// ----------------------------------------------------------------------------
// -                        Open3D: www.open3d.org                            -
// ----------------------------------------------------------------------------
// The MIT License (MIT)
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// Copyright (c) 2018 www.open3d.org
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#include "Open3D/Odometry/Odometry.h"

#include <Eigen/Dense>
#include <memory>

#include "Open3D/Geometry/Image.h"
#include "Open3D/Geometry/RGBDImage.h"
#include "Open3D/Odometry/RGBDOdometryJacobian.h"
#include "Open3D/Utility/Eigen.h"
#include "Open3D/Utility/Timer.h"

namespace open3d {

namespace {
using namespace odometry;

std::tuple<std::shared_ptr<geometry::Image>, std::shared_ptr<geometry::Image>>
InitializeCorrespondenceMap(int width, int height) {
    // initialization: filling with any (u,v) to (-1,-1)
    auto correspondence_map = std::make_shared<geometry::Image>();
    auto depth_buffer = std::make_shared<geometry::Image>();
    correspondence_map->Prepare(width, height, 2, 4);
    depth_buffer->Prepare(width, height, 1, 4);
    for (int v = 0; v < correspondence_map->height_; v++) {
        for (int u = 0; u < correspondence_map->width_; u++) {
            *correspondence_map->PointerAt<int>(u, v, 0) = -1;
            *correspondence_map->PointerAt<int>(u, v, 1) = -1;
            *depth_buffer->PointerAt<float>(u, v, 0) = -1.0f;
        }
    }
    return std::make_tuple(correspondence_map, depth_buffer);
}

inline void AddElementToCorrespondenceMap(geometry::Image &correspondence_map,
                                          geometry::Image &depth_buffer,
                                          int u_s,
                                          int v_s,
                                          int u_t,
                                          int v_t,
                                          float transformed_d_t) {
    int exist_u_t, exist_v_t;
    double exist_d_t;
    exist_u_t = *correspondence_map.PointerAt<int>(u_s, v_s, 0);
    exist_v_t = *correspondence_map.PointerAt<int>(u_s, v_s, 1);
    if (exist_u_t != -1 && exist_v_t != -1) {
        exist_d_t = *depth_buffer.PointerAt<float>(u_s, v_s);
        if (transformed_d_t <
            exist_d_t) {  // update nearer point as correspondence
            *correspondence_map.PointerAt<int>(u_s, v_s, 0) = u_t;
            *correspondence_map.PointerAt<int>(u_s, v_s, 1) = v_t;
            *depth_buffer.PointerAt<float>(u_s, v_s) = transformed_d_t;
        }
    } else {  // register correspondence
        *correspondence_map.PointerAt<int>(u_s, v_s, 0) = u_t;
        *correspondence_map.PointerAt<int>(u_s, v_s, 1) = v_t;
        *depth_buffer.PointerAt<float>(u_s, v_s) = transformed_d_t;
    }
}

void MergeCorrespondenceMaps(geometry::Image &correspondence_map,
                             geometry::Image &depth_buffer,
                             geometry::Image &correspondence_map_part,
                             geometry::Image &depth_buffer_part) {
    for (int v_s = 0; v_s < correspondence_map.height_; v_s++) {
        for (int u_s = 0; u_s < correspondence_map.width_; u_s++) {
            int u_t = *correspondence_map_part.PointerAt<int>(u_s, v_s, 0);
            int v_t = *correspondence_map_part.PointerAt<int>(u_s, v_s, 1);
            if (u_t != -1 && v_t != -1) {
                float transformed_d_t =
                        *depth_buffer_part.PointerAt<float>(u_s, v_s);
                AddElementToCorrespondenceMap(correspondence_map, depth_buffer,
                                              u_s, v_s, u_t, v_t,
                                              transformed_d_t);
            }
        }
    }
}

int CountCorrespondence(const geometry::Image &correspondence_map) {
    int correspondence_count = 0;
    for (int v_s = 0; v_s < correspondence_map.height_; v_s++) {
        for (int u_s = 0; u_s < correspondence_map.width_; u_s++) {
            int u_t = *correspondence_map.PointerAt<int>(u_s, v_s, 0);
            int v_t = *correspondence_map.PointerAt<int>(u_s, v_s, 1);
            if (u_t != -1 && v_t != -1) {
                correspondence_count++;
            }
        }
    }
    return correspondence_count;
}

