camera_models.h

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// ----------------------------------------------------------------------------
// -                        CloudViewer: www.cloudViewer.org                  -
// ----------------------------------------------------------------------------
// Copyright (c) 2018-2024 www.cloudViewer.org
// SPDX-License-Identifier: MIT
// ----------------------------------------------------------------------------
 
#pragma once
 
#include <ceres/ceres.h>
 
#include <Eigen/Core>
#include <Eigen/Dense>
#include <cfloat>
#include <string>
#include <vector>
 
namespace colmap {
 
// This file defines several different camera models and arbitrary new camera
// models can be added by the following steps:
//
//  1. Add a new struct in this file which implements all the necessary methods.
//  2. Define an unique model_name and model_id for the camera model.
//  3. Add camera model to `CAMERA_MODEL_CASES` macro in this file.
//  4. Add new template specialization of test case for camera model to
//     `camera_models_test.cc`.
//
// A camera model can have three different types of camera parameters: focal
// length, principal point, extra parameters (distortion parameters). The
// parameter array is split into different groups, so that we can enable or
// disable the refinement of the individual groups during bundle adjustment. It
// is up to the camera model to access the parameters correctly (it is free to
// do so in an arbitrary manner) - the parameters are not accessed from outside.
//
// A camera model must have the following methods:
//
//  - `WorldToImage`: transform normalized camera coordinates to image
//    coordinates (the inverse of `ImageToWorld`). Assumes that the world
//    coordinates are given as (u, v, 1).
//  - `ImageToWorld`: transform image coordinates to normalized camera
//    coordinates (the inverse of `WorldToImage`). Produces world coordinates
//    as (u, v, 1).
//  - `ImageToWorldThreshold`: transform a threshold given in pixels to
//    normalized units (e.g. useful for reprojection error thresholds).
//
// Whenever you specify the camera parameters in a list, they must appear
// exactly in the order as they are accessed in the defined model struct.
//
// The camera models follow the convention that the upper left image corner has
// the coordinate (0, 0), the lower right corner (width, height), i.e. that
// the upper left pixel center has coordinate (0.5, 0.5) and the lower right
// pixel center has the coordinate (width - 0.5, height - 0.5).
 
static const int kInvalidCameraModelId = -1;
 
#ifndef CAMERA_MODEL_DEFINITIONS
#define CAMERA_MODEL_DEFINITIONS(model_id_value, model_name_value,             \
                                 num_params_value)                             \
    static const int kModelId = model_id_value;                                \
    static const size_t kNumParams = num_params_value;                         \
    static const int model_id;                                                 \
    static const std::string model_name;                                       \
    static const size_t num_params;                                            \
    static const std::string params_info;                                      \
    static const std::vector<size_t> focal_length_idxs;                        \
    static const std::vector<size_t> principal_point_idxs;                     \
    static const std::vector<size_t> extra_params_idxs;                        \
                                                                               \
    static inline int InitializeModelId() { return model_id_value; };          \
    static inline std::string InitializeModelName() {                          \
        return model_name_value;                                               \
    };                                                                         \
    static inline size_t InitializeNumParams() { return num_params_value; };   \
    static inline std::string InitializeParamsInfo();                          \
    static inline std::vector<size_t> InitializeFocalLengthIdxs();             \
    static inline std::vector<size_t> InitializePrincipalPointIdxs();          \
    static inline std::vector<size_t> InitializeExtraParamsIdxs();             \
    static inline std::vector<double> InitializeParams(                        \
            const double focal_length, const size_t width,                     \
            const size_t height);                                              \
                                                                               \
    template <typename T>                                                      \
    static void WorldToImage(const T* params, const T u, const T v, T* x,      \
                             T* y);                                            \
    template <typename T>                                                      \
    static void ImageToWorld(const T* params, const T x, const T y, T* u,      \
                             T* v);                                            \
    template <typename T>                                                      \
    static void Distortion(const T* extra_params, const T u, const T v, T* du, \
                           T* dv);
#endif
 
#ifndef CAMERA_MODEL_CASES
#define CAMERA_MODEL_CASES                            \
    CAMERA_MODEL_CASE(SimplePinholeCameraModel)       \
    CAMERA_MODEL_CASE(PinholeCameraModel)             \
    CAMERA_MODEL_CASE(SimpleRadialCameraModel)        \
    CAMERA_MODEL_CASE(SimpleRadialFisheyeCameraModel) \
    CAMERA_MODEL_CASE(RadialCameraModel)              \
    CAMERA_MODEL_CASE(RadialFisheyeCameraModel)       \
    CAMERA_MODEL_CASE(OpenCVCameraModel)              \
    CAMERA_MODEL_CASE(OpenCVFisheyeCameraModel)       \
    CAMERA_MODEL_CASE(FullOpenCVCameraModel)          \
    CAMERA_MODEL_CASE(FOVCameraModel)                 \
    CAMERA_MODEL_CASE(ThinPrismFisheyeCameraModel)
#endif
 
#ifndef CAMERA_MODEL_SWITCH_CASES
#define CAMERA_MODEL_SWITCH_CASES             \
    CAMERA_MODEL_CASES                        \
    default:                                  \
        CAMERA_MODEL_DOES_NOT_EXIST_EXCEPTION \
        break;
#endif
 
#define CAMERA_MODEL_DOES_NOT_EXIST_EXCEPTION \
    throw std::domain_error("Camera model does not exist");
 
