)) {
                fwd++;
                if (fwd == fend) {
                    LOGL_DEBUG(_log, "Reached fend");
                } else {
                    LOGL_DEBUG(_log, "Advanced to forward span %i, [%i, %i]",
                               fy, fwd.x0(), fwd.x1());
                }
            }
        } else if (fdxlo > bdxlo) {
            LOGL_DEBUG(_log, "Advancing backward.");
            // While the "backward" span is entirely to the "left" of the "foreward" span,
            // (in dx coords), ie, |---back---X   X---fwd---|
            // and we are comparing the edges marked X
            while ((back != bend) && (back.dxhi() < fdxlo)) {
                back++;
                if (back == bend) {
                    LOGL_DEBUG(_log, "Reached bend");
                } else {
                    LOGL_DEBUG(_log, "Advanced to backward span %i, [%i, %i]",
                               by, back.x0(), back.x1());
                }
            }
        }

        if ((back == bend) || (fwd == fend)) {
            // We reached the end of the row without finding spans that could
            // overlap.  Move onto the next dy.
            if (back == bend) {
                LOGL_DEBUG(_log, "Reached bend");
            }
            if (fwd == fend) {
                LOGL_DEBUG(_log, "Reached fend");
            }
            back = bend;
            fwd  = fend;
            dy++;
            continue;
        }

        // Spans may overlap -- find the overlapping part.
        int dxlo = std::max(fwd.dxlo(), back.dxlo());
        int dxhi = std::min(fwd.dxhi(), back.dxhi());
        if (dxlo <= dxhi) {
            LOGL_DEBUG(_log, "Adding span fwd %i, [%i, %i],  back %i, [%i, %i]",
                       fy, cx+dxlo, cx+dxhi, by, cx-dxhi, cx-dxlo);
            sfoot->addSpan(fy, cx + dxlo, cx + dxhi);
            sfoot->addSpan(by, cx - dxhi, cx - dxlo);
        }

        // Advance the one whose "hi" edge is smallest
        if (fwd.dxhi() < back.dxhi()) {
            fwd++;
            if (fwd == fend) {
                LOGL_DEBUG(_log, "Stepped to fend");
            } else {
                LOGL_DEBUG(_log, "Stepped forward to span %i, [%i, %i]",
                           fwd.y(), fwd.x0(), fwd.x1());
            }
        } else {
            back++;
            if (back == bend) {
                LOGL_DEBUG(_log, "Stepped to bend");
            } else {
                LOGL_DEBUG(_log, "Stepped backward to span %i, [%i, %i]",
                           back.y(), back.x0(), back.x1());
            }
        }

        if ((back == bend) || (fwd == fend)) {
            // Reached the end of the row.  On to the next dy!
            if (back == bend) {
                LOGL_DEBUG(_log, "Reached bend");
            }
            if (fwd == fend) {
                LOGL_DEBUG(_log, "Reached fend");
            }
            back = bend;
            fwd  = fend;
            dy++;
            continue;
        }

    }
    sfoot->normalize();
    return sfoot;
}

template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
std::pair<typename PTR(lsst::afw::image::Image<ImagePixelT>),
          typename PTR(lsst::afw::detection::Footprint) >
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
buildSymmetricTemplate(
    MaskedImageT const& img,
    det::Footprint const& foot,
    det::PeakRecord const& peak,
    double sigma1,
    bool minZero,
    bool patchEdge,
    bool* patchedEdges) {

    typedef typename MaskedImageT::const_xy_locator xy_loc;
    typedef typename det::Footprint::SpanList SpanList;

    *patchedEdges = false;

    int cx = peak.getIx();
    int cy = peak.getIy();

    LOG_LOGGER _log = LOG_GET("meas.deblender.symmetricFootprint");

    if (!img.getBBox(image::PARENT).contains(foot.getBBox())) {
        throw LSST_EXCEPT(lsst::pex::exceptions::LengthError, "Image too small for footprint");
    }

    FootprintPtrT sfoot = symmetrizeFootprint(foot, cx, cy);
    if (!sfoot) {
        return std::pair<ImagePtrT, FootprintPtrT>(ImagePtrT(), sfoot);
    }

    if (!img.getBBox(image::PARENT).contains(sfoot->getBBox())) {
        throw LSST_EXCEPT(lsst::pex::exceptions::LengthError,
                          "Image too small for symmetrized footprint");
    }
    const SpanList spans = sfoot->getSpans();