std::shared_ptr<CorrespondenceSetPixelWise> ComputeCorrespondence(
        const Eigen::Matrix3d intrinsic_matrix,
        const Eigen::Matrix4d &extrinsic,
        const geometry::Image &depth_s,
        const geometry::Image &depth_t,
        const OdometryOption &option) {
    const Eigen::Matrix3d K = intrinsic_matrix;
    const Eigen::Matrix3d K_inv = K.inverse();
    const Eigen::Matrix3d R = extrinsic.block<3, 3>(0, 0);
    const Eigen::Matrix3d KRK_inv = K * R * K_inv;
    Eigen::Vector3d Kt = K * extrinsic.block<3, 1>(0, 3);

    std::shared_ptr<geometry::Image> correspondence_map;
    std::shared_ptr<geometry::Image> depth_buffer;
    std::tie(correspondence_map, depth_buffer) =
            InitializeCorrespondenceMap(depth_t.width_, depth_t.height_);

#ifdef _OPENMP
#pragma omp parallel
    {
#endif
        std::shared_ptr<geometry::Image> correspondence_map_private;
        std::shared_ptr<geometry::Image> depth_buffer_private;
        std::tie(correspondence_map_private, depth_buffer_private) =
                InitializeCorrespondenceMap(depth_t.width_, depth_t.height_);
#ifdef _OPENMP
#pragma omp for nowait
#endif
        for (int v_s = 0; v_s < depth_s.height_; v_s++) {
            for (int u_s = 0; u_s < depth_s.width_; u_s++) {
                double d_s = *depth_s.PointerAt<float>(u_s, v_s);
                if (!std::isnan(d_s)) {
                    Eigen::Vector3d uv_in_s =
                            d_s * KRK_inv * Eigen::Vector3d(u_s, v_s, 1.0) + Kt;
                    double transformed_d_s = uv_in_s(2);
                    int u_t = (int)(uv_in_s(0) / transformed_d_s + 0.5);
                    int v_t = (int)(uv_in_s(1) / transformed_d_s + 0.5);
                    if (u_t >= 0 && u_t < depth_t.width_ && v_t >= 0 &&
                        v_t < depth_t.height_) {
                        double d_t = *depth_t.PointerAt<float>(u_t, v_t);
                        if (!std::isnan(d_t) &&
                            std::abs(transformed_d_s - d_t) <=
                                    option.max_depth_diff_) {
                            AddElementToCorrespondenceMap(
                                    *correspondence_map_private,
                                    *depth_buffer_private, u_s, v_s, u_t, v_t,
                                    (float)d_s);
                        }
                    }
                }
            }
        }
#ifdef _OPENMP
#pragma omp critical
        {
#endif
            MergeCorrespondenceMaps(*correspondence_map, *depth_buffer,
                                    *correspondence_map_private,
                                    *depth_buffer_private);
#ifdef _OPENMP
        }  //    omp critical
    }      //    omp parallel
#endif

    auto correspondence = std::make_shared<CorrespondenceSetPixelWise>();
    int correspondence_count = CountCorrespondence(*correspondence_map);
    correspondence->resize(correspondence_count);
    int cnt = 0;
    for (int v_s = 0; v_s < correspondence_map->height_; v_s++) {
        for (int u_s = 0; u_s < correspondence_map->width_; u_s++) {
            int u_t = *correspondence_map->PointerAt<int>(u_s, v_s, 0);
            int v_t = *correspondence_map->PointerAt<int>(u_s, v_s, 1);
            if (u_t != -1 && v_t != -1) {
                Eigen::Vector4i pixel_correspondence(u_s, v_s, u_t, v_t);
                (*correspondence)[cnt] = pixel_correspondence;
                cnt++;
            }
        }
    }
    return correspondence;
}