// The "Curiously Recurring Template Pattern" (CRTP) is used here, so that we
// can reuse some shared functionality between all camera models -
// defined in the BaseCameraModel.
template <typename CameraModel>
struct BaseCameraModel {
    template <typename T>
    static inline bool HasBogusParams(const std::vector<T>& params,
                                      const size_t width,
                                      const size_t height,
                                      const T min_focal_length_ratio,
                                      const T max_focal_length_ratio,
                                      const T max_extra_param);
 
    template <typename T>
    static inline bool HasBogusFocalLength(const std::vector<T>& params,
                                           const size_t width,
                                           const size_t height,
                                           const T min_focal_length_ratio,
                                           const T max_focal_length_ratio);
 
    template <typename T>
    static inline bool HasBogusPrincipalPoint(const std::vector<T>& params,
                                              const size_t width,
                                              const size_t height);
 
    template <typename T>
    static inline bool HasBogusExtraParams(const std::vector<T>& params,
                                           const T max_extra_param);
 
    template <typename T>
    static inline T ImageToWorldThreshold(const T* params, const T threshold);
 
    template <typename T>
    static inline void IterativeUndistortion(const T* params, T* u, T* v);
};
 
// Simple Pinhole camera model.
//
// No Distortion is assumed. Only focal length and principal point is modeled.
//
// Parameter list is expected in the following order:
//
//   f, cx, cy
//
// See https://en.wikipedia.org/wiki/Pinhole_camera_model
struct SimplePinholeCameraModel
    : public BaseCameraModel<SimplePinholeCameraModel> {
    CAMERA_MODEL_DEFINITIONS(0, "SIMPLE_PINHOLE", 3)
};
 
// Pinhole camera model.
//
// No Distortion is assumed. Only focal length and principal point is modeled.
//
// Parameter list is expected in the following order:
//
//    fx, fy, cx, cy
//
// See https://en.wikipedia.org/wiki/Pinhole_camera_model
struct PinholeCameraModel : public BaseCameraModel<PinholeCameraModel> {
    CAMERA_MODEL_DEFINITIONS(1, "PINHOLE", 4)
};
 
// Simple camera model with one focal length and one radial distortion
// parameter.
//
// This model is similar to the camera model that VisualSfM uses with the
// difference that the distortion here is applied to the projections and
// not to the measurements.
//
// Parameter list is expected in the following order:
//
//    f, cx, cy, k
//
struct SimpleRadialCameraModel
    : public BaseCameraModel<SimpleRadialCameraModel> {
    CAMERA_MODEL_DEFINITIONS(2, "SIMPLE_RADIAL", 4)
};
 
// Simple camera model with one focal length and two radial distortion
// parameters.
//
// This model is equivalent to the camera model that Bundler uses
// (except for an inverse z-axis in the camera coordinate system).
//
// Parameter list is expected in the following order:
//
//    f, cx, cy, k1, k2
//
struct RadialCameraModel : public BaseCameraModel<RadialCameraModel> {
    CAMERA_MODEL_DEFINITIONS(3, "RADIAL", 5)
};
 
// OpenCV camera model.
//
// Based on the pinhole camera model. Additionally models radial and
// tangential distortion (up to 2nd degree of coefficients). Not suitable for
// large radial distortions of fish-eye cameras.
//
// Parameter list is expected in the following order:
//
//    fx, fy, cx, cy, k1, k2, p1, p2
//
// See
// http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html
struct OpenCVCameraModel : public BaseCameraModel<OpenCVCameraModel> {
    CAMERA_MODEL_DEFINITIONS(4, "OPENCV", 8)
};
 
// OpenCV fish-eye camera model.
//
// Based on the pinhole camera model. Additionally models radial and
// tangential Distortion (up to 2nd degree of coefficients). Suitable for
// large radial distortions of fish-eye cameras.
//
// Parameter list is expected in the following order:
//
//    fx, fy, cx, cy, k1, k2, k3, k4
//
// See
// http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html
struct OpenCVFisheyeCameraModel
    : public BaseCameraModel<OpenCVFisheyeCameraModel> {
    CAMERA_MODEL_DEFINITIONS(5, "OPENCV_FISHEYE", 8)
};
 
// Full OpenCV camera model.
//
// Based on the pinhole camera model. Additionally models radial and
// tangential Distortion.
//
// Parameter list is expected in the following order:
//
//    fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, k5, k6
//
// See
// http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html
struct FullOpenCVCameraModel : public BaseCameraModel<FullOpenCVCameraModel> {
    CAMERA_MODEL_DEFINITIONS(6, "FULL_OPENCV", 12)
};
 
// FOV camera model.
//
// Based on the pinhole camera model. Additionally models radial distortion.
// This model is for example used by Project Tango for its equidistant
// calibration type.
//
// Parameter list is expected in the following order:
//
//    fx, fy, cx, cy, omega
//
// See:
// Frederic Devernay, Olivier Faugeras. Straight lines have to be straight:
// Automatic calibration and removal of distortion from scenes of structured
// environments. Machine vision and applications, 2001.
struct FOVCameraModel : public BaseCameraModel<FOVCameraModel> {
    CAMERA_MODEL_DEFINITIONS(7, "FOV", 5)
 
    template <typename T>
    static void Undistortion(
            const T* extra_params, const T u, const T v, T* du, T* dv);
};
 
// Simple camera model with one focal length and one radial distortion
// parameter, suitable for fish-eye cameras.
//
// This model is equivalent to the OpenCVFisheyeCameraModel but has only one
// radial distortion coefficient.
//
// Parameter list is expected in the following order:
//
//    f, cx, cy, k
//
struct SimpleRadialFisheyeCameraModel
    : public BaseCameraModel<SimpleRadialFisheyeCameraModel> {
    CAMERA_MODEL_DEFINITIONS(8, "SIMPLE_RADIAL_FISHEYE", 4)
};
 
// Simple camera model with one focal length and two radial distortion
// parameters, suitable for fish-eye cameras.
//
// This model is equivalent to the OpenCVFisheyeCameraModel but has only two
// radial distortion coefficients.
//
// Parameter list is expected in the following order:
//
//    f, cx, cy, k1, k2
//
struct RadialFisheyeCameraModel
    : public BaseCameraModel<RadialFisheyeCameraModel> {
    CAMERA_MODEL_DEFINITIONS(9, "RADIAL_FISHEYE", 5)
};
 
// Camera model with radial and tangential distortion coefficients and
// additional coefficients accounting for thin-prism distortion.
//
// This camera model is described in
//
//    "Camera Calibration with Distortion Models and Accuracy Evaluation",
//    J Weng et al., TPAMI, 1992.
//
// Parameter list is expected in the following order:
//
//    fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, sx1, sy1
//
struct ThinPrismFisheyeCameraModel
    : public BaseCameraModel<ThinPrismFisheyeCameraModel> {
    CAMERA_MODEL_DEFINITIONS(10, "THIN_PRISM_FISHEYE", 12)
};
 
// Check whether camera model with given name or identifier exists.
bool ExistsCameraModelWithName(const std::string& model_name);
bool ExistsCameraModelWithId(const int model_id);
 
// Convert camera name to unique camera model identifier.
//
// @param name         Unique name of camera model.
//
// @return             Unique identifier of camera model.
int CameraModelNameToId(const std::string& model_name);
 
// Convert camera model identifier to unique camera model name.
//
// @param model_id     Unique identifier of camera model.
//
// @return             Unique name of camera model.
std::string CameraModelIdToName(const int model_id);
 
// Initialize camera parameters using given image properties.
//
// Initializes all focal length parameters to the same given focal length and
// sets the principal point to the image center.
//
// @param model_id      Unique identifier of camera model.
// @param focal_length  Focal length, equal for all focal length parameters.
// @param width         Sensor width of the camera.
// @param height        Sensor height of the camera.
std::vector<double> CameraModelInitializeParams(const int model_id,
                                                const double focal_length,
                                                const size_t width,
                                                const size_t height);
 
// Get human-readable information about the parameter vector order.
//
// @param model_id     Unique identifier of camera model.
std::string CameraModelParamsInfo(const int model_id);
 
// Get the indices of the parameter groups in the parameter vector.
//
// @param model_id     Unique identifier of camera model.
const std::vector<size_t>& CameraModelFocalLengthIdxs(const int model_id);
const std::vector<size_t>& CameraModelPrincipalPointIdxs(const int model_id);
const std::vector<size_t>& CameraModelExtraParamsIdxs(const int model_id);
 
// Get the total number of parameters of a camera model.
size_t CameraModelNumParams(const int model_id);
 
// Check whether parameters are valid, i.e. the parameter vector has
// the correct dimensions that match the specified camera model.
//
// @param model_id      Unique identifier of camera model.
// @param params        Array of camera parameters.
bool CameraModelVerifyParams(const int model_id,
                             const std::vector<double>& params);
 
// Check whether camera has bogus parameters.
//
// @param model_id                Unique identifier of camera model.
// @param params                  Array of camera parameters.
// @param width                   Sensor width of the camera.
// @param height                  Sensor height of the camera.
// @param min_focal_length_ratio  Minimum ratio of focal length over
//                                minimum sensor dimension.
// @param max_focal_length_ratio  Maximum ratio of focal length over
//                                maximum sensor dimension.
// @param max_extra_param         Maximum magnitude of each extra parameter.
bool CameraModelHasBogusParams(const int model_id,
                               const std::vector<double>& params,
                               const size_t width,
                               const size_t height,
                               const double min_focal_length_ratio,
                               const double max_focal_length_ratio,
                               const double max_extra_param);
 
// Transform world coordinates in camera coordinate system to image coordinates.
//
// This is the inverse of `CameraModelImageToWorld`.
//
// @param model_id     Unique model_id of camera model as defined in
//                     `CAMERA_MODEL_NAME_TO_CODE`.
// @param params       Array of camera parameters.
// @param u, v         Coordinates in camera system as (u, v, 1).
// @param x, y         Output image coordinates in pixels.
inline void CameraModelWorldToImage(const int model_id,
                                    const std::vector<double>& params,
                                    const double u,
                                    const double v,
                                    double* x,
                                    double* y);
 
// Transform image coordinates to world coordinates in camera coordinate system.
//
// This is the inverse of `CameraModelWorldToImage`.
//
// @param model_id      Unique identifier of camera model.
// @param params        Array of camera parameters.
// @param x, y          Image coordinates in pixels.
// @param v, u          Output Coordinates in camera system as (u, v, 1).
inline void CameraModelImageToWorld(const int model_id,
                                    const std::vector<double>& params,
                                    const double x,
                                    const double y,
                                    double* u,
                                    double* v);
 
// Convert pixel threshold in image plane to world space by dividing
// the threshold through the mean focal length.
//
// @param model_id      Unique identifier of camera model.
// @param params        Array of camera parameters.
// @param threshold     Image space threshold in pixels.
//
// @ return             World space threshold.
inline double CameraModelImageToWorldThreshold(
        const int model_id,
        const std::vector<double>& params,
        const double threshold);
 
