NonMaximumSuppression.h

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/*
 * Copyright (c) Meta Platforms, Inc. and affiliates.
 *
 * This source code is licensed under the MIT license found in the
 * LICENSE file in the root directory of this source tree.
 */
 
#ifndef META_OCEAN_CV_NON_MAXIMUM_SUPPRESSION_H
#define META_OCEAN_CV_NON_MAXIMUM_SUPPRESSION_H
 
#include "ocean/cv/CV.h"
#include "ocean/cv/PixelPosition.h"
 
#include "ocean/base/Callback.h"
#include "ocean/base/ShiftVector.h"
#include "ocean/base/Worker.h"
 
namespace Ocean
{
 
namespace CV
{
 
/**
 * This class implements the possibility to find local maximum in a 2D array by applying a non-maximum-suppression search.
 * The search is done within a 3x3 neighborhood (centered around the point of interest).<br>
 * Use this class to determine e.g. reliable feature points.<br>
 * The class supports bin accuracy (pixel accuracy) and sub-bin accuracy (sub-pixel accuracy).
 *
 * The non-maximum-suppression search is implemented by a vertical list holding maps of horizontal array elements.<br>
 * The performance depends on the number of elements inserted into the individual maps.<br>
 * Thus, do not add data elements with negligible value.
 *
 * It should be mentioned that the application of this class should be restricted to situations in which the entire filter response values do not exist already.<br>
 * The performance boost comes with a simultaneous determination of filter responses and the insertion of possible candidates for maximum locations.
 * @tparam T The data type of the individual elements that are applied for the non-maximum-suppression search.
 * @ingroup cv
 */
template <typename T>
class NonMaximumSuppression
{
    public:
 
        /**
         * This class extends a 2D position by a third parameter storing a strength value.
         * @tparam TCoordinate The data type of a scalar coordinate
         * @tparam TStrength The data type of the strength parameter
         */
        template <typename TCoordinate, typename TStrength>
        class StrengthPosition : public VectorT2<TCoordinate>
        {
            public:
 
                /**
                 * Creates a new object with default strength parameter.
                 */
                StrengthPosition() = default;
 
                /**
                 * Creates a new object with explicit position and strength parameter.
                 * @param x Horizontal position
                 * @param y Vertical position
                 * @param strength The strength parameter
                 */
                inline StrengthPosition(const TCoordinate x, const TCoordinate y, const TStrength& strength);
 
                /**
                 * Returns the strength parameter of this object.
                 * @return Strength parameter
                 */
                inline const TStrength& strength() const;
 
                /**
                 * Compares the strength value of two objects.
                 * @param left The left object to compare
                 * @param right The right object to compare
                 * @return True, if so
                 * @tparam tLeftLargerThanRight True, to return whether left's strength is larger than right's strength; False, to return whether right is larger than left
                 */
                template <bool tLeftLargerThanRight = true>
                static inline bool compareStrength(const StrengthPosition<TCoordinate, TStrength>& left, const StrengthPosition<TCoordinate, TStrength>& right);
 
            private:
 
                /// Strength parameter of this object.
                TStrength strength_ = TStrength();
        };
 
        /**
         * Definition of a vector holding strength pixel positions.
         */
        template <typename TCoordinate, typename TStrength>
        using StrengthPositions = std::vector<StrengthPosition<TCoordinate, TStrength>>;
 
        /**
         * Definition of a callback function used to determine the precise sub-pixel position of a specific point.
         * The first parameter provides the horizontal position.<br>
         * The second parameter provides the vertical position.<br>
         * The third parameter provides the strength value.<br>
         * The fourth parameter receives the precise horizontal position.<br>
         * The fifth parameter receives the precise vertical position.<br>
         * The sixth parameter receives the precise strength value.<br>
         * The return parameter should be True if the precise position could be determined
         */
        template <typename TCoordinate, typename TStrength>
        using PositionCallback = Callback<bool, const unsigned int, const unsigned int, const T, TCoordinate&, TCoordinate&, TStrength&>;
 
    private:
 
        /**
         * This class holds the horizontal position and strength parameter of an interest pixel.
         */
        class StrengthCandidate
        {
            public:
 
