Jungfraujoch/image_analysis/pixel_refinement/PixelRefine.cpp

// SPDX-FileCopyrightText: 2025 Filip Leonarski, Paul Scherrer Institute <filip.leonarski@psi.ch>
// SPDX-License-Identifier: GPL-3.0-only

#include "PixelRefine.h"

#include <Eigen/Dense>
#include <ceres/ceres.h>
#include <ceres/rotation.h>

#include "../geom_refinement/LatticeReduction.h"

namespace {

// Per-pixel observation, in *corrected* intensity units (solid-angle and
// polarization correction already folded in, consistently for signal and
// background). Geometry-independent quantities are precomputed here so that the
// Ceres cost functor stays cheap.
struct PixelObs {
    double x, y;          // detector pixel coordinate
    double Iobs;          // corrected pixel value (signal + background)
    double Ibkg;          // corrected background estimate (azimuthal bin mean)
    double weight;        // 1 / sigma_pixel
    double A_recip;       // reciprocal-space area subtended by the pixel (Jacobian)
    double angle_rad;     // goniometer angle of this observation
};

// One reflection together with the pixels of its shoebox.
struct ReflGroup {
    int h, k, l;
    double d;
    double Itrue;             // reference intensity (held fixed)
    double R_bw_sq;           // bandwidth radial-width^2 contribution (0 = monochromatic)
    double predicted_x, predicted_y;
    std::vector<PixelObs> pixels;
};

double SafeInv(double x, double fallback) {
    if (!std::isfinite(x) || std::fabs(x) < 1e-30)
        return fallback;
    return 1.0 / x;
}

// Per-pixel: map a detector pixel through the current geometry into the
// reference reciprocal frame. Cheap (a few trig + one rotation); depends on the
// pixel and the detector geometry, not on the lattice.
template<typename T>
void ObservedRecip(const T *beam, const T *distance_mm, const T *detector_rot,
                   const T *rotation_axis, double obs_x, double obs_y,
                   double pixel_size, double inv_lambda, double angle_rad,
                   Eigen::Matrix<T, 3, 1> &e_obs_recip) {
    // PyFAI convention (left-handed for rot1/rot2): rot3 = 0 assumed.
    const T c1 = ceres::cos(detector_rot[0]);
    const T s1 = ceres::sin(detector_rot[0]);
    const T c2 = ceres::cos(detector_rot[1]);
    const T s2 = ceres::sin(detector_rot[1]);

    const T det_x = (T(obs_x) - beam[0]) * T(pixel_size);
    const T det_y = (T(obs_y) - beam[1]) * T(pixel_size);
    const T det_z = T(distance_mm[0]);

    const T t1_x = c1 * det_x + s1 * det_z;
    const T t1_y = det_y;
    const T t1_z = -s1 * det_x + c1 * det_z;

    const T x = t1_x;
    const T y = c2 * t1_y + s2 * t1_z;
    const T z = -s2 * t1_y + c2 * t1_z;

    const T inv_norm = T(1) / ceres::sqrt(x * x + y * y + z * z);

    T recip_raw[3] = {
        x * inv_norm * T(inv_lambda),
        y * inv_norm * T(inv_lambda),
        (z * inv_norm - T(1.0)) * T(inv_lambda)
    };
    const T aa_back[3] = {
        T(angle_rad) * rotation_axis[0],
        T(angle_rad) * rotation_axis[1],
        T(angle_rad) * rotation_axis[2]
    };
    T recip_obs[3];
    ceres::AngleAxisRotatePoint(aa_back, recip_raw, recip_obs);
    e_obs_recip = Eigen::Matrix<T, 3, 1>(recip_obs[0], recip_obs[1], recip_obs[2]);
}

// Per-reflection: predicted node g_hkl, |g_hkl|^2, and the Ewald-sphere normal.
// This is the expensive part (symmetry-aware B matrix, three rotations, cross
// products) - it depends only on the lattice (p0,p1,p2) and hkl, so for a whole
// shoebox it can be computed once. Convention identical to XtalOptimizer.
template<typename T>
bool PredictedNode(const T *p0, const T *p1, const T *p2,
                   double exp_h, double exp_k, double exp_l,
                   gemmi::CrystalSystem symmetry, double inv_lambda,
                   Eigen::Matrix<T, 3, 1> &e_pred_recip,
                   Eigen::Matrix<T, 3, 1> &n_radial, T &q_sq) {
    Eigen::Matrix<T, 3, 1> e_uc_len = Eigen::Matrix<T, 3, 1>::Zero();
    Eigen::Matrix<T, 3, 3> Bmat = Eigen::Matrix<T, 3, 3>::Identity();

    if (symmetry == gemmi::CrystalSystem::Hexagonal) {
        e_uc_len << p1[0], p1[0], p1[2];
        Bmat(0, 1) = T(-0.5);
        Bmat(1, 1) = T(sqrt(3.0) / 2.0);
    } else if (symmetry == gemmi::CrystalSystem::Orthorhombic) {
        e_uc_len << p1[0], p1[1], p1[2];
    } else if (symmetry == gemmi::CrystalSystem::Tetragonal) {
        e_uc_len << p1[0], p1[0], p1[2];
    } else if (symmetry == gemmi::CrystalSystem::Cubic) {
        e_uc_len << p1[0], p1[0], p1[0];
    } else if (symmetry == gemmi::CrystalSystem::Monoclinic) {
        e_uc_len << p1[0], p1[1], p1[2];
        Bmat(0, 2) = ceres::cos(p2[0]);
        Bmat(2, 2) = ceres::sin(p2[0]);
    } else {
        const T ca = ceres::cos(p2[0]);
        const T cb = ceres::cos(p2[1]);
        const T cg = ceres::cos(p2[2]);
        const T sg = ceres::sin(p2[2]);

        e_uc_len << p1[0], p1[1], p1[2];

        Bmat(0, 1) = cg;
        Bmat(1, 1) = sg;

        const T cx = cb;
        const T cy = (ca - cb * cg) / sg;
        const T v = T(1) - cx * cx - cy * cy;
        const T cz = (v >= T(0)) ? ceres::sqrt(v) : T(0);

        Bmat(0, 2) = cx;
        Bmat(1, 2) = cy;
        Bmat(2, 2) = cz;
    }

    const T L0 = e_uc_len[0];
    const T L1 = e_uc_len[1];
    const T L2 = e_uc_len[2];

    T col0_unrot[3] = {Bmat(0, 0) * L0, Bmat(1, 0) * L0, Bmat(2, 0) * L0};
    T col1_unrot[3] = {Bmat(0, 1) * L1, Bmat(1, 1) * L1, Bmat(2, 1) * L1};
    T col2_unrot[3] = {Bmat(0, 2) * L2, Bmat(1, 2) * L2, Bmat(2, 2) * L2};