// Implementation
 
// BaseCameraModel
 
template <typename CameraModel>
template <typename T>
bool BaseCameraModel<CameraModel>::HasBogusParams(
        const std::vector<T>& params,
        const size_t width,
        const size_t height,
        const T min_focal_length_ratio,
        const T max_focal_length_ratio,
        const T max_extra_param) {
    if (HasBogusPrincipalPoint(params, width, height)) {
        return true;
    }
 
    if (HasBogusFocalLength(params, width, height, min_focal_length_ratio,
                            max_focal_length_ratio)) {
        return true;
    }
 
    if (HasBogusExtraParams(params, max_extra_param)) {
        return true;
    }
 
    return false;
}
 
template <typename CameraModel>
template <typename T>
bool BaseCameraModel<CameraModel>::HasBogusFocalLength(
        const std::vector<T>& params,
        const size_t width,
        const size_t height,
        const T min_focal_length_ratio,
        const T max_focal_length_ratio) {
    const size_t max_size = std::max(width, height);
 
    for (const auto& idx : CameraModel::focal_length_idxs) {
        const T focal_length_ratio = params[idx] / max_size;
        if (focal_length_ratio < min_focal_length_ratio ||
            focal_length_ratio > max_focal_length_ratio) {
            return true;
        }
    }
 
    return false;
}
 
template <typename CameraModel>
template <typename T>
bool BaseCameraModel<CameraModel>::HasBogusPrincipalPoint(
        const std::vector<T>& params, const size_t width, const size_t height) {
    const T cx = params[CameraModel::principal_point_idxs[0]];
    const T cy = params[CameraModel::principal_point_idxs[1]];
    return cx < 0 || cx > width || cy < 0 || cy > height;
}
 
template <typename CameraModel>
template <typename T>
bool BaseCameraModel<CameraModel>::HasBogusExtraParams(
        const std::vector<T>& params, const T max_extra_param) {
    for (const auto& idx : CameraModel::extra_params_idxs) {
        if (std::abs(params[idx]) > max_extra_param) {
            return true;
        }
    }
 
    return false;
}
 
template <typename CameraModel>
template <typename T>
T BaseCameraModel<CameraModel>::ImageToWorldThreshold(const T* params,
                                                      const T threshold) {
    T mean_focal_length = 0;
    for (const auto& idx : CameraModel::focal_length_idxs) {
        mean_focal_length += params[idx];
    }
    mean_focal_length /= CameraModel::focal_length_idxs.size();
    return threshold / mean_focal_length;
}
 
template <typename CameraModel>
template <typename T>
void BaseCameraModel<CameraModel>::IterativeUndistortion(const T* params,
                                                         T* u,
                                                         T* v) {
    // Parameters for Newton iteration using numerical differentiation with
    // central differences, 100 iterations should be enough even for complex
    // camera models with higher order terms.
    const size_t kNumIterations = 100;
    const double kMaxStepNorm = 1e-10;
    const double kRelStepSize = 1e-6;
 
    Eigen::Matrix2d J;
    const Eigen::Vector2d x0(*u, *v);
    Eigen::Vector2d x(*u, *v);
    Eigen::Vector2d dx;
    Eigen::Vector2d dx_0b;
    Eigen::Vector2d dx_0f;
    Eigen::Vector2d dx_1b;
    Eigen::Vector2d dx_1f;
 
    for (size_t i = 0; i < kNumIterations; ++i) {
        const double step0 = std::max(std::numeric_limits<double>::epsilon(),
                                      std::abs(kRelStepSize * x(0)));
        const double step1 = std::max(std::numeric_limits<double>::epsilon(),
                                      std::abs(kRelStepSize * x(1)));
        CameraModel::Distortion(params, x(0), x(1), &dx(0), &dx(1));
        CameraModel::Distortion(params, x(0) - step0, x(1), &dx_0b(0),
                                &dx_0b(1));
        CameraModel::Distortion(params, x(0) + step0, x(1), &dx_0f(0),
                                &dx_0f(1));
        CameraModel::Distortion(params, x(0), x(1) - step1, &dx_1b(0),
                                &dx_1b(1));
        CameraModel::Distortion(params, x(0), x(1) + step1, &dx_1f(0),
                                &dx_1f(1));
        J(0, 0) = 1 + (dx_0f(0) - dx_0b(0)) / (2 * step0);
        J(0, 1) = (dx_1f(0) - dx_1b(0)) / (2 * step1);
        J(1, 0) = (dx_0f(1) - dx_0b(1)) / (2 * step0);
        J(1, 1) = 1 + (dx_1f(1) - dx_1b(1)) / (2 * step1);
        const Eigen::Vector2d step_x = J.inverse() * (x + dx - x0);
        x -= step_x;
        if (step_x.squaredNorm() < kMaxStepNorm) {
            break;
        }
    }
 
    *u = x(0);
    *v = x(1);
}
 
// SimplePinholeCameraModel
 
std::string SimplePinholeCameraModel::InitializeParamsInfo() {
    return "f, cx, cy";
}
 
std::vector<size_t> SimplePinholeCameraModel::InitializeFocalLengthIdxs() {
    return {0};
}
 
std::vector<size_t> SimplePinholeCameraModel::InitializePrincipalPointIdxs() {
    return {1, 2};
}
 
std::vector<size_t> SimplePinholeCameraModel::InitializeExtraParamsIdxs() {
    return {};
}
 
std::vector<double> SimplePinholeCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length, width / 2.0, height / 2.0};
}
 
template <typename T>
void SimplePinholeCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // No Distortion
 
    // Transform to image coordinates
    *x = f * u + c1;
    *y = f * v + c2;
}
 
template <typename T>
void SimplePinholeCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    *u = (x - c1) / f;
    *v = (y - c2) / f;
}
 