    // does this footprint touch an EDGE?
    bool touchesEdge = false;
    if (patchEdge) {
        LOGL_DEBUG(_log, "Checking footprint for EDGE bits");
        MaskPtrT mask = img.getMask();
        bool edge = false;
        MaskPixelT edgebit = mask->getPlaneBitMask("EDGE");
        for (SpanList::const_iterator fwd=spans.begin();
             fwd != spans.end(); ++fwd) {
            int x0 = (*fwd)->getX0();
            int x1 = (*fwd)->getX1();
            typename MaskT::x_iterator xiter =
                mask->x_at(x0 - mask->getX0(), (*fwd)->getY() - mask->getY0());
            for (int x=x0; x<=x1; ++x, ++xiter) {
                if ((*xiter) & edgebit) {
                    edge = true;
                    break;
                }
            }
            if (edge)
                break;
        }
        if (edge) {
            LOGL_DEBUG(_log, "Footprint includes an EDGE pixel.");
            touchesEdge = true;
        }
    }

    // The result image:
    ImagePtrT targetimg(new ImageT(sfoot->getBBox()));

    SpanList::const_iterator fwd  = spans.begin();
    SpanList::const_iterator back = spans.end()-1;

    ImagePtrT theimg = img.getImage();

    for (; fwd <= back; fwd++, back--) {
        int fy = (*fwd)->getY();
        int by = (*back)->getY();

        for (int fx=(*fwd)->getX0(), bx=(*back)->getX1();
             fx <= (*fwd)->getX1();
             fx++, bx--) {
            // FIXME -- CURRENTLY WE IGNORE THE MASK PLANE!  options
            // include ORing the mask bits, or being clever about
            // ignoring some masked pixels, or copying the mask bits
            // of the min pixel

            // We have already checked the bounding box, so this should always be satisfied
            assert(theimg->getBBox(image::PARENT).contains(geom::Point2I(fx, fy)));
            assert(theimg->getBBox(image::PARENT).contains(geom::Point2I(bx, by)));

            // FIXME -- we could do this with image iterators instead.
            // But first profile to show that it's necessary and an
            // improvement.
            ImagePixelT pixf = theimg->get0(fx, fy);
            ImagePixelT pixb = theimg->get0(bx, by);
            ImagePixelT pix = std::min(pixf, pixb);
            if (minZero) {
                pix = std::max(pix, static_cast<ImagePixelT>(0));
            }
            targetimg->set0(fx, fy, pix);
            targetimg->set0(bx, by, pix);

        }
    }


    if (touchesEdge) {
        // Find spans whose mirrors fall outside the image bounds,
        // grow the footprint to include those spans, and plug in
        // their pixel values.
        geom::Box2I bb = sfoot->getBBox();

        // Actually, it's not necessarily the IMAGE bounds that count
        //-- the footprint may not go right to the image edge.
        //geom::Box2I imbb = img.getBBox();
        geom::Box2I imbb = foot.getBBox();

        LOGL_DEBUG(_log, "Footprint touches EDGE: start bbox [%i,%i],[%i,%i]",
                   bb.getMinX(), bb.getMaxX(), bb.getMinY(), bb.getMaxY());
        // original footprint spans
        const SpanList ospans = foot.getSpans();
        for (fwd = ospans.begin(); fwd != ospans.end(); ++fwd) {
            int y = (*fwd)->getY();
            int x = (*fwd)->getX0();
            // mirrored coords
            int ym = cy + (cy - y);
            int xm = cx + (cx - x);
            if (!imbb.contains(geom::Point2I(xm, ym))) {
                bb.include(geom::Point2I(x, y));
            }
            x = (*fwd)->getX1();
            xm = cx + (cx - x);
            if (!imbb.contains(geom::Point2I(xm, ym))) {
                bb.include(geom::Point2I(x, y));
            }
        }
        LOGL_DEBUG(_log, "Footprint touches EDGE: grown bbox [%i,%i],[%i,%i]",
                   bb.getMinX(), bb.getMaxX(), bb.getMinY(), bb.getMaxY());

        // New template image
        ImagePtrT targetimg2(new ImageT(bb));
        copyWithinFootprint(*sfoot, targetimg, targetimg2);

        LOGL_DEBUG(_log, "Symmetric footprint spans:");
        const SpanList sspans = sfoot->getSpans();
        for (fwd = sspans.begin(); fwd != sspans.end(); ++fwd) {
            LOGL_DEBUG(_log, "  %s", (*fwd)->toString().c_str());
        }