std::shared_ptr<geometry::Image> ConvertDepthImageToXYZImage(
        const geometry::Image &depth, const Eigen::Matrix3d &intrinsic_matrix) {
    auto image_xyz = std::make_shared<geometry::Image>();
    if (depth.num_of_channels_ != 1 || depth.bytes_per_channel_ != 4) {
        utility::LogError(
                "[ConvertDepthImageToXYZImage] Unsupported image format.");
    }
    const double inv_fx = 1.0 / intrinsic_matrix(0, 0);
    const double inv_fy = 1.0 / intrinsic_matrix(1, 1);
    const double ox = intrinsic_matrix(0, 2);
    const double oy = intrinsic_matrix(1, 2);
    image_xyz->Prepare(depth.width_, depth.height_, 3, 4);

    for (int y = 0; y < image_xyz->height_; y++) {
        for (int x = 0; x < image_xyz->width_; x++) {
            float *px = image_xyz->PointerAt<float>(x, y, 0);
            float *py = image_xyz->PointerAt<float>(x, y, 1);
            float *pz = image_xyz->PointerAt<float>(x, y, 2);
            float z = *depth.PointerAt<float>(x, y);
            *px = (float)((x - ox) * z * inv_fx);
            *py = (float)((y - oy) * z * inv_fy);
            *pz = z;
        }
    }
    return image_xyz;
}

std::vector<Eigen::Matrix3d> CreateCameraMatrixPyramid(
        const camera::PinholeCameraIntrinsic &pinhole_camera_intrinsic,
        int levels) {
    std::vector<Eigen::Matrix3d> pyramid_camera_matrix;
    pyramid_camera_matrix.reserve(levels);
    for (int i = 0; i < levels; i++) {
        Eigen::Matrix3d level_camera_matrix;
        if (i == 0)
            level_camera_matrix = pinhole_camera_intrinsic.intrinsic_matrix_;
        else
            level_camera_matrix = 0.5 * pyramid_camera_matrix[i - 1];
        level_camera_matrix(2, 2) = 1.;
        pyramid_camera_matrix.push_back(level_camera_matrix);
    }
    return pyramid_camera_matrix;
}

Eigen::Matrix6d CreateInformationMatrix(
        const Eigen::Matrix4d &extrinsic,
        const camera::PinholeCameraIntrinsic &pinhole_camera_intrinsic,
        const geometry::Image &depth_s,
        const geometry::Image &depth_t,
        const OdometryOption &option) {
    auto correspondence =
            ComputeCorrespondence(pinhole_camera_intrinsic.intrinsic_matrix_,
                                  extrinsic, depth_s, depth_t, option);

    auto xyz_t = ConvertDepthImageToXYZImage(
            depth_t, pinhole_camera_intrinsic.intrinsic_matrix_);

    // write q^*
    // see http://redwood-data.org/indoor/registration.html
    // note: I comes first and q_skew is scaled by factor 2.
    Eigen::Matrix6d GTG = Eigen::Matrix6d::Identity();
#ifdef _OPENMP
#pragma omp parallel
    {
#endif
        Eigen::Matrix6d GTG_private = Eigen::Matrix6d::Identity();
        Eigen::Vector6d G_r_private = Eigen::Vector6d::Zero();
#ifdef _OPENMP
#pragma omp for nowait
#endif
        for (int row = 0; row < int(correspondence->size()); row++) {
            int u_t = (*correspondence)[row](2);
            int v_t = (*correspondence)[row](3);
            double x = *xyz_t->PointerAt<float>(u_t, v_t, 0);
            double y = *xyz_t->PointerAt<float>(u_t, v_t, 1);
            double z = *xyz_t->PointerAt<float>(u_t, v_t, 2);
            G_r_private.setZero();
            G_r_private(1) = z;
            G_r_private(2) = -y;
            G_r_private(3) = 1.0;
            GTG_private.noalias() += G_r_private * G_r_private.transpose();
            G_r_private.setZero();
            G_r_private(0) = -z;
            G_r_private(2) = x;
            G_r_private(4) = 1.0;
            GTG_private.noalias() += G_r_private * G_r_private.transpose();
            G_r_private.setZero();
            G_r_private(0) = y;
            G_r_private(1) = -x;
            G_r_private(5) = 1.0;
            GTG_private.noalias() += G_r_private * G_r_private.transpose();
        }
#ifdef _OPENMP
#pragma omp critical
#endif
        { GTG += GTG_private; }
#ifdef _OPENMP
    }
#endif
    return GTG;
}