    T col0_rot[3], col1_rot[3], col2_rot[3];
    ceres::AngleAxisRotatePoint(p0, col0_unrot, col0_rot);
    ceres::AngleAxisRotatePoint(p0, col1_unrot, col1_rot);
    ceres::AngleAxisRotatePoint(p0, col2_unrot, col2_rot);

    const Eigen::Matrix<T, 3, 1> A(col0_rot[0], col0_rot[1], col0_rot[2]);
    const Eigen::Matrix<T, 3, 1> Bv(col1_rot[0], col1_rot[1], col1_rot[2]);
    const Eigen::Matrix<T, 3, 1> C(col2_rot[0], col2_rot[1], col2_rot[2]);

    const Eigen::Matrix<T, 3, 1> BxC = Bv.cross(C);
    const Eigen::Matrix<T, 3, 1> CxA = C.cross(A);
    const Eigen::Matrix<T, 3, 1> AxB = A.cross(Bv);

    const T Vol = A.dot(BxC);
    if (ceres::abs(Vol) < T(1e-12))
        return false;
    const T invV = T(1) / Vol;

    e_pred_recip = (BxC * T(exp_h) + CxA * T(exp_k) + AxB * T(exp_l)) * invV;
    q_sq = e_pred_recip.squaredNorm();

    // Ewald sphere centre at -k_i = (0,0,-inv_lambda); radial normal at g_hkl.
    const Eigen::Matrix<T, 3, 1> S_pred(
        e_pred_recip[0],
        e_pred_recip[1],
        e_pred_recip[2] + T(inv_lambda));
    const T S_pred_norm = S_pred.norm();
    if (S_pred_norm < T(1e-10))
        return false;

    n_radial = S_pred / S_pred_norm;
    return true;
}

} // namespace

// ---------------------------------------------------------------------------
// Cost functor
//
//   I_pred(pixel) = G * Itrue * B_term * P_radial * P_tangential + I_bkg
//
//   B_term       = exp(-B |q|^2 / 4)                    (Debye-Waller)
//   P_radial     = exp(-eps_r^2 / R0_eff^2)             (partiality: fraction of
//                                                        the mosaic blob on the
//                                                        Ewald sphere; <= 1)
//   P_tangential = A_recip/(pi R1^2) * exp(-eps_t^2/R1^2)(spatial profile on the
//                                                        detector, normalized so
//                                                        that sum over pixels ~ 1)
//
// The tangential factor is what makes this "profile fitting": summing
// I_pred - I_bkg over the shoebox reproduces G * Itrue * B_term * P_radial.
// The 1/(pi R1^2) normalization is the missing piece that decouples the profile
// width R1 from the overall scale G.
//
// X-ray bandwidth: a spread in lambda is a spread in the Ewald-sphere radius,
// i.e. a purely *radial* thickening of the shell. It adds (in quadrature) a
// resolution-dependent term to the radial width:
//     R0_eff^2 = R0^2 + R_bw^2 ,   R_bw^2 = (b*lambda)^2 / (2 d^4)
// where b = relative bandwidth (sigma of dlambda/lambda). R_bw grows like 1/d^2,
// so bandwidth leaves low-resolution spots sharp and smears high-resolution ones
// radially - the pink-beam/DMM signature. R_bw_sq is a fixed per-reflection
// constant (b is known), so R0 keeps meaning "intrinsic" width (mosaic +
// divergence + beam). b = 0 makes R_bw = 0: a monochromatic no-op.
// ---------------------------------------------------------------------------
struct PixelResidual {
    PixelResidual(const PixelObs &obs, double Itrue,
                  double lambda, double pixel_size,
                  double exp_h, double exp_k, double exp_l,
                  double R_bw_sq,
                  gemmi::CrystalSystem symmetry)
        : Itrue(Itrue), Iobs(obs.Iobs), Ibkg(obs.Ibkg), weight(obs.weight),
          A_recip(obs.A_recip), obs_x(obs.x), obs_y(obs.y),
          inv_lambda(1.0 / lambda), pixel_size(pixel_size),
          exp_h(exp_h), exp_k(exp_k), exp_l(exp_l),
          R_bw_sq(R_bw_sq), angle_rad(obs.angle_rad), symmetry(symmetry) {
        if (std::fabs(lambda) < 1e-6)
            throw JFJochException(JFJochExceptionCategory::InputParameterInvalid,
                                  "Lambda cannot be close to zero");
    }

    // Maps a detector pixel through the current geometry + lattice into the
    // reference reciprocal frame and returns:
    //   q_sq        = |g_hkl|^2                 (predicted node, for B-factor)
    //   eps_radial  = deviation along Ewald normal (partiality direction)
    //   eps_tang_sq = squared deviation in the detector-tangential plane (profile)
    template<typename T>
    bool GeometryTerms(const T *const beam,
                       const T *const distance_mm,
                       const T *const detector_rot,
                       const T *const rotation_axis,
                       const T *const p0,
                       const T *const p1,
                       const T *const p2,
                       T &q_sq, T &eps_radial, T &eps_tang_sq) const {
        Eigen::Matrix<T, 3, 1> e_obs_recip;
        ObservedRecip(beam, distance_mm, detector_rot, rotation_axis,
                      obs_x, obs_y, pixel_size, inv_lambda, angle_rad, e_obs_recip);

        Eigen::Matrix<T, 3, 1> e_pred_recip, n_radial;
        if (!PredictedNode(p0, p1, p2, exp_h, exp_k, exp_l, symmetry, inv_lambda,
                           e_pred_recip, n_radial, q_sq))
            return false;

        const Eigen::Matrix<T, 3, 1> delta_q = e_obs_recip - e_pred_recip;
        eps_radial = delta_q.dot(n_radial);
        eps_tang_sq = (delta_q - eps_radial * n_radial).squaredNorm();
        return true;
    }

    // Assembles the full model intensity for the pixel from the geometry terms.
    template<typename T>
    bool Model(const T *const beam, const T *const distance_mm,
               const T *const detector_rot, const T *const rotation_axis,
               const T *const p0, const T *const p1, const T *const p2,
               const T *const scale_factor, const T *const B, const T *const R,
               T &Ipred) const {
        T q_sq, eps_radial, eps_tang_sq;
        if (!GeometryTerms(beam, distance_mm, detector_rot, rotation_axis,
                           p0, p1, p2, q_sq, eps_radial, eps_tang_sq))
            return false;

        if (R[0] < T(1e-10) || R[1] < T(1e-10))
            return false;

        const T B_term = ceres::exp(-B[0] * q_sq / T(4.0));