        // copy original 'img' pixels for the portion of spans whose
        // mirrors are out of bounds.
        for (fwd = ospans.begin(); fwd != ospans.end(); ++fwd) {
            int y   = (*fwd)->getY();
            int x0  = (*fwd)->getX0();
            int x1 = (*fwd)->getX1();
            // mirrored coords
            int ym  = cy + (cy - y);
            int xm0 = cx + (cx - x0);
            int xm1 = cx + (cx - x1);
            bool in0 = imbb.contains(geom::Point2I(xm0, ym));
            bool in1 = imbb.contains(geom::Point2I(xm1, ym));
            if (in0 && in1) {
                // both endpoints of the symmetric span are in bounds; nothing to do
                continue;
            }
            // clip to the part of the span where the mirror is out of bounds
            if (in0) {
                // the mirror of x0 is in-bounds; move x0 to be the first pixel
                // whose mirror would be out-of-bounds
                x0 = cx + (cx - (imbb.getMinX() - 1));
            }
            if (in1) {
                x1 = cx + (cx - (imbb.getMaxX() + 1));
            }
            LOGL_DEBUG(_log, "Span y=%i, x=[%i,%i] has mirror (%i,[%i,%i]) out-of-bounds; clipped to %i,[%i,%i]",
                       y, (*fwd)->getX0(), (*fwd)->getX1(), ym, xm1, xm0, y, x0, x1);
            typename MaskedImageT::x_iterator initer =
                img.x_at(x0 - img.getX0(), y - img.getY0());
            typename ImageT::x_iterator outiter =
                targetimg2->x_at(x0 - targetimg2->getX0(), y - targetimg2->getY0());
            for (int x=x0; x<=x1; ++x, ++outiter, ++initer) {
                *outiter = initer.image();
            }
            sfoot->addSpan(y, x0, x1);
        }
        sfoot->normalize();
        targetimg = targetimg2;
    }

    *patchedEdges = touchesEdge;
    return std::pair<ImagePtrT, FootprintPtrT>(targetimg, sfoot);
}

template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
bool
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
hasSignificantFluxAtEdge(ImagePtrT img,
                         PTR(det::Footprint) sfoot,
                         ImagePixelT thresh) {
    typedef typename det::Footprint::SpanList SpanList;

    LOG_LOGGER _log = LOG_GET("meas.deblender.hasSignificantFluxAtEdge");

    // Find edge template pixels with significant flux -- perhaps
    // because their symmetric pixels were outside the footprint?
    // (clipped by an image edge, etc)
    PTR(det::Footprint) edge = sfoot->findEdgePixels();

    const SpanList spans = edge->getSpans();
    for (SpanList::const_iterator sp = spans.begin(); sp != spans.end(); ++sp) {
        int const y  = (*sp)->getY();
        int const x0 = (*sp)->getX0();
        int const x1 = (*sp)->getX1();
        int x;
        typename ImageT::const_x_iterator xiter;
        for (xiter = img->x_at(x0 - img->getX0(), y - img->getY0()), x=x0; x<=x1; ++x, ++xiter) {
            if (*xiter >= thresh) {
                return true;
            }
        }
    }
    return false;
}

template<typename ImagePixelT, typename MaskPixelT, typename VariancePixelT>
std::shared_ptr<det::Footprint>
deblend::BaselineUtils<ImagePixelT,MaskPixelT,VariancePixelT>::
getSignificantEdgePixels(ImagePtrT img,
                         PTR(det::Footprint) sfoot,
                         ImagePixelT thresh) {
    LOG_LOGGER _log = LOG_GET("meas.deblender.getSignificantEdgePixels");

    sfoot->normalize();                 // Algorithms require spans sorted by y

    PTR(det::Footprint) significant(new det::Footprint(sfoot->getPeaks().getSchema()));

    int const x0 = img->getX0(), y0 = img->getY0();
    CONST_PTR(det::Footprint) const edges = sfoot->findEdgePixels();
    for (det::Footprint::SpanList::const_iterator ss = edges->getSpans().begin();
         ss != edges->getSpans().end(); ++ss) {
        geom::Span const& span = **ss;
        int const y = span.getY();
        int x = span.getX0();
        typename ImageT::const_x_iterator iter = img->x_at(x - x0, y - y0);
        bool onSpan = false;            // Are we in a span of interest
        int xSpan;                      // Starting x of span
        for (; x <= span.getX1(); ++x, ++iter) {
            if (*iter >= thresh) {
                onSpan = true;
                xSpan = x;
            } else if (onSpan) {
                onSpan = false;
                significant->addSpanInSeries(y, xSpan, x - 1);
            }
        }
        if (onSpan) {
            significant->addSpanInSeries(y, xSpan, span.getX1());
        }
    }

    return significant;
}


// Instantiate
template class deblend::BaselineUtils<float>;