void NormalizeIntensity(geometry::Image &image_s,
                        geometry::Image &image_t,
                        CorrespondenceSetPixelWise &correspondence) {
    if (image_s.width_ != image_t.width_ ||
        image_s.height_ != image_t.height_) {
        utility::LogError(
                "[NormalizeIntensity] Size of two input images should be "
                "same");
    }
    double mean_s = 0.0, mean_t = 0.0;
    for (size_t row = 0; row < correspondence.size(); row++) {
        int u_s = correspondence[row](0);
        int v_s = correspondence[row](1);
        int u_t = correspondence[row](2);
        int v_t = correspondence[row](3);
        mean_s += *image_s.PointerAt<float>(u_s, v_s);
        mean_t += *image_t.PointerAt<float>(u_t, v_t);
    }
    mean_s /= (double)correspondence.size();
    mean_t /= (double)correspondence.size();
    image_s.LinearTransform(0.5 / mean_s, 0.0);
    image_t.LinearTransform(0.5 / mean_t, 0.0);
}

inline std::shared_ptr<geometry::RGBDImage> PackRGBDImage(
        const geometry::Image &color, const geometry::Image &depth) {
    return std::make_shared<geometry::RGBDImage>(
            geometry::RGBDImage(color, depth));
}

std::shared_ptr<geometry::Image> PreprocessDepth(
        const geometry::Image &depth_orig, const OdometryOption &option) {
    std::shared_ptr<geometry::Image> depth_processed =
            std::make_shared<geometry::Image>();
    *depth_processed = depth_orig;
    for (int y = 0; y < depth_processed->height_; y++) {
        for (int x = 0; x < depth_processed->width_; x++) {
            float *p = depth_processed->PointerAt<float>(x, y);
            if ((*p < option.min_depth_ || *p > option.max_depth_ || *p <= 0))
                *p = std::numeric_limits<float>::quiet_NaN();
        }
    }
    return depth_processed;
}

inline bool CheckImagePair(const geometry::Image &image_s,
                           const geometry::Image &image_t) {
    return (image_s.width_ == image_t.width_ &&
            image_s.height_ == image_t.height_);
}

inline bool IsColorImageRGB(const geometry::Image &image) {
    return (image.num_of_channels_ == 3);
}

inline bool CheckRGBDImagePair(const geometry::RGBDImage &source,
                               const geometry::RGBDImage &target) {
    if (IsColorImageRGB(source.color_) && IsColorImageRGB(target.color_)) {
        return (CheckImagePair(source.color_, target.color_) &&
                CheckImagePair(source.depth_, target.depth_) &&
                CheckImagePair(source.color_, source.depth_) &&
                CheckImagePair(target.color_, target.depth_) &&
                CheckImagePair(source.color_, target.color_) &&
                source.color_.num_of_channels_ == 3 &&
                target.color_.num_of_channels_ == 3 &&
                source.depth_.num_of_channels_ == 1 &&
                target.depth_.num_of_channels_ == 1 &&
                source.color_.bytes_per_channel_ == 1 &&
                target.color_.bytes_per_channel_ == 1 &&
                source.depth_.bytes_per_channel_ == 4 &&
                target.depth_.bytes_per_channel_ == 4);
    }
    if (!IsColorImageRGB(source.color_) && !IsColorImageRGB(target.color_)) {
        return (CheckImagePair(source.color_, target.color_) &&
                CheckImagePair(source.depth_, target.depth_) &&
                CheckImagePair(source.color_, source.depth_) &&
                CheckImagePair(target.color_, target.depth_) &&
                CheckImagePair(source.color_, target.color_) &&
                source.color_.num_of_channels_ == 1 &&
                source.depth_.num_of_channels_ == 1 &&
                target.color_.num_of_channels_ == 1 &&
                target.depth_.num_of_channels_ == 1 &&
                source.color_.bytes_per_channel_ == 4 &&
                target.color_.bytes_per_channel_ == 4 &&
                source.depth_.bytes_per_channel_ == 4 &&
                target.depth_.bytes_per_channel_ == 4);
    }
    return false;
}

