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/*
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* RobustNorms.h
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*
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* Copyright (c) 2014-2022 SEACAVE
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*
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* Author(s):
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*
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* cDc <cdc.seacave@gmail.com>
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*
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU Affero General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Affero General Public License for more details.
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*
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* You should have received a copy of the GNU Affero General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*
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*
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* Additional Terms:
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*
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* You are required to preserve legal notices and author attributions in
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* that material or in the Appropriate Legal Notices displayed by works
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* containing it.
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*/
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#ifndef _SEACAVE_ROBUSTNORMS_H_
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#define _SEACAVE_ROBUSTNORMS_H_
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// I N C L U D E S /////////////////////////////////////////////////
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// D E F I N E S ///////////////////////////////////////////////////
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// S T R U C T S ///////////////////////////////////////////////////
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namespace SEACAVE {
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// M-estimators to be used during nonlinear refinement for increased robustness to outlier residuals:
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// new_residual = robustNorm(residual)
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namespace RobustNorm {
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template<typename TYPE>
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struct Identity {
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inline TYPE operator()(const TYPE& r) const {
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return r;
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}
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};
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template<typename TYPE>
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struct L1 {
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inline TYPE operator()(const TYPE& r) const {
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return r / (std::sqrt(std::abs(r)) + TYPE(1e-12));
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}
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};
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template<typename TYPE>
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struct Exp {
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inline Exp(const TYPE& _threshold)
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: sigma(TYPE(-1) / (TYPE(2) * SQUARE(_threshold))) { ASSERT(_threshold > 0); }
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inline TYPE operator()(const TYPE& r) const {
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return r * std::exp(SQUARE(r)*sigma);
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}
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const TYPE sigma;
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};
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template<typename TYPE>
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struct BlakeZisserman {
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inline BlakeZisserman(const TYPE& _threshold)
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: threshold(_threshold), invThreshold(TYPE(1)/threshold), eps(std::exp(-SQUARE(threshold))) { ASSERT(_threshold > 0); }
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inline TYPE operator()(const TYPE& r) const {
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return -log(std::exp(-SQUARE(r) * invThreshold) + eps);
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}
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const TYPE threshold;
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const TYPE invThreshold;
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const TYPE eps;
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};
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template<typename TYPE>
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struct Huber {
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inline Huber(const TYPE& _threshold)
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: threshold(_threshold) { ASSERT(_threshold > 0); }
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inline TYPE operator()(const TYPE& r) const {
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const TYPE dAbs(std::abs(r));
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if (dAbs <= threshold)
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return r;
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return std::copysign(std::sqrt(threshold * (TYPE(2) * dAbs - threshold)), r);
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}
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const TYPE threshold;
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};
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template<typename TYPE>
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struct PseudoHuber {
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inline PseudoHuber(const TYPE& _threshold)
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: threshold(_threshold), thresholdSq(SQUARE(_threshold)), invThreshold(TYPE(1)/threshold) { ASSERT(_threshold > 0); }
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inline TYPE operator()(const TYPE& r) const {
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return std::sqrt(TYPE(2) * thresholdSq * (std::sqrt(TYPE(1) + SQUARE(r * invThreshold)) - TYPE(1)));
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}
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const TYPE threshold;
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const TYPE thresholdSq;
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const TYPE invThreshold;
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};
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template<typename TYPE>
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struct GemanMcClure {
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inline GemanMcClure(const TYPE& _threshold)
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: thresholdSq(SQUARE(_threshold)) { ASSERT(_threshold > 0); }
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inline TYPE operator()(const TYPE& r) const {
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return r * std::sqrt(thresholdSq/(thresholdSq+SQUARE(r)));
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}
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const TYPE thresholdSq;
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};
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template<typename TYPE>
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struct Cauchy {
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inline Cauchy(const TYPE& _threshold)
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: thresholdSq(SQUARE(_threshold)), invThresholdSq(TYPE(1)/thresholdSq) { ASSERT(_threshold > 0); }
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inline TYPE operator()(const TYPE& r) const {
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return std::sqrt(thresholdSq*log(TYPE(1)+SQUARE(r)*invThresholdSq));
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}
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const TYPE thresholdSq;
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const TYPE invThresholdSq;
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};
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template<typename TYPE>
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struct Tukey {
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inline Tukey(const TYPE& _threshold)
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: threshold(_threshold), thresholdCb6(CUBE(_threshold)/TYPE(6)), invThreshold(TYPE(1)/threshold), sqrtThresholdCb6(std::sqrt(thresholdCb6)) { ASSERT(_threshold > 0); }
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inline TYPE operator()(const TYPE& r) const {
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return std::abs(r) < threshold ? std::sqrt(thresholdCb6*(TYPE(1)-CUBE(TYPE(1)-SQUARE(r*invThreshold)))) : sqrtThresholdCb6;
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}
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const TYPE threshold;
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const TYPE thresholdCb6;
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const TYPE invThreshold;
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const TYPE sqrtThresholdCb6;
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};
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} // namespace RobustNorm
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/*----------------------------------------------------------------*/
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// makes sure the inverse NCC score does not exceed 0.3
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#if 0
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template <typename T>
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inline T robustincc(const T x) { return x / (T(1) + T(3) * x); }
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template <typename T>
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inline T robustinccg(const T x) { return T(1)/SQUARE(T(1) + T(3) * x); }
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template <typename T>
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inline T unrobustincc(const T y) { return y / (T(1) - T(3) * y); }
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#elif 0
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template <typename T>
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inline T robustincc(const T x) { return T(1)-EXP(x*x*T(-4)); }
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template <typename T>
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inline T robustinccg(const T x) { return T(8)*x*EXP(x*x*T(-4)); }
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template <typename T>
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inline T unrobustincc(const T y) { return SQRT(-LOGN(T(1) - y))/T(2); }
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#else
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template <typename T>
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inline T robustincc(const T x) { return x/SQRT(T(0.3)+x*x); }
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template <typename T>
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inline T robustinccg(const T x) { return T(0.3)/((T(0.3)+x*x)*SQRT(T(0.3)+x*x)); }
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template <typename T>
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inline T unrobustincc(const T y) { return (SQRT(30)*y)/(T(10)*SQRT(T(1) - y*y)); }
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#endif
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/*----------------------------------------------------------------*/
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} // namespace SEACAVE
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#endif // _SEACAVE_ROBUSTNORMS_H_
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