        // Separable Gaussian spot model:
        //   radial  P_r(e) = exp(-e^2/R0_eff^2)                      (peak-normalized, in (0,1])
        //   tangent g_t(e) = exp(-|e|^2/R1^2) / (pi R1^2)            [1/A^-2]
        // The pixel captures the fraction g_t * A_recip of the tangential profile
        // (A_recip = reciprocal area the pixel subtends; sum over shoebox ~ 1).
        // The radial factor is the still-image partiality (how far the reflection
        // sits from the Ewald sphere); the overall scale is carried by the free G.
        //
        // IMPORTANT: the radial factor MUST use the same convention here as the
        // extraction's `partiality` (peak-normalized), otherwise image_scale_corr
        // = 1/(partiality*G*B) does not invert the model and a leftover, R0_eff-
        // dependent (hence resolution-dependent) factor biases the intensities.
        // R0_eff folds in the energy-bandwidth broadening via R_bw_sq.
        const T R0_eff_sq = R[0] * R[0] + T(R_bw_sq);
        const T P_radial = ceres::exp(-eps_radial * eps_radial / R0_eff_sq);
        const T P_tang = T(A_recip) * ceres::exp(-eps_tang_sq / (R[1] * R[1]))
                         / (T(M_PI) * R[1] * R[1]);

        const T signal = scale_factor[0] * T(Itrue) * B_term * P_radial * P_tang;
        Ipred = signal + T(Ibkg);
        return true;
    }

    template<typename T>
    bool operator()(const T *const beam,
                    const T *const distance_mm,
                    const T *const detector_rot,
                    const T *const rotation_axis,
                    const T *const p0,
                    const T *const p1,
                    const T *const p2,
                    const T *const scale_factor,
                    const T *const B,
                    const T *const R,
                    T *residual) const {
        T Ipred;
        if (!Model(beam, distance_mm, detector_rot, rotation_axis,
                   p0, p1, p2, scale_factor, B, R, Ipred))
            return false;

        residual[0] = (Ipred - T(Iobs)) * T(weight);
        return true;
    }

    const double Itrue, Iobs, Ibkg, weight, A_recip;
    const double obs_x, obs_y;
    const double inv_lambda;
    const double pixel_size;
    const double exp_h, exp_k, exp_l;
    const double R_bw_sq;   // bandwidth radial-width^2 contribution (0 = monochromatic)
    const double angle_rad;
    gemmi::CrystalSystem symmetry;
};

// ---------------------------------------------------------------------------
// Per-shoebox cost functor
//
// One residual block per reflection emitting N residuals (one per shoebox pixel).
// The expensive per-reflection geometry (PredictedNode: symmetry-aware B matrix,
// three rotations, cross products) is computed ONCE; only the cheap per-pixel
// ObservedRecip + Gaussian profile run in the pixel loop. This is identical in
// value to the old one-block-per-pixel formulation but ~(pixels-per-shoebox)x
// fewer evaluations of the costly node computation. Uses the same shared helpers
// (and hence the same conventions) as PixelResidual.
// ---------------------------------------------------------------------------
struct ShoeboxResidual {
    ShoeboxResidual(const ReflGroup &g, double lambda, double pixel_size,
                    gemmi::CrystalSystem symmetry)
        : pixels(g.pixels), Itrue(g.Itrue), R_bw_sq(g.R_bw_sq),
          exp_h(g.h), exp_k(g.k), exp_l(g.l),
          inv_lambda(1.0 / lambda), pixel_size(pixel_size),
          angle_rad(g.pixels.empty() ? 0.0 : g.pixels.front().angle_rad),
          symmetry(symmetry) {}

    template<typename T>
    bool operator()(const T *const *params, T *residual) const {
        // Parameter blocks (order matches AddParameterBlock in Run):
        // 0 beam[2] 1 distance[1] 2 detector_rot[2] 3 rotation_axis[3]
        // 4 p0[3] 5 p1[3] 6 p2[3] 7 scale[1] 8 B[1] 9 R[2]
        const T *beam = params[0];
        const T *distance_mm = params[1];
        const T *detector_rot = params[2];
        const T *rotation_axis = params[3];
        const T *p0 = params[4];
        const T *p1 = params[5];
        const T *p2 = params[6];
        const T *scale_factor = params[7];
        const T *B = params[8];
        const T *R = params[9];

        if (R[0] < T(1e-10) || R[1] < T(1e-10))
            return false;

        // --- per-reflection: computed once ---------------------------------
        Eigen::Matrix<T, 3, 1> e_pred_recip, n_radial;
        T q_sq;
        if (!PredictedNode(p0, p1, p2, exp_h, exp_k, exp_l, symmetry, inv_lambda,
                           e_pred_recip, n_radial, q_sq))
            return false;

        const T B_term = ceres::exp(-B[0] * q_sq / T(4.0));
        const T R0_eff_sq = R[0] * R[0] + T(R_bw_sq);

        // --- per-pixel loop -------------------------------------------------
        for (size_t i = 0; i < pixels.size(); ++i) {
            const PixelObs &obs = pixels[i];

            Eigen::Matrix<T, 3, 1> e_obs_recip;
            ObservedRecip(beam, distance_mm, detector_rot, rotation_axis,
                          obs.x, obs.y, pixel_size, inv_lambda, angle_rad, e_obs_recip);

            const Eigen::Matrix<T, 3, 1> delta_q = e_obs_recip - e_pred_recip;
            const T eps_radial = delta_q.dot(n_radial);
            const T eps_tang_sq = (delta_q - eps_radial * n_radial).squaredNorm();

            const T P_radial = ceres::exp(-eps_radial * eps_radial / R0_eff_sq);
            const T P_tang = T(obs.A_recip) * ceres::exp(-eps_tang_sq / (R[1] * R[1]))
                             / (T(M_PI) * R[1] * R[1]);

            const T signal = scale_factor[0] * T(Itrue) * B_term * P_radial * P_tang;
            const T Ipred = signal + T(obs.Ibkg);
            residual[i] = (Ipred - T(obs.Iobs)) * T(obs.weight);
        }
        return true;
    }

    std::vector<PixelObs> pixels;
    const double Itrue, R_bw_sq;
    const double exp_h, exp_k, exp_l;
    const double inv_lambda, pixel_size, angle_rad;
    gemmi::CrystalSystem symmetry;
};

PixelRefine::PixelRefine(const DiffractionExperiment &experiment,
                         const AzimuthalIntegrationMapping &mapping,
                         const std::vector<MergedReflection> &reference)
    : mapping(mapping),
      xpixel(experiment.GetXPixelsNum()),
      ypixel(experiment.GetYPixelsNum()),
      experiment(experiment),
      hkl_key_generator(experiment.GetScalingSettings().GetMergeFriedel(),
                        experiment.GetSpaceGroupNumber().value_or(1)) {
    for (const auto &ref: reference)
        reference_data[hkl_key_generator(ref)] = ref.I;
}

void PixelRefine::BuildParameterBlocks(const PixelRefineData &data,
                                       double beam[2], double &dist_mm,
                                       double detector_rot[2], double rot_vec[3],
                                       double latt_vec0[3], double latt_vec1[3], double latt_vec2[3]) const {
    beam[0] = data.geom.GetBeamX_pxl();
    beam[1] = data.geom.GetBeamY_pxl();
    dist_mm = data.geom.GetDetectorDistance_mm();
    detector_rot[0] = data.geom.GetPoniRot1_rad();
    detector_rot[1] = data.geom.GetPoniRot2_rad();
    rot_vec[0] = 1.0; rot_vec[1] = 0.0; rot_vec[2] = 0.0;
    if (auto axis = data.geom.GetRotation()) {
        rot_vec[0] = axis->GetAxis().x;
        rot_vec[1] = axis->GetAxis().y;
        rot_vec[2] = axis->GetAxis().z;
    }

    for (int i = 0; i < 3; ++i)
        latt_vec0[i] = latt_vec1[i] = latt_vec2[i] = 0.0;

    double beta = data.latt.GetUnitCell().beta;
    switch (data.crystal_system) {
        case gemmi::CrystalSystem::Orthorhombic:
            LatticeToRodriguesAndLengths_GS(data.latt, latt_vec0, latt_vec1);
            break;
        case gemmi::CrystalSystem::Tetragonal:
            LatticeToRodriguesAndLengths_GS(data.latt, latt_vec0, latt_vec1);
            latt_vec1[0] = (latt_vec1[0] + latt_vec1[1]) / 2.0;
            break;
        case gemmi::CrystalSystem::Cubic:
            LatticeToRodriguesAndLengths_GS(data.latt, latt_vec0, latt_vec1);
            latt_vec1[0] = (latt_vec1[0] + latt_vec1[1] + latt_vec1[2]) / 3.0;
            break;
        case gemmi::CrystalSystem::Hexagonal:
            LatticeToRodriguesAndLengths_Hex(data.latt, latt_vec0, latt_vec1);
            break;
        case gemmi::CrystalSystem::Monoclinic:
            LatticeToRodriguesLengthsBeta_Mono(data.latt, latt_vec0, latt_vec1, beta);
            latt_vec2[0] = beta;
            break;
        default: {
            LatticeToRodriguesAndLengths_GS(data.latt, latt_vec0, latt_vec1);
            const auto uc = data.latt.GetUnitCell();
            latt_vec2[0] = uc.alpha * M_PI / 180.0;
            latt_vec2[1] = uc.beta * M_PI / 180.0;
            latt_vec2[2] = uc.gamma * M_PI / 180.0;
            break;
        }
    }
}

template<class T>
void PixelRefine::Run(const T *image,
                      const AzimuthalIntegrationProfile &profile,
                      BraggPrediction &prediction,
                      PixelRefineData &data) {
    data.solved = false;
    data.reflections.clear();

    const double lambda = data.geom.GetWavelength_A();
    const double pixel_size = data.geom.GetPixelSize_mm();

    const BraggPredictionSettings settings_prediction{
        .high_res_A = experiment.GetBraggIntegrationSettings().GetDMinLimit_A(),
        .max_hkl = 100,
        .centering = data.centering,
        .bandwidth_sigma = static_cast<float>(data.bandwidth)  // relative Δλ/λ sigma
    };

    const auto azim_result = profile.GetResult();
    const auto azim_std = profile.GetStd();
    const auto &pixel_to_bin = mapping.GetPixelToBin();
    const auto &corrections = mapping.Corrections();
    // pixel_to_bin stores the *full* bin index (azimuthal_sector * q_bins + q_bin),
    // so the valid range is the total number of bins, i.e. the profile size - NOT
    // GetAzimuthalBinCount() (which is only the number of azimuthal sectors).
    const int total_bin_count = static_cast<int>(azim_result.size());

    const double angle_rad = data.angle_deg * M_PI / 180.0;
    const int radius = data.shoebox_radius;

    // Exact reciprocal-space area a 1x1 pixel subtends, |dq/dx x dq/dy|, via
    // finite differences of the detector->reciprocal map. This is the Jacobian
    // between the curved Ewald-sphere sampling and flat reciprocal space, and it
    // is exactly the geometric factor that plays the role of the Lorentz factor
    // for stills: where the sphere grazes reciprocal space obliquely, a pixel
    // covers more reciprocal volume and the captured fraction grows. It tracks
    // the refined geometry because it reads the current data.geom each iteration.
    auto recip_area = [&](double x, double y) -> double {
        const Coord qx = data.geom.DetectorToRecip(x + 0.5, y) - data.geom.DetectorToRecip(x - 0.5, y);
        const Coord qy = data.geom.DetectorToRecip(x, y + 0.5) - data.geom.DetectorToRecip(x, y - 0.5);
        return (qx % qy).Length();
    };

    // Bandwidth radial-width^2 (in the code's R = sqrt(2)*sigma convention):
    //   R_bw^2 = (b*lambda)^2 / (2 d^4),   b = relative bandwidth (sigma).
    // A fixed per-reflection constant; data.bandwidth == 0 -> monochromatic no-op.
    const double bw = data.bandwidth;
    auto bandwidth_radial_sq = [&](double d) -> double {
        if (bw <= 0.0 || d <= 0.0)
            return 0.0;
        const double bl = bw * lambda;
        return bl * bl / (2.0 * d * d * d * d);
    };

    // Mutable experiment whose geometry is re-synced from the refined data.geom
    // before each prediction, so shoeboxes track the refined geometry/cell.
    DiffractionExperiment exp_iter = experiment;

    // State retained after the loop for the final reflection extraction.
    std::vector<ReflGroup> groups;
    double beam[2] = {0, 0};
    double dist_mm = data.geom.GetDetectorDistance_mm();
    double detector_rot[2] = {0, 0};
    double rot_vec[3] = {1.0, 0.0, 0.0};
    double latt_vec0[3] = {0, 0, 0}; // orientation (Rodrigues)
    double latt_vec1[3] = {0, 0, 0}; // lengths
    double latt_vec2[3] = {0, 0, 0}; // angles (rad)

    const bool eval_only = (data.max_iterations <= 0);
    const int n_iter = std::max(1, data.max_iterations);
    for (int iter = 0; iter < n_iter; ++iter) {
        // ---- 1. Re-sync prediction geometry from the (refined) model ----------
        exp_iter.BeamX_pxl(data.geom.GetBeamX_pxl())
                .BeamY_pxl(data.geom.GetBeamY_pxl())
                .DetectorDistance_mm(data.geom.GetDetectorDistance_mm())
                .PoniRot1_rad(data.geom.GetPoniRot1_rad())
                .PoniRot2_rad(data.geom.GetPoniRot2_rad());

        const int nrefl = prediction.Calc(exp_iter, data.latt, settings_prediction);