                /**
                 * Creates a new candidate object.
                 */
                inline StrengthCandidate();
 
                /**
                 * Creates a new candidate object with horizontal position and strength parameter.
                 * @param x Horizontal position in pixel
                 * @param strength The strength parameter
                 */
                inline StrengthCandidate(const unsigned int x, const T& strength);
 
                /**
                 * Returns the horizontal position of this candidate object.
                 * @return Horizontal position in pixel
                 */
                inline unsigned int x() const;
 
                /**
                 * Returns the strength parameter of this object.
                 * @return Strength parameter
                 */
                inline const T& strength() const;
 
            private:
 
                /// Horizontal position of this object.
                unsigned int positionX_ = (unsigned int)(-1);
 
                /// Strength parameter of this object.
                T strength_ = T();
        };
 
        /**
         * Definition of a vector holding strength candidate objects.
         */
        typedef std::vector<StrengthCandidate> StrengthCandidateRow;
 
        /**
         * Definition of a vector holding a vector of strength candidates.
         */
        typedef ShiftVector<StrengthCandidateRow> StrengthCandidateRows;
 
    public:
 
        /**
         * Move constructor.
         * @param nonMaximumSuppression The object to be moved
         */
        NonMaximumSuppression(NonMaximumSuppression<T>&& nonMaximumSuppression) noexcept;
 
        /**
         * Copy constructor.
         * @param nonMaximumSuppression The object to be moved
         */
        NonMaximumSuppression(const NonMaximumSuppression<T>& nonMaximumSuppression) noexcept;
 
        /**
         * Creates a new maximum suppression object with a predefined size.
         * @param width The width of this object in pixel, with range [3, infinity)
         * @param height The height of this object in pixel, with range [3, infinity)
         * @param yOffset Optional offset in the vertical direction moving the suppression region by the specified number of rows, with range [0, infinity)
         */
        NonMaximumSuppression(const unsigned int width, const unsigned int height, const unsigned int yOffset = 0u) noexcept;
 
        /**
         * Returns the width of this object.
         * @return Width in pixel
         */
        inline unsigned int width() const;
 
        /**
         * Returns the height of this object.
         * @return Height in pixel
         */
        inline unsigned int height() const;
 
        /**
         * Returns the optional offset in the vertical direction.
         * @return Optional vertical direction offset, 0 by default
         */
        inline unsigned int yOffset() const;
 
        /**
         * Adds a new candidate to this object.
         * Beware: Due to performance issues do no add candidates with negligible strength parameter.
         * @param x Horizontal position in pixel, with range [0, width() - 1]
         * @param y Vertical position in pixel, with range [yOffset(), yOffset() + height() - 1]
         * @param strength The strength parameter
         * @see addCandidates(), removeCandidatesFromRight().
         */
        inline void addCandidate(const unsigned int x, const unsigned int y, const T& strength);
 
        /**
         * Adds new candidates to this object from a given buffer providing one value for each bin/pixel of this object.
         * Beware: Due to performance reasons, you should use the addCandidate() function to add one single new candidate in the moment the filter response is larger than a specific threshold.<br>
         * @param values The from which candidates will be added, must be width() * height() elements
         * @param valuesPaddingElements The number of padding elements at the end of each values row, in elements, with range [0, infinity)
         * @param firstColumn First column to be handled, with range [0, width() - 1]
         * @param numberColumns Number of columns to be handled, with range [1, width() - firstColumn]
         * @param firstRow First row to be handled, with range [yOffset(), height() - 1]
         * @param numberRows Number of rows to be handled, with range [1, height() - firstRow]
         * @param minimalThreshold The minimal threshold so that a value counts as candidate
         * @param worker Optional worker object to distribute the computation
         * @see addCandidate(), removeCandidatesFromRight().
         */
        void addCandidates(const T* values, const unsigned int valuesPaddingElements, const unsigned int firstColumn, const unsigned int numberColumns, const unsigned int firstRow, const unsigned int numberRows, const T& minimalThreshold, Worker* worker);
 