// PinholeCameraModel
 
std::string PinholeCameraModel::InitializeParamsInfo() {
    return "fx, fy, cx, cy";
}
 
std::vector<size_t> PinholeCameraModel::InitializeFocalLengthIdxs() {
    return {0, 1};
}
 
std::vector<size_t> PinholeCameraModel::InitializePrincipalPointIdxs() {
    return {2, 3};
}
 
std::vector<size_t> PinholeCameraModel::InitializeExtraParamsIdxs() {
    return {};
}
 
std::vector<double> PinholeCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length, focal_length, width / 2.0, height / 2.0};
}
 
template <typename T>
void PinholeCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // No Distortion
 
    // Transform to image coordinates
    *x = f1 * u + c1;
    *y = f2 * v + c2;
}
 
template <typename T>
void PinholeCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    *u = (x - c1) / f1;
    *v = (y - c2) / f2;
}
 
// SimpleRadialCameraModel
 
std::string SimpleRadialCameraModel::InitializeParamsInfo() {
    return "f, cx, cy, k";
}
 
std::vector<size_t> SimpleRadialCameraModel::InitializeFocalLengthIdxs() {
    return {0};
}
 
std::vector<size_t> SimpleRadialCameraModel::InitializePrincipalPointIdxs() {
    return {1, 2};
}
 
std::vector<size_t> SimpleRadialCameraModel::InitializeExtraParamsIdxs() {
    return {3};
}
 
std::vector<double> SimpleRadialCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length, width / 2.0, height / 2.0, 0};
}
 
template <typename T>
void SimpleRadialCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // Distortion
    T du, dv;
    Distortion(&params[3], u, v, &du, &dv);
    *x = u + du;
    *y = v + dv;
 
    // Transform to image coordinates
    *x = f * *x + c1;
    *y = f * *y + c2;
}
 
template <typename T>
void SimpleRadialCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // Lift points to normalized plane
    *u = (x - c1) / f;
    *v = (y - c2) / f;
 
    IterativeUndistortion(&params[3], u, v);
}
 
template <typename T>
void SimpleRadialCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T k = extra_params[0];
 
    const T u2 = u * u;
    const T v2 = v * v;
    const T r2 = u2 + v2;
    const T radial = k * r2;
    *du = u * radial;
    *dv = v * radial;
}
 
// RadialCameraModel
 
std::string RadialCameraModel::InitializeParamsInfo() {
    return "f, cx, cy, k1, k2";
}
 
std::vector<size_t> RadialCameraModel::InitializeFocalLengthIdxs() {
    return {0};
}
 
std::vector<size_t> RadialCameraModel::InitializePrincipalPointIdxs() {
    return {1, 2};
}
 
std::vector<size_t> RadialCameraModel::InitializeExtraParamsIdxs() {
    return {3, 4};
}
 
std::vector<double> RadialCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length, width / 2.0, height / 2.0, 0, 0};
}
 
template <typename T>
void RadialCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // Distortion
    T du, dv;
    Distortion(&params[3], u, v, &du, &dv);
    *x = u + du;
    *y = v + dv;
 
    // Transform to image coordinates
    *x = f * *x + c1;
    *y = f * *y + c2;
}
 
template <typename T>
void RadialCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // Lift points to normalized plane
    *u = (x - c1) / f;
    *v = (y - c2) / f;
 
    IterativeUndistortion(&params[3], u, v);
}
 
template <typename T>
void RadialCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T k1 = extra_params[0];
    const T k2 = extra_params[1];
 
    const T u2 = u * u;
    const T v2 = v * v;
    const T r2 = u2 + v2;
    const T radial = k1 * r2 + k2 * r2 * r2;
    *du = u * radial;
    *dv = v * radial;
}
 
// OpenCVCameraModel
 
std::string OpenCVCameraModel::InitializeParamsInfo() {
    return "fx, fy, cx, cy, k1, k2, p1, p2";
}
 
std::vector<size_t> OpenCVCameraModel::InitializeFocalLengthIdxs() {
    return {0, 1};
}
 
std::vector<size_t> OpenCVCameraModel::InitializePrincipalPointIdxs() {
    return {2, 3};
}
 
std::vector<size_t> OpenCVCameraModel::InitializeExtraParamsIdxs() {
    return {4, 5, 6, 7};
}
 
std::vector<double> OpenCVCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length, focal_length, width / 2.0, height / 2.0, 0, 0, 0, 0};
}
 
template <typename T>
void OpenCVCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Distortion
    T du, dv;
    Distortion(&params[4], u, v, &du, &dv);
    *x = u + du;
    *y = v + dv;
 
    // Transform to image coordinates
    *x = f1 * *x + c1;
    *y = f2 * *y + c2;
}
 
template <typename T>
void OpenCVCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Lift points to normalized plane
    *u = (x - c1) / f1;
    *v = (y - c2) / f2;
 
    IterativeUndistortion(&params[4], u, v);
}
 
template <typename T>
void OpenCVCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T k1 = extra_params[0];
    const T k2 = extra_params[1];
    const T p1 = extra_params[2];
    const T p2 = extra_params[3];
 
    const T u2 = u * u;
    const T uv = u * v;
    const T v2 = v * v;
    const T r2 = u2 + v2;
    const T radial = k1 * r2 + k2 * r2 * r2;
    *du = u * radial + T(2) * p1 * uv + p2 * (r2 + T(2) * u2);
    *dv = v * radial + T(2) * p2 * uv + p1 * (r2 + T(2) * v2);
}
 