std::tuple<std::shared_ptr<geometry::RGBDImage>,
           std::shared_ptr<geometry::RGBDImage>>
InitializeRGBDOdometry(
        const geometry::RGBDImage &source,
        const geometry::RGBDImage &target,
        const camera::PinholeCameraIntrinsic &pinhole_camera_intrinsic,
        const Eigen::Matrix4d &odo_init,
        const OdometryOption &option) {
    std::shared_ptr<geometry::Image> source_color, target_color;
    if (IsColorImageRGB(source.color_) && IsColorImageRGB(target.color_)) {
        source_color = source.color_.CreateFloatImage();
        target_color = target.color_.CreateFloatImage();
    } else {
        source_color = std::make_shared<geometry::Image>(source.color_);
        target_color = std::make_shared<geometry::Image>(target.color_);
    }

    auto source_gray =
            source_color->Filter(geometry::Image::FilterType::Gaussian3);
    auto target_gray =
            target_color->Filter(geometry::Image::FilterType::Gaussian3);
    auto source_depth_preprocessed = PreprocessDepth(source.depth_, option);
    auto target_depth_preprocessed = PreprocessDepth(target.depth_, option);
    auto source_depth = source_depth_preprocessed->Filter(
            geometry::Image::FilterType::Gaussian3);
    auto target_depth = target_depth_preprocessed->Filter(
            geometry::Image::FilterType::Gaussian3);

    auto correspondence = ComputeCorrespondence(
            pinhole_camera_intrinsic.intrinsic_matrix_, odo_init, *source_depth,
            *target_depth, option);
    NormalizeIntensity(*source_gray, *target_gray, *correspondence);

    auto source_out = PackRGBDImage(*source_gray, *source_depth);
    auto target_out = PackRGBDImage(*target_gray, *target_depth);
    return std::make_tuple(source_out, target_out);
}

std::tuple<bool, Eigen::Matrix4d> DoSingleIteration(
        int iter,
        int level,
        const geometry::RGBDImage &source,
        const geometry::RGBDImage &target,
        const geometry::Image &source_xyz,
        const geometry::RGBDImage &target_dx,
        const geometry::RGBDImage &target_dy,
        const Eigen::Matrix3d intrinsic,
        const Eigen::Matrix4d &extrinsic_initial,
        const RGBDOdometryJacobian &jacobian_method,
        const OdometryOption &option) {
    auto correspondence = ComputeCorrespondence(
            intrinsic, extrinsic_initial, source.depth_, target.depth_, option);
    int corresps_count = (int)correspondence->size();

    auto f_lambda =
            [&](int i,
                std::vector<Eigen::Vector6d, utility::Vector6d_allocator> &J_r,
                std::vector<double> &r) {
                jacobian_method.ComputeJacobianAndResidual(
                        i, J_r, r, source, target, source_xyz, target_dx,
                        target_dy, intrinsic, extrinsic_initial,
                        *correspondence);
            };
    utility::LogDebug("Iter : {:d}, Level : {:d}, ", iter, level);
    Eigen::Matrix6d JTJ;
    Eigen::Vector6d JTr;
    double r2;
    std::tie(JTJ, JTr, r2) =
            utility::ComputeJTJandJTr<Eigen::Matrix6d, Eigen::Vector6d>(
                    f_lambda, corresps_count);

    bool is_success;
    Eigen::Matrix4d extrinsic;
    std::tie(is_success, extrinsic) =
            utility::SolveJacobianSystemAndObtainExtrinsicMatrix(JTJ, JTr);
    if (!is_success) {
        utility::LogWarning("[ComputeOdometry] no solution!");
        return std::make_tuple(false, Eigen::Matrix4d::Identity());
    } else {
        return std::make_tuple(true, extrinsic);
    }
}

std::tuple<bool, Eigen::Matrix4d> ComputeMultiscale(
        const geometry::RGBDImage &source,
        const geometry::RGBDImage &target,
        const camera::PinholeCameraIntrinsic &pinhole_camera_intrinsic,
        const Eigen::Matrix4d &extrinsic_initial,
        const RGBDOdometryJacobian &jacobian_method,
        const OdometryOption &option) {
    std::vector<int> iter_counts = option.iteration_number_per_pyramid_level_;
    int num_levels = (int)iter_counts.size();

    auto source_pyramid = source.CreatePyramid(num_levels);
    auto target_pyramid = target.CreatePyramid(num_levels);
    auto target_pyramid_dx = geometry::RGBDImage::FilterPyramid(
            target_pyramid, geometry::Image::FilterType::Sobel3Dx);
    auto target_pyramid_dy = geometry::RGBDImage::FilterPyramid(
            target_pyramid, geometry::Image::FilterType::Sobel3Dy);