        // ---- 2. Collect per-reflection shoebox pixels -------------------------
        // GetReflections() returns the full pre-sized buffer; only the first
        // nrefl entries are valid for this image (the rest are stale/zeroed).
        groups.clear();
        const auto &predicted = prediction.GetReflections();
        for (int ri = 0; ri < nrefl; ++ri) {
            const auto &refl = predicted[ri];
            const auto hkl = hkl_key_generator(refl);
            if (!reference_data.contains(hkl))
                continue;

            ReflGroup g;
            g.h = refl.h;
            g.k = refl.k;
            g.l = refl.l;
            g.d = refl.d;
            g.Itrue = reference_data[hkl];
            g.R_bw_sq = bandwidth_radial_sq(refl.d);
            g.predicted_x = refl.predicted_x;
            g.predicted_y = refl.predicted_y;

            const int min_y = std::max<int>(refl.predicted_y - radius, 0);
            const int max_y = std::min<int>(refl.predicted_y + radius, ypixel - 1);
            const int min_x = std::max<int>(refl.predicted_x - radius, 0);
            const int max_x = std::min<int>(refl.predicted_x + radius, xpixel - 1);

            for (int y = min_y; y <= max_y; ++y) {
                for (int x = min_x; x <= max_x; ++x) {
                    const size_t npixel = xpixel * y + x;
                    const int azim_bin = pixel_to_bin[npixel];

                    // Skip pixels not mapped to a bin or carrying a sentinel
                    // (masked / saturated) value. We assume the pixel mask is
                    // already applied upstream.
                    if (azim_bin >= total_bin_count)
                        continue;
                    if (image[npixel] == std::numeric_limits<T>::max())
                        continue;
                    if (std::is_signed_v<T> && (image[npixel] == std::numeric_limits<T>::min()))
                        continue;

                    const double correction = corrections[npixel];
                    const double Ibkg = azim_result[azim_bin]; // already in corrected units
                    const double Ibkg_sigma = azim_std[azim_bin];
                    const double raw = static_cast<double>(image[npixel]);
                    const double Iobs = raw * correction;

                    // Per-pixel variance: Poisson noise of the corrected counts
                    // (var(c*N) = c^2 * N = c * Iobs) plus the background spread.
                    double var = correction * std::max(Iobs, 0.0) + Ibkg_sigma * Ibkg_sigma;
                    if (!(var > 1.0))
                        var = 1.0;

                    PixelObs obs{
                        .x = static_cast<double>(x),
                        .y = static_cast<double>(y),
                        .Iobs = Iobs,
                        .Ibkg = Ibkg,
                        .weight = 1.0 / std::sqrt(var),
                        .A_recip = recip_area(x, y),
                        .angle_rad = angle_rad
                    };
                    g.pixels.push_back(obs);
                }
            }

            if (!g.pixels.empty())
                groups.push_back(std::move(g));
        }

        if (groups.empty())
            return;

        // ---- 3. Set up parameter blocks (geometry part mirrors XtalOptimizer) -
        BuildParameterBlocks(data, beam, dist_mm, detector_rot, rot_vec,
                             latt_vec0, latt_vec1, latt_vec2);

        // ---- 4. Build the problem ---------------------------------------------
        // One residual block per shoebox (N residuals), so the expensive
        // per-reflection node geometry is evaluated once per reflection instead
        // of once per pixel.
        ceres::Problem problem;
        size_t residual_pixels = 0;
        for (const auto &g : groups) {
            auto *cost = new ceres::DynamicAutoDiffCostFunction<ShoeboxResidual>(
                new ShoeboxResidual(g, lambda, pixel_size, data.crystal_system));
            cost->AddParameterBlock(2); // beam
            cost->AddParameterBlock(1); // distance
            cost->AddParameterBlock(2); // detector_rot
            cost->AddParameterBlock(3); // rotation_axis
            cost->AddParameterBlock(3); // p0 (orientation)
            cost->AddParameterBlock(3); // p1 (lengths)
            cost->AddParameterBlock(3); // p2 (angles)
            cost->AddParameterBlock(1); // scale G
            cost->AddParameterBlock(1); // B
            cost->AddParameterBlock(2); // R
            cost->SetNumResiduals(static_cast<int>(g.pixels.size()));
            // No robust loss here: a per-block (whole-shoebox) Huber would act on
            // the sum of ~N squared residuals and mis-scale, unlike the previous
            // per-pixel Huber. Per-pixel sigma weighting is retained; per-pixel
            // outlier rejection (zingers) is a TODO if needed.
            problem.AddResidualBlock(cost, nullptr,
                                     beam, &dist_mm, detector_rot, rot_vec,
                                     latt_vec0, latt_vec1, latt_vec2,
                                     &data.scale_factor, &data.B_factor, data.R);
            residual_pixels += g.pixels.size();
        }
        data.residual_count = residual_pixels;

        // ---- 5. Constrain / bound parameter blocks ----------------------------
        if (!data.refine_orientation)
            problem.SetParameterBlockConstant(latt_vec0);

        if (!data.refine_unit_cell) {
            problem.SetParameterBlockConstant(latt_vec1);
            problem.SetParameterBlockConstant(latt_vec2);
        } else {
            for (int i = 0; i < 3; ++i) {
                problem.SetParameterLowerBound(latt_vec1, i, 5.0);
                problem.SetParameterUpperBound(latt_vec1, i, 1000.0);
            }
            if (data.crystal_system != gemmi::CrystalSystem::Monoclinic &&
                data.crystal_system != gemmi::CrystalSystem::Triclinic)
                problem.SetParameterBlockConstant(latt_vec2);
        }

        if (!data.refine_beam_center)
            problem.SetParameterBlockConstant(beam);

        if (!data.refine_distance) {
            problem.SetParameterBlockConstant(&dist_mm);
        } else {
            problem.SetParameterLowerBound(&dist_mm, 0, dist_mm * 0.9);
            problem.SetParameterUpperBound(&dist_mm, 0, dist_mm * 1.1);
        }

        if (!data.refine_detector_angles) {
            problem.SetParameterBlockConstant(detector_rot);
        } else {
            const double rng = 3.0 / 180.0 * M_PI;
            for (int i = 0; i < 2; ++i) {
                problem.SetParameterLowerBound(detector_rot, i, detector_rot[i] - rng);
                problem.SetParameterUpperBound(detector_rot, i, detector_rot[i] + rng);
            }
        }

        if (!data.refine_rotation_axis)
            problem.SetParameterBlockConstant(rot_vec);

        if (data.refine_scale)
            problem.SetParameterLowerBound(&data.scale_factor, 0, 0.0);
        else
            problem.SetParameterBlockConstant(&data.scale_factor);

        if (!data.refine_B)
            problem.SetParameterBlockConstant(&data.B_factor);

        if (data.refine_R) {
            problem.SetParameterLowerBound(data.R, 0, 1e-5);
            problem.SetParameterLowerBound(data.R, 1, 1e-5);
        } else {
            problem.SetParameterBlockConstant(data.R);
        }

        // ---- 6. Solve (or, for max_iterations<=0, just evaluate the cost) -----
        // Evaluate-only is the live-residual path: it reports the current cost
        // without moving any parameter, so a UI can show how good the present
        // R0/R1/bandwidth/geometry are as the user drags sliders.
        if (eval_only) {
            double cost = 0.0;
            problem.Evaluate(ceres::Problem::EvaluateOptions(), &cost, nullptr, nullptr, nullptr);
            data.final_cost = cost;
            data.solved = true;
        } else {
            ceres::Solver::Options options;
            options.linear_solver_type = ceres::DENSE_QR;
            options.minimizer_progress_to_stdout = false;
            options.logging_type = ceres::LoggingType::SILENT;
            options.max_solver_time_in_seconds = data.max_time_s;
            options.num_threads = 1;

            ceres::Solver::Summary summary;
            ceres::Solve(options, &problem, &summary);

            data.final_cost = summary.final_cost;
            data.solved = summary.IsSolutionUsable();
        }

        // ---- 7. Write refined geometry + lattice back into data ---------------
        if (data.refine_beam_center)
            data.geom.BeamX_pxl(beam[0]).BeamY_pxl(beam[1]);
        if (data.refine_distance)
            data.geom.DetectorDistance_mm(dist_mm);
        if (data.refine_detector_angles)
            data.geom.PoniRot1_rad(detector_rot[0]).PoniRot2_rad(detector_rot[1]);

        if (data.refine_orientation || data.refine_unit_cell) {
            switch (data.crystal_system) {
                case gemmi::CrystalSystem::Orthorhombic:
                    data.latt = AngleAxisAndCellToLattice(latt_vec0, latt_vec1, M_PI/2, M_PI/2, M_PI/2);
                    break;
                case gemmi::CrystalSystem::Tetragonal:
                    latt_vec1[1] = latt_vec1[0];
                    data.latt = AngleAxisAndCellToLattice(latt_vec0, latt_vec1, M_PI/2, M_PI/2, M_PI/2);
                    break;
                case gemmi::CrystalSystem::Cubic:
                    latt_vec1[1] = latt_vec1[0];
                    latt_vec1[2] = latt_vec1[0];
                    data.latt = AngleAxisAndCellToLattice(latt_vec0, latt_vec1, M_PI/2, M_PI/2, M_PI/2);
                    break;
                case gemmi::CrystalSystem::Hexagonal:
                    latt_vec1[1] = latt_vec1[0];
                    data.latt = AngleAxisAndCellToLattice(latt_vec0, latt_vec1, M_PI/2, M_PI/2, 2.0*M_PI/3.0);
                    break;
                case gemmi::CrystalSystem::Monoclinic:
                    data.latt = AngleAxisAndCellToLattice(latt_vec0, latt_vec1, M_PI/2, latt_vec2[0], M_PI/2);
                    break;
                default:
                    data.latt = AngleAxisAndCellToLattice(latt_vec0, latt_vec1,
                                                          latt_vec2[0], latt_vec2[1], latt_vec2[2]);
                    break;
            }
        }
    } // predict<->refine iterations

    // ---- Extract integrated reflections ---------------------------------------
    // Profile fitting gives the recorded amplitude (against the normalized
    // tangential profile P_t):
    //     J      = sum_p[ P_t,p (Iobs_p - Ibkg_p)/v_p ] / sum_p[ P_t,p^2 / v_p ]
    //            ~ G * Itrue * B_term * partiality            (recorded intensity)
    //     var(J) = 1 / sum_p[ P_t,p^2 / v_p ]
    //
    // Output split (Merge multiplies r.I * image_scale_corr and weights by
    // 1/(sigma*image_scale_corr)^2 - see Merge.cpp):
    //   r.I              = J / (B_term * partiality)   = G * Itrue  (B/partiality corrected)
    //   r.sigma          = sqrt(var(J)) / (B_term * partiality)
    //   r.partiality     = profile-weighted peak radial factor in (0,1]  (Merge filter only)
    //   r.image_scale_corr = 1/G                         (per-image scale ONLY)
    // so r.I * image_scale_corr = Itrue. B and partiality live on the intensity,
    // G lives on image_scale_corr - one clean meaning per field.
    data.reflections.reserve(groups.size());
    for (const auto &g : groups) {
        double num = 0.0, den = 0.0, bkg_sum = 0.0;
        double radial_sum = 0.0, radial_w = 0.0;
        size_t n = 0;

        for (const auto &obs : g.pixels) {
            PixelResidual pr(obs, 1.0, lambda, pixel_size, g.h, g.k, g.l, g.R_bw_sq, data.crystal_system);
            double q_sq, eps_r, eps_t_sq;
            if (!pr.GeometryTerms(beam, &dist_mm, detector_rot, rot_vec,
                                  latt_vec0, latt_vec1, latt_vec2, q_sq, eps_r, eps_t_sq))
                continue;
            if (!(data.R[0] > 0.0) || !(data.R[1] > 0.0))
                continue;

            // Normalized tangential profile (sum over shoebox ~ 1) -> fit weight.
            const double P_t = obs.A_recip * std::exp(-eps_t_sq / (data.R[1] * data.R[1]))
                               / (M_PI * data.R[1] * data.R[1]);
            // Peak-normalized radial factor (the partiality), in (0,1].
            // Bandwidth-broadened radial width, matching the model in Model().
            const double R0_eff_sq = data.R[0] * data.R[0] + g.R_bw_sq;
            const double P_radial = std::exp(-eps_r * eps_r / R0_eff_sq);

            const double v = SafeInv(obs.weight * obs.weight, 1.0); // pixel variance
            const double signal = obs.Iobs - obs.Ibkg;

            num += P_t * signal / v;
            den += P_t * P_t / v;
            radial_sum += P_radial * P_t;   // weight partiality by the spot core
            radial_w += P_t;
            bkg_sum += obs.Ibkg;
            ++n;
        }

        Reflection r{};
        r.h = g.h;
        r.k = g.k;
        r.l = g.l;
        r.d = static_cast<float>(g.d);
        r.predicted_x = static_cast<float>(g.predicted_x);
        r.predicted_y = static_cast<float>(g.predicted_y);
        r.observed_x = NAN;
        r.observed_y = NAN;
        r.rlp = 1.0f;
        r.partiality = (radial_w > 0.0) ? static_cast<float>(radial_sum / radial_w) : 1.0f;

        if (den > 0.0 && n > 0) {
            const double I_amp = num / den;             // ~ G*Itrue*B_term*partiality
            const double sigma_amp = std::sqrt(1.0 / den);
            const double B_term = std::exp(-data.B_factor / (4.0 * g.d * g.d));
            const double corr = static_cast<double>(r.partiality) * B_term; // B & partiality
            r.bkg = static_cast<float>(bkg_sum / static_cast<double>(n));
            r.observed = true;

            if (corr > 0.0 && data.scale_factor > 0.0) {
                r.I = static_cast<float>(I_amp / corr);       // = G*Itrue
                r.sigma = static_cast<float>(sigma_amp / corr);
                r.image_scale_corr = static_cast<float>(1.0 / data.scale_factor); // G only
            } else {
                r.I = static_cast<float>(I_amp);
                r.sigma = static_cast<float>(sigma_amp);
                r.image_scale_corr = NAN;
            }
        } else {
            r.I = 0.0f;
            r.sigma = NAN;
            r.bkg = 0.0f;
            r.observed = false;
        }
        data.reflections.push_back(r);
    }