// OpenCVFisheyeCameraModel
 
std::string OpenCVFisheyeCameraModel::InitializeParamsInfo() {
    return "fx, fy, cx, cy, k1, k2, k3, k4";
}
 
std::vector<size_t> OpenCVFisheyeCameraModel::InitializeFocalLengthIdxs() {
    return {0, 1};
}
 
std::vector<size_t> OpenCVFisheyeCameraModel::InitializePrincipalPointIdxs() {
    return {2, 3};
}
 
std::vector<size_t> OpenCVFisheyeCameraModel::InitializeExtraParamsIdxs() {
    return {4, 5, 6, 7};
}
 
std::vector<double> OpenCVFisheyeCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length, focal_length, width / 2.0, height / 2.0, 0, 0, 0, 0};
}
 
template <typename T>
void OpenCVFisheyeCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Distortion
    T du, dv;
    Distortion(&params[4], u, v, &du, &dv);
    *x = u + du;
    *y = v + dv;
 
    // Transform to image coordinates
    *x = f1 * *x + c1;
    *y = f2 * *y + c2;
}
 
template <typename T>
void OpenCVFisheyeCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Lift points to normalized plane
    *u = (x - c1) / f1;
    *v = (y - c2) / f2;
 
    IterativeUndistortion(&params[4], u, v);
}
 
template <typename T>
void OpenCVFisheyeCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T k1 = extra_params[0];
    const T k2 = extra_params[1];
    const T k3 = extra_params[2];
    const T k4 = extra_params[3];
 
    const T r = ceres::sqrt(u * u + v * v);
 
    if (r > T(std::numeric_limits<double>::epsilon())) {
        const T theta = ceres::atan(r);
        const T theta2 = theta * theta;
        const T theta4 = theta2 * theta2;
        const T theta6 = theta4 * theta2;
        const T theta8 = theta4 * theta4;
        const T thetad = theta * (T(1) + k1 * theta2 + k2 * theta4 +
                                  k3 * theta6 + k4 * theta8);
        *du = u * thetad / r - u;
        *dv = v * thetad / r - v;
    } else {
        *du = T(0);
        *dv = T(0);
    }
}
 
// FullOpenCVCameraModel
 
std::string FullOpenCVCameraModel::InitializeParamsInfo() {
    return "fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, k5, k6";
}
 
std::vector<size_t> FullOpenCVCameraModel::InitializeFocalLengthIdxs() {
    return {0, 1};
}
 
std::vector<size_t> FullOpenCVCameraModel::InitializePrincipalPointIdxs() {
    return {2, 3};
}
 
std::vector<size_t> FullOpenCVCameraModel::InitializeExtraParamsIdxs() {
    return {4, 5, 6, 7, 8, 9, 10, 11};
}
 
std::vector<double> FullOpenCVCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length,
            focal_length,
            width / 2.0,
            height / 2.0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0};
}
 
template <typename T>
void FullOpenCVCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Distortion
    T du, dv;
    Distortion(&params[4], u, v, &du, &dv);
    *x = u + du;
    *y = v + dv;
 
    // Transform to image coordinates
    *x = f1 * *x + c1;
    *y = f2 * *y + c2;
}
 
template <typename T>
void FullOpenCVCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Lift points to normalized plane
    *u = (x - c1) / f1;
    *v = (y - c2) / f2;
 
    IterativeUndistortion(&params[4], u, v);
}
 
template <typename T>
void FullOpenCVCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T k1 = extra_params[0];
    const T k2 = extra_params[1];
    const T p1 = extra_params[2];
    const T p2 = extra_params[3];
    const T k3 = extra_params[4];
    const T k4 = extra_params[5];
    const T k5 = extra_params[6];
    const T k6 = extra_params[7];
 
    const T u2 = u * u;
    const T uv = u * v;
    const T v2 = v * v;
    const T r2 = u2 + v2;
    const T r4 = r2 * r2;
    const T r6 = r4 * r2;
    const T radial = (T(1) + k1 * r2 + k2 * r4 + k3 * r6) /
                     (T(1) + k4 * r2 + k5 * r4 + k6 * r6);
    *du = u * radial + T(2) * p1 * uv + p2 * (r2 + T(2) * u2) - u;
    *dv = v * radial + T(2) * p2 * uv + p1 * (r2 + T(2) * v2) - v;
}
 
// FOVCameraModel
 
std::string FOVCameraModel::InitializeParamsInfo() {
    return "fx, fy, cx, cy, omega";
}
 
std::vector<size_t> FOVCameraModel::InitializeFocalLengthIdxs() {
    return {0, 1};
}
 
std::vector<size_t> FOVCameraModel::InitializePrincipalPointIdxs() {
    return {2, 3};
}
 
std::vector<size_t> FOVCameraModel::InitializeExtraParamsIdxs() { return {4}; }
 
std::vector<double> FOVCameraModel::InitializeParams(const double focal_length,
                                                     const size_t width,
                                                     const size_t height) {
    return {focal_length, focal_length, width / 2.0, height / 2.0, 1e-2};
}
 
template <typename T>
void FOVCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Distortion
    Distortion(&params[4], u, v, x, y);
 
    // Transform to image coordinates
    *x = f1 * *x + c1;
    *y = f2 * *y + c2;
}
 
template <typename T>
void FOVCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Lift points to normalized plane
    const T uu = (x - c1) / f1;
    const T vv = (y - c2) / f2;
 
    // Undistortion
    Undistortion(&params[4], uu, vv, u, v);
}
 
template <typename T>
void FOVCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T omega = extra_params[0];
 
    // Chosen arbitrarily.
    const T kEpsilon = T(1e-4);
 
    const T radius2 = u * u + v * v;
    const T omega2 = omega * omega;
 
    T factor;
    if (omega2 < kEpsilon) {
        // Derivation of this case with Matlab:
        // syms radius omega;
        // factor(radius) = atan(radius * 2 * tan(omega / 2)) / ...
        //                  (radius * omega);
        // simplify(taylor(factor, omega, 'order', 3))
        factor = (omega2 * radius2) / T(3) - omega2 / T(12) + T(1);
    } else if (radius2 < kEpsilon) {
        // Derivation of this case with Matlab:
        // syms radius omega;
        // factor(radius) = atan(radius * 2 * tan(omega / 2)) / ...
        //                  (radius * omega);
        // simplify(taylor(factor, radius, 'order', 3))
        const T tan_half_omega = ceres::tan(omega / T(2));
        factor = (T(-2) * tan_half_omega *
                  (T(4) * radius2 * tan_half_omega * tan_half_omega - T(3))) /
                 (T(3) * omega);
    } else {
        const T radius = ceres::sqrt(radius2);
        const T numerator =
                ceres::atan(radius * T(2) * ceres::tan(omega / T(2)));
        factor = numerator / (radius * omega);
    }
 
    *du = u * factor;
    *dv = v * factor;
}
 
template <typename T>
void FOVCameraModel::Undistortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    T omega = extra_params[0];
 
    // Chosen arbitrarily.
    const T kEpsilon = T(1e-4);
 
    const T radius2 = u * u + v * v;
    const T omega2 = omega * omega;
 
    T factor;
    if (omega2 < kEpsilon) {
        // Derivation of this case with Matlab:
        // syms radius omega;
        // factor(radius) = tan(radius * omega) / ...
        //                  (radius * 2*tan(omega/2));
        // simplify(taylor(factor, omega, 'order', 3))
        factor = (omega2 * radius2) / T(3) - omega2 / T(12) + T(1);
    } else if (radius2 < kEpsilon) {
        // Derivation of this case with Matlab:
        // syms radius omega;
        // factor(radius) = tan(radius * omega) / ...
        //                  (radius * 2*tan(omega/2));
        // simplify(taylor(factor, radius, 'order', 3))
        factor = (omega * (omega * omega * radius2 + T(3))) /
                 (T(6) * ceres::tan(omega / T(2)));
    } else {
        const T radius = ceres::sqrt(radius2);
        const T numerator = ceres::tan(radius * omega);
        factor = numerator / (radius * T(2) * ceres::tan(omega / T(2)));
    }
 
    *du = u * factor;
    *dv = v * factor;
}
 
// SimpleRadialFisheyeCameraModel
 
std::string SimpleRadialFisheyeCameraModel::InitializeParamsInfo() {
    return "f, cx, cy, k";
}
 
std::vector<size_t>
SimpleRadialFisheyeCameraModel::InitializeFocalLengthIdxs() {
    return {0};
}
 
std::vector<size_t>
SimpleRadialFisheyeCameraModel::InitializePrincipalPointIdxs() {
    return {1, 2};
}
 
std::vector<size_t>
SimpleRadialFisheyeCameraModel::InitializeExtraParamsIdxs() {
    return {3};
}
 
std::vector<double> SimpleRadialFisheyeCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length, width / 2.0, height / 2.0, 0};
}
 
template <typename T>
void SimpleRadialFisheyeCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // Distortion
    T du, dv;
    Distortion(&params[3], u, v, &du, &dv);
    *x = u + du;
    *y = v + dv;
 
    // Transform to image coordinates
    *x = f * *x + c1;
    *y = f * *y + c2;
}
 
template <typename T>
void SimpleRadialFisheyeCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // Lift points to normalized plane
    *u = (x - c1) / f;
    *v = (y - c2) / f;
 
    IterativeUndistortion(&params[3], u, v);
}
 
template <typename T>
void SimpleRadialFisheyeCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T k = extra_params[0];
 
    const T r = ceres::sqrt(u * u + v * v);
 
    if (r > T(std::numeric_limits<double>::epsilon())) {
        const T theta = ceres::atan(r);
        const T theta2 = theta * theta;
        const T thetad = theta * (T(1) + k * theta2);
        *du = u * thetad / r - u;
        *dv = v * thetad / r - v;
    } else {
        *du = T(0);
        *dv = T(0);
    }
}
 
// RadialFisheyeCameraModel
 
std::string RadialFisheyeCameraModel::InitializeParamsInfo() {
    return "f, cx, cy, k1, k2";
}
 
std::vector<size_t> RadialFisheyeCameraModel::InitializeFocalLengthIdxs() {
    return {0};
}
 
std::vector<size_t> RadialFisheyeCameraModel::InitializePrincipalPointIdxs() {
    return {1, 2};
}
 
std::vector<size_t> RadialFisheyeCameraModel::InitializeExtraParamsIdxs() {
    return {3, 4};
}
 
std::vector<double> RadialFisheyeCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length, width / 2.0, height / 2.0, 0, 0};
}
 
template <typename T>
void RadialFisheyeCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // Distortion
    T du, dv;
    Distortion(&params[3], u, v, &du, &dv);
    *x = u + du;
    *y = v + dv;
 
    // Transform to image coordinates
    *x = f * *x + c1;
    *y = f * *y + c2;
}
 
template <typename T>
void RadialFisheyeCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f = params[0];
    const T c1 = params[1];
    const T c2 = params[2];
 
    // Lift points to normalized plane
    *u = (x - c1) / f;
    *v = (y - c2) / f;
 
