calibration_tools_v1.0/lidar_driver/include/open3d/pipelines/registration/RobustKernel.h

// ----------------------------------------------------------------------------
// -                        Open3D: www.open3d.org                            -
// ----------------------------------------------------------------------------
// Copyright (c) 2018-2023 www.open3d.org
// SPDX-License-Identifier: MIT
// ----------------------------------------------------------------------------
// @author Ignacio Vizzo     [ivizzo@uni-bonn.de]
//
// Copyright (c) 2020 Ignacio Vizzo, Cyrill Stachniss, University of Bonn.
// ----------------------------------------------------------------------------

#pragma once

namespace open3d {
namespace pipelines {
namespace registration {

/// \class RobustKernel
///
/// Base class that models a robust kernel for outlier rejection. The virtual
/// function Weight(double residual); must be implemented in derived classes.
/// This method will be only difference between different types of kernels and
/// can be easily extended.
///
/// The kernels implemented so far and the notation has been inspired by the
/// publication: "Analysis of Robust Functions for Registration Algorithms",
/// Philippe Babin et al.
///
/// We obtain the correspondendent weights for each residual and turn the
/// non-linear least-square problem into a IRSL (Iteratively Reweighted
/// Least-Squares) problem. Changing the weight of each residual is equivalent
/// to changing the robust kernel used for outlier rejection.
///
/// The different loss functions will only impact in the weight for each
/// residual during the optimization step. For more information please see also:
/// “Adaptive Robust Kernels for Non-Linear Least Squares Problems”, N.
/// Chebrolu et al.
/// The weight w(r) for a given residual `r` and a given loss function `p(r)` is
/// computed as follow:
///     w(r) = (1 / r) * (dp(r) / dr) , for all r
/// Therefore, the only impact of the choice on the kernel is through its first
/// order derivate.
class RobustKernel {
public:
    virtual ~RobustKernel() = default;
    /// Obtain the weight for the given residual according to the robust kernel
    /// model. This method must be implemented in the derived classes that model
    /// the different robust kernels.
    ///
    /// \param residual Residual value obtained during the optimization step.
    virtual double Weight(double residual) const = 0;
};

/// \class L2Loss
///
/// Classical loss function used for outlier rejection.
///
/// The loss p(r) for a given residual 'r' is computed as follow:
///    p(r) = r^2 / 2
class L2Loss : public RobustKernel {
public:
    /// The weight w(r) for a given residual 'r' is computed as follow:
    ///   w(r) = 1.0, for all r
    ///
    /// \param residual [ignored]
    double Weight(double residual) const override;
};

/// \class L1Loss
///
/// L1 loss function used for outlier rejection.
///
/// The loss p(r) for a given residual 'r' is computed as follow:
//    p(r) = abs(r)
class L1Loss : public RobustKernel {
public:
    /// The weight w(r) for a given residual 'r' is computed as follow:
    ///   w(r) = 1.0 / abs(r), for all r
    ///
    /// \param residual Residual value obtained during the optimization step.
    double Weight(double residual) const override;
};

/// \class HuberLoss
///
/// HuberLoss loss function used for outlier rejection.
///
/// The loss p(r) for a given residual 'r' is computed as follow:
///   p(r) = r^2                   for abs(r) <= k,
///   p(r) = k^2 * (abs(r) - k/2)  for abs(r) > k
///
/// For more information: http://en.wikipedia.org/wiki/Huber_Loss_Function
class HuberLoss : public RobustKernel {
public:
    /// \brief Parametrized Constructor.
    ///
    /// \param k Is the scaling parameter of the huber loss function. 'k'
    /// corresponds to 'delta' on this page:
    /// http://en.wikipedia.org/wiki/Huber_Loss_Function
    explicit HuberLoss(double k) : k_(k) {}

    /// The weight w(r) for a given residual 'r' is computed as follow:
    ///   w(r) = 1.0         for abs(r) <= k,
    ///   w(r) = k / abs(r)  for abs(r) > k
    /// Where k Is the scaling parameter of the loss function.
    ///
    /// \param residual Residual value obtained during the optimization step.
    double Weight(double residual) const override;

public:
    /// Scaling parameter.
    double k_;
};

/// \class CauchyLoss
///
/// CauchyLoss loss function used for outlier rejection.
///
/// The loss p(r) for a given residual 'r' is computed as follow:
///   p(r) = (k^2 / 2) * log(1 + (r / k)^2), for all r
class CauchyLoss : public RobustKernel {
public:
    /// \brief Parametrized Constructor.
    ///
    /// \param k Is the scaling parameter of the loss function.
    explicit CauchyLoss(double k) : k_(k) {}

    /// The weight w(r) for a given residual 'r' is computed as follow:
    ///   w(r) = 1 / (1 + (r / k)^2)
    /// Where k Is the scaling parameter of the loss function.
    ///
    /// \param residual Residual value obtained during the optimization step.
    double Weight(double residual) const override;

public:
    /// Scaling parameter.
    double k_;
};

/// \class GMLoss
///
/// German-McClure loss function used for outlier rejection.
///
/// The loss p(r) for a given residual 'r' is computed as follow:
///   p(r) = (r^2 / 2) / (1 + (r / k)^2), for all r
class GMLoss : public RobustKernel {
public:
    /// \brief Parametrized Constructor.
    ///
    /// \param k Is the scaling parameter of the loss function.
    explicit GMLoss(double k) : k_(k) {}

    /// The weight w(r) for a given residual 'r' is computed as follow:
    ///   w(r) = k / (k + r^2)^2, for all r
    /// Where k Is the scaling parameter of the loss function.
    ///
    /// \param residual Residual value obtained during the optimization step.
    double Weight(double residual) const override;

public:
    /// Scaling parameter.
    double k_;
};

/// \class TukeyLoss
///
/// This is the so called Tukey loss function which aggressively attempts to
/// suppress large errors.
///
/// The loss p(r) for a given residual 'r' is computed as follow:
///
///   p(r) = k^2 * (1 - (1 - r / k^2)^3 ) / 2   for abs(r) <= k,
///   p(r) = k^2 / 2                            for abs(r) >  k.
///
class TukeyLoss : public RobustKernel {
public:
    /// \brief Parametrized Constructor.
    ///
    /// \param k Is a running constant for the Tukey Loss function.
    explicit TukeyLoss(double k) : k_(k) {}

public:
    /// The weight w(r) for a given residual 'r' is computed as follow:
    ///   p(r) = (1 - (r / k)^2 )^2  for abs(r) <= k,
    ///   p(r) = 0.0                 for abs(r) >  k.
    /// Where k Is the scaling parameter of the loss function.
    ///
    /// \param residual Residual value obtained during the optimization step.
    double Weight(double residual) const override;

public:
    double k_;
};

}  // namespace registration
}  // namespace pipelines
}  // namespace open3d