    // ---- Per-image CC vs reference (the half/ref correlation diagnostic) -------
    // Pearson CC of the scaled estimate (r.I * image_scale_corr = Itrue_est)
    // against the reference intensities, over the matched reflections.
    {
        double sx = 0, sy = 0, sxx = 0, syy = 0, sxy = 0;
        size_t cn = 0;
        for (const auto &r : data.reflections) {
            if (!r.observed || !std::isfinite(r.I) || !std::isfinite(r.image_scale_corr))
                continue;
            const auto it = reference_data.find(hkl_key_generator(r));
            if (it == reference_data.end())
                continue;
            const double x = static_cast<double>(r.I) * static_cast<double>(r.image_scale_corr);
            const double y = it->second;
            if (!std::isfinite(x) || !std::isfinite(y))
                continue;
            sx += x; sy += y; sxx += x * x; syy += y * y; sxy += x * y; ++cn;
        }
        data.cc = NAN;
        data.cc_n = static_cast<int64_t>(cn);
        if (cn >= 3) {
            const double nd = static_cast<double>(cn);
            const double cov = sxy - sx * sy / nd;
            const double vx = sxx - sx * sx / nd;
            const double vy = syy - sy * sy / nd;
            if (vx > 0.0 && vy > 0.0)
                data.cc = cov / std::sqrt(vx * vy);
        }
    }
}

std::vector<float> PixelRefine::PredictImage(const AzimuthalIntegrationProfile &profile,
                                             BraggPrediction &prediction,
                                             const PixelRefineData &data,
                                             bool include_background) const {
    std::vector<float> img(xpixel * ypixel, 0.0f);

    const double lambda = data.geom.GetWavelength_A();
    const double pixel_size = data.geom.GetPixelSize_mm();
    const auto azim_result = profile.GetResult();
    const auto &pixel_to_bin = mapping.GetPixelToBin();
    const auto &corrections = mapping.Corrections();
    const int total_bin_count = static_cast<int>(azim_result.size());
    const double angle_rad = data.angle_deg * M_PI / 180.0;
    const int radius = data.shoebox_radius;
    const double bw = data.bandwidth;

    auto recip_area = [&](double x, double y) -> double {
        const Coord qx = data.geom.DetectorToRecip(x + 0.5, y) - data.geom.DetectorToRecip(x - 0.5, y);
        const Coord qy = data.geom.DetectorToRecip(x, y + 0.5) - data.geom.DetectorToRecip(x, y - 0.5);
        return (qx % qy).Length();
    };
    auto bandwidth_radial_sq = [&](double d) -> double {
        if (bw <= 0.0 || d <= 0.0)
            return 0.0;
        const double bl = bw * lambda;
        return bl * bl / (2.0 * d * d * d * d);
    };

    // The model works in solid-angle/polarization-corrected units (as in Run,
    // where Iobs = raw * correction). Map back to raw detector units (/ correction)
    // so the predicted image overlays directly on the original image.
    auto to_raw = [&](size_t npixel, double corrected) -> float {
        const double corr = corrections[npixel];
        return (corr > 0.0) ? static_cast<float>(corrected / corr) : 0.0f;
    };

    // Background base layer (per-pixel azimuthal mean), full-frame pass.
    if (include_background) {
        for (size_t p = 0; p < img.size(); ++p) {
            const int bin = pixel_to_bin[p];
            if (bin >= 0 && bin < total_bin_count)
                img[p] = to_raw(p, azim_result[bin]);
        }
    }

    double beam[2], dist_mm, detector_rot[2], rot_vec[3];
    double latt_vec0[3], latt_vec1[3], latt_vec2[3];
    BuildParameterBlocks(data, beam, dist_mm, detector_rot, rot_vec, latt_vec0, latt_vec1, latt_vec2);

    DiffractionExperiment exp_iter = experiment;
    exp_iter.BeamX_pxl(data.geom.GetBeamX_pxl())
            .BeamY_pxl(data.geom.GetBeamY_pxl())
            .DetectorDistance_mm(data.geom.GetDetectorDistance_mm())
            .PoniRot1_rad(data.geom.GetPoniRot1_rad())
            .PoniRot2_rad(data.geom.GetPoniRot2_rad());

    const BraggPredictionSettings settings_prediction{
        .high_res_A = experiment.GetBraggIntegrationSettings().GetDMinLimit_A(),
        .max_hkl = 100,
        .centering = data.centering,
        .bandwidth_sigma = static_cast<float>(data.bandwidth)  // relative Δλ/λ sigma
    };
    const int nrefl = prediction.Calc(exp_iter, data.latt, settings_prediction);
    const auto &predicted = prediction.GetReflections();

    for (int ri = 0; ri < nrefl; ++ri) {
        const auto &refl = predicted[ri];
        const auto it = reference_data.find(hkl_key_generator(refl));
        if (it == reference_data.end())
            continue;

        const double Itrue = it->second;
        const double R_bw_sq = bandwidth_radial_sq(refl.d);

        const int min_y = std::max<int>(refl.predicted_y - radius, 0);
        const int max_y = std::min<int>(refl.predicted_y + radius, ypixel - 1);
        const int min_x = std::max<int>(refl.predicted_x - radius, 0);
        const int max_x = std::min<int>(refl.predicted_x + radius, xpixel - 1);

        for (int y = min_y; y <= max_y; ++y) {
            for (int x = min_x; x <= max_x; ++x) {
                const size_t npixel = xpixel * y + x;