    IterativeUndistortion(&params[3], u, v);
}
 
template <typename T>
void RadialFisheyeCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T k1 = extra_params[0];
    const T k2 = extra_params[1];
 
    const T r = ceres::sqrt(u * u + v * v);
 
    if (r > T(std::numeric_limits<double>::epsilon())) {
        const T theta = ceres::atan(r);
        const T theta2 = theta * theta;
        const T theta4 = theta2 * theta2;
        const T thetad = theta * (T(1) + k1 * theta2 + k2 * theta4);
        *du = u * thetad / r - u;
        *dv = v * thetad / r - v;
    } else {
        *du = T(0);
        *dv = T(0);
    }
}
 
// ThinPrismFisheyeCameraModel
 
std::string ThinPrismFisheyeCameraModel::InitializeParamsInfo() {
    return "fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, sx1, sy1";
}
 
std::vector<size_t> ThinPrismFisheyeCameraModel::InitializeFocalLengthIdxs() {
    return {0, 1};
}
 
std::vector<size_t>
ThinPrismFisheyeCameraModel::InitializePrincipalPointIdxs() {
    return {2, 3};
}
 
std::vector<size_t> ThinPrismFisheyeCameraModel::InitializeExtraParamsIdxs() {
    return {4, 5, 6, 7, 8, 9, 10, 11};
}
 
std::vector<double> ThinPrismFisheyeCameraModel::InitializeParams(
        const double focal_length, const size_t width, const size_t height) {
    return {focal_length,
            focal_length,
            width / 2.0,
            height / 2.0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0};
}
 
template <typename T>
void ThinPrismFisheyeCameraModel::WorldToImage(
        const T* params, const T u, const T v, T* x, T* y) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    const T r = ceres::sqrt(u * u + v * v);
 
    T uu, vv;
    if (r > T(std::numeric_limits<double>::epsilon())) {
        const T theta = ceres::atan(r);
        uu = theta * u / r;
        vv = theta * v / r;
    } else {
        uu = u;
        vv = v;
    }
 
    // Distortion
    T du, dv;
    Distortion(&params[4], uu, vv, &du, &dv);
    *x = uu + du;
    *y = vv + dv;
 
    // Transform to image coordinates
    *x = f1 * *x + c1;
    *y = f2 * *y + c2;
}
 
template <typename T>
void ThinPrismFisheyeCameraModel::ImageToWorld(
        const T* params, const T x, const T y, T* u, T* v) {
    const T f1 = params[0];
    const T f2 = params[1];
    const T c1 = params[2];
    const T c2 = params[3];
 
    // Lift points to normalized plane
    *u = (x - c1) / f1;
    *v = (y - c2) / f2;
 
    IterativeUndistortion(&params[4], u, v);
 
    const T theta = ceres::sqrt(*u * *u + *v * *v);
    const T theta_cos_theta = theta * ceres::cos(theta);
    if (theta_cos_theta > T(std::numeric_limits<double>::epsilon())) {
        const T scale = ceres::sin(theta) / theta_cos_theta;
        *u *= scale;
        *v *= scale;
    }
}
 
template <typename T>
void ThinPrismFisheyeCameraModel::Distortion(
        const T* extra_params, const T u, const T v, T* du, T* dv) {
    const T k1 = extra_params[0];
    const T k2 = extra_params[1];
    const T p1 = extra_params[2];
    const T p2 = extra_params[3];
    const T k3 = extra_params[4];
    const T k4 = extra_params[5];
    const T sx1 = extra_params[6];
    const T sy1 = extra_params[7];
 
    const T u2 = u * u;
    const T uv = u * v;
    const T v2 = v * v;
    const T r2 = u2 + v2;
    const T r4 = r2 * r2;
    const T r6 = r4 * r2;
    const T r8 = r6 * r2;
    const T radial = k1 * r2 + k2 * r4 + k3 * r6 + k4 * r8;
    *du = u * radial + T(2) * p1 * uv + p2 * (r2 + T(2) * u2) + sx1 * r2;
    *dv = v * radial + T(2) * p2 * uv + p1 * (r2 + T(2) * v2) + sy1 * r2;
}
 
 
void CameraModelWorldToImage(const int model_id,
                             const std::vector<double>& params,
                             const double u,
                             const double v,
                             double* x,
                             double* y) {
    switch (model_id) {
#define CAMERA_MODEL_CASE(CameraModel)                        \
    case CameraModel::kModelId:                               \
        CameraModel::WorldToImage(params.data(), u, v, x, y); \
        break;
 
        CAMERA_MODEL_SWITCH_CASES
 
#undef CAMERA_MODEL_CASE
    }
}
 
void CameraModelImageToWorld(const int model_id,
                             const std::vector<double>& params,
                             const double x,
                             const double y,
                             double* u,
                             double* v) {
    switch (model_id) {
#define CAMERA_MODEL_CASE(CameraModel)                        \
    case CameraModel::kModelId:                               \
        CameraModel::ImageToWorld(params.data(), x, y, u, v); \
        break;
 
        CAMERA_MODEL_SWITCH_CASES
 
#undef CAMERA_MODEL_CASE
    }
}
 
double CameraModelImageToWorldThreshold(const int model_id,
                                        const std::vector<double>& params,
                                        const double threshold) {
    switch (model_id) {
#define CAMERA_MODEL_CASE(CameraModel)                                       \
    case CameraModel::kModelId:                                              \
        return CameraModel::ImageToWorldThreshold(params.data(), threshold); \
        break;
 
        CAMERA_MODEL_SWITCH_CASES
 
#undef CAMERA_MODEL_CASE
    }
 
    return -1;
}
 
}  // namespace colmap