    Eigen::Matrix4d result_odo = extrinsic_initial.isZero()
                                         ? Eigen::Matrix4d::Identity()
                                         : extrinsic_initial;

    std::vector<Eigen::Matrix3d> pyramid_camera_matrix =
            CreateCameraMatrixPyramid(pinhole_camera_intrinsic,
                                      (int)iter_counts.size());

    for (int level = num_levels - 1; level >= 0; level--) {
        const Eigen::Matrix3d level_camera_matrix =
                pyramid_camera_matrix[level];

        auto source_xyz_level = ConvertDepthImageToXYZImage(
                source_pyramid[level]->depth_, level_camera_matrix);
        auto source_level = PackRGBDImage(source_pyramid[level]->color_,
                                          source_pyramid[level]->depth_);
        auto target_level = PackRGBDImage(target_pyramid[level]->color_,
                                          target_pyramid[level]->depth_);
        auto target_dx_level = PackRGBDImage(target_pyramid_dx[level]->color_,
                                             target_pyramid_dx[level]->depth_);
        auto target_dy_level = PackRGBDImage(target_pyramid_dy[level]->color_,
                                             target_pyramid_dy[level]->depth_);

        for (int iter = 0; iter < iter_counts[num_levels - level - 1]; iter++) {
            Eigen::Matrix4d curr_odo;
            bool is_success;
            std::tie(is_success, curr_odo) = DoSingleIteration(
                    iter, level, *source_level, *target_level,
                    *source_xyz_level, *target_dx_level, *target_dy_level,
                    level_camera_matrix, result_odo, jacobian_method, option);
            result_odo = curr_odo * result_odo;

            if (!is_success) {
                utility::LogWarning("[ComputeOdometry] no solution!");
                return std::make_tuple(false, Eigen::Matrix4d::Identity());
            }
        }
    }
    return std::make_tuple(true, result_odo);
}

}  // unnamed namespace

namespace odometry {

std::tuple<bool, Eigen::Matrix4d, Eigen::Matrix6d> ComputeRGBDOdometry(
        const geometry::RGBDImage &source,
        const geometry::RGBDImage &target,
        const camera::PinholeCameraIntrinsic &pinhole_camera_intrinsic
        /*= camera::PinholeCameraIntrinsic()*/,
        const Eigen::Matrix4d &odo_init /*= Eigen::Matrix4d::Identity()*/,
        const RGBDOdometryJacobian &jacobian_method
        /*=RGBDOdometryJacobianFromHybridTerm*/,
        const OdometryOption &option /*= OdometryOption()*/) {
    if (!CheckRGBDImagePair(source, target)) {
        utility::LogWarning(
                "[RGBDOdometry] Two RGBD pairs should be same in size.");
        return std::make_tuple(false, Eigen::Matrix4d::Identity(),
                               Eigen::Matrix6d::Zero());
    }

    std::shared_ptr<geometry::RGBDImage> source_processed, target_processed;
    std::tie(source_processed, target_processed) = InitializeRGBDOdometry(
            source, target, pinhole_camera_intrinsic, odo_init, option);

    Eigen::Matrix4d extrinsic;
    bool is_success;
    std::tie(is_success, extrinsic) = ComputeMultiscale(
            *source_processed, *target_processed, pinhole_camera_intrinsic,
            odo_init, jacobian_method, option);

    if (is_success) {
        Eigen::Matrix4d trans_output = extrinsic;
        Eigen::MatrixXd info_output = CreateInformationMatrix(
                extrinsic, pinhole_camera_intrinsic, source_processed->depth_,
                target_processed->depth_, option);
        return std::make_tuple(true, trans_output, info_output);
    } else {
        return std::make_tuple(false, Eigen::Matrix4d::Identity(),
                               Eigen::Matrix6d::Identity());
    }
}

}  // namespace odometry
}  // namespace open3d