                // Pure Bragg signal: Ibkg = 0 so Model() returns signal only; the
                // background is already laid down above. Same code path as Run.
                PixelObs obs{
                    .x = static_cast<double>(x),
                    .y = static_cast<double>(y),
                    .Iobs = 0.0,
                    .Ibkg = 0.0,
                    .weight = 1.0,
                    .A_recip = recip_area(x, y),
                    .angle_rad = angle_rad
                };
                PixelResidual pr(obs, Itrue, lambda, pixel_size,
                                 refl.h, refl.k, refl.l, R_bw_sq, data.crystal_system);

                double signal = 0.0;
                if (pr.Model(beam, &dist_mm, detector_rot, rot_vec,
                             latt_vec0, latt_vec1, latt_vec2,
                             &data.scale_factor, &data.B_factor, data.R, signal))
                    img[npixel] += to_raw(npixel, signal);
            }
        }
    }

    return img;
}

template<class T>
std::vector<float> PixelRefine::ChiSquaredImage(const T *image,
                                                const AzimuthalIntegrationProfile &profile,
                                                BraggPrediction &prediction,
                                                const PixelRefineData &data) const {
    std::vector<float> img(xpixel * ypixel, 0.0f);

    const double lambda = data.geom.GetWavelength_A();
    const double pixel_size = data.geom.GetPixelSize_mm();
    const auto azim_result = profile.GetResult();
    const auto azim_std = profile.GetStd();
    const auto &pixel_to_bin = mapping.GetPixelToBin();
    const auto &corrections = mapping.Corrections();
    const int total_bin_count = static_cast<int>(azim_result.size());
    const double angle_rad = data.angle_deg * M_PI / 180.0;
    const int radius = data.shoebox_radius;
    const double bw = data.bandwidth;

    auto recip_area = [&](double x, double y) -> double {
        const Coord qx = data.geom.DetectorToRecip(x + 0.5, y) - data.geom.DetectorToRecip(x - 0.5, y);
        const Coord qy = data.geom.DetectorToRecip(x, y + 0.5) - data.geom.DetectorToRecip(x, y - 0.5);
        return (qx % qy).Length();
    };
    auto bandwidth_radial_sq = [&](double d) -> double {
        if (bw <= 0.0 || d <= 0.0)
            return 0.0;
        const double bl = bw * lambda;
        return bl * bl / (2.0 * d * d * d * d);
    };

    double beam[2], dist_mm, detector_rot[2], rot_vec[3];
    double latt_vec0[3], latt_vec1[3], latt_vec2[3];
    BuildParameterBlocks(data, beam, dist_mm, detector_rot, rot_vec, latt_vec0, latt_vec1, latt_vec2);

    DiffractionExperiment exp_iter = experiment;
    exp_iter.BeamX_pxl(data.geom.GetBeamX_pxl())
            .BeamY_pxl(data.geom.GetBeamY_pxl())
            .DetectorDistance_mm(data.geom.GetDetectorDistance_mm())
            .PoniRot1_rad(data.geom.GetPoniRot1_rad())
            .PoniRot2_rad(data.geom.GetPoniRot2_rad());

    const BraggPredictionSettings settings_prediction{
        .high_res_A = experiment.GetBraggIntegrationSettings().GetDMinLimit_A(),
        .max_hkl = 100,
        .centering = data.centering,
        .bandwidth_sigma = static_cast<float>(data.bandwidth)
    };
    const int nrefl = prediction.Calc(exp_iter, data.latt, settings_prediction);
    const auto &predicted = prediction.GetReflections();

    for (int ri = 0; ri < nrefl; ++ri) {
        const auto &refl = predicted[ri];
        const auto it = reference_data.find(hkl_key_generator(refl));
        if (it == reference_data.end())
            continue;

        const double Itrue = it->second;
        const double R_bw_sq = bandwidth_radial_sq(refl.d);

        const int min_y = std::max<int>(refl.predicted_y - radius, 0);
        const int max_y = std::min<int>(refl.predicted_y + radius, ypixel - 1);
        const int min_x = std::max<int>(refl.predicted_x - radius, 0);
        const int max_x = std::min<int>(refl.predicted_x + radius, xpixel - 1);

        for (int y = min_y; y <= max_y; ++y) {
            for (int x = min_x; x <= max_x; ++x) {
                const size_t npixel = xpixel * y + x;
                const int azim_bin = pixel_to_bin[npixel];

                // Same gating as Run(): only pixels that actually enter the fit.
                if (azim_bin >= total_bin_count)
                    continue;
                if (image[npixel] == std::numeric_limits<T>::max())
                    continue;
                if (std::is_signed_v<T> && (image[npixel] == std::numeric_limits<T>::min()))
                    continue;

                const double correction = corrections[npixel];
                const double Ibkg = azim_result[azim_bin];
                const double Ibkg_sigma = azim_std[azim_bin];
                const double raw = static_cast<double>(image[npixel]);
                const double Iobs = raw * correction;

                double var = correction * std::max(Iobs, 0.0) + Ibkg_sigma * Ibkg_sigma;
                if (!(var > 1.0))
                    var = 1.0;
                const double weight = 1.0 / std::sqrt(var);

                PixelObs obs{
                    .x = static_cast<double>(x),
                    .y = static_cast<double>(y),
                    .Iobs = Iobs,
                    .Ibkg = Ibkg,
                    .weight = weight,
                    .A_recip = recip_area(x, y),
                    .angle_rad = angle_rad
                };
                PixelResidual pr(obs, Itrue, lambda, pixel_size,
                                 refl.h, refl.k, refl.l, R_bw_sq, data.crystal_system);

                double Ipred = 0.0;
                if (pr.Model(beam, &dist_mm, detector_rot, rot_vec,
                             latt_vec0, latt_vec1, latt_vec2,
                             &data.scale_factor, &data.B_factor, data.R, Ipred)) {
                    // residual_i = (I_pred - I_obs) * weight (== Ceres residual);
                    // its square is this pixel's contribution to the cost.
                    const double rw = (Ipred - Iobs) * weight;
                    img[npixel] += static_cast<float>(rw * rw);
                }
            }
        }
    }

    return img;
}

// Explicit instantiations for the supported (uncompressed) image pixel types.
template void PixelRefine::Run<int8_t>(const int8_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, PixelRefineData &);
template void PixelRefine::Run<int16_t>(const int16_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, PixelRefineData &);
template void PixelRefine::Run<int32_t>(const int32_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, PixelRefineData &);
template void PixelRefine::Run<uint8_t>(const uint8_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, PixelRefineData &);
template void PixelRefine::Run<uint16_t>(const uint16_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, PixelRefineData &);
template void PixelRefine::Run<uint32_t>(const uint32_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, PixelRefineData &);

template std::vector<float> PixelRefine::ChiSquaredImage<int8_t>(const int8_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, const PixelRefineData &) const;
template std::vector<float> PixelRefine::ChiSquaredImage<int16_t>(const int16_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, const PixelRefineData &) const;
template std::vector<float> PixelRefine::ChiSquaredImage<int32_t>(const int32_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, const PixelRefineData &) const;
template std::vector<float> PixelRefine::ChiSquaredImage<uint8_t>(const uint8_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, const PixelRefineData &) const;
template std::vector<float> PixelRefine::ChiSquaredImage<uint16_t>(const uint16_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, const PixelRefineData &) const;
template std::vector<float> PixelRefine::ChiSquaredImage<uint32_t>(const uint32_t *, const AzimuthalIntegrationProfile &, BraggPrediction &, const PixelRefineData &) const;