        /**
         * Removes all candidates from a specified row having a horizontal location equal or larger than a specified coordinate.
         * @param x The horizontal coordinate specifying which candidates will be removed, all candidates with horizontal location >= x will be removed, with range [0, infinity)
         * @param y The index of the row in which the candidates will be removed, with range [yOffset(), yOffset() + height() - 1]
         */
        inline void removeCandidatesRightFrom(const unsigned int x, const unsigned int y);
 
        /**
         * Applies a non-maximum-suppression search on a given 2D frame in a 3x3 neighborhood (eight neighbors).
         * This function allows to determine the precise position of the individual maximum value positions by application of a callback function determining the individual positions.<br>
         * @param firstColumn First column to be handled, with range [1, width() - 1)
         * @param numberColumns Number of columns to be handled
         * @param firstRow First row to be handled, with range [yOffset() + 1, height() - 1)
         * @param numberRows Number of rows to be handled
         * @param worker Optional worker object to distribute the computation
         * @param positionCallback Optional callback function allowing to determine the precise position of the individual maximum value positions
         * @return Resulting non maximum suppressed positions including the strength parameters
         * @tparam TCoordinate The data type of a scalar coordinate
         * @tparam TStrength The data type of the strength parameter
         * @tparam tStrictMaximum True, to search for a strict maximum (larger than all eight neighbors); False, to allow equal values in the upper left neighborhood
         */
        template <typename TCoordinate, typename TStrength, bool tStrictMaximum = true>
        StrengthPositions<TCoordinate, TStrength> suppressNonMaximum(const unsigned int firstColumn, const unsigned int numberColumns, const unsigned int firstRow, const unsigned int numberRows, Worker* worker = nullptr, const PositionCallback<TCoordinate, TStrength>* positionCallback = nullptr) const;
 
        /**
         * Removes the gathered non-maximum suppression information so that this object can be reused again (for the same task with same resolution etc.).
         * The allocated memory will remain so that reusing this object may improve performance.
         */
        void reset();
 
        /**
         * Move operator.
         * @param nonMaximumSuppression Object to be moved
         * @return Reference to this object
         */
        NonMaximumSuppression<T>& operator=(NonMaximumSuppression<T>&& nonMaximumSuppression);
 
        /**
         * Copy operator.
         * @param nonMaximumSuppression The object to be copied
         * @return Reference to this object
         */
        NonMaximumSuppression<T>& operator=(const NonMaximumSuppression<T>& nonMaximumSuppression);
 
        /**
         * Applies a non-maximum-suppression based on already existing strength positions (just with a custom suppression radius) e.g., as a post-processing step.
         * @param width The width of the image/domain in which the strength positions are located, e.g., in pixel, with range [1, infinity)
         * @param height The height of the image/domain in which the strength positions are located, e.g., in pixel, with range [1, infinity)
         * @param strengthPositions The strength positions for which a custom suppression-radius will be applied
         * @param radius The suppression radius to be applied, with range [1, infinity)
         * @param validIndices Optional resulting indices of all strength positions which remain after suppression
         * @return The resulting strength positions
         * @tparam TCoordinate The data type of a scalar coordinate
         * @tparam TStrength The data type of the strength parameter
         * @tparam tStrictMaximum True, to search for a strict maximum (larger than all eight neighbors); False, to allow equal values in the upper left neighborhood
         */
        template <typename TCoordinate, typename TStrength, bool tStrictMaximum>
        static StrengthPositions<TCoordinate, TStrength> suppressNonMaximum(const unsigned int width, const unsigned int height, const StrengthPositions<TCoordinate, TStrength>& strengthPositions, const TCoordinate radius, Indices32* validIndices = nullptr);
 
        /**
         * Determines the precise peak location in 1D space for three discrete neighboring measurements at location x == 0.
         * The precise peak is determined based on the first and second derivatives of the measurement values.
         * @param leftValue The left discrete value, e.g., at location x - 1, with range (-infinity, middleValue]
         * @param middleValue The middle discrete value, e.g., at location x, with range (-infinity, infinity)
         * @param rightValue The  discrete value, e.g., at location x + 1, with range (-infinity, middleValue]
         * @param location The location of the precise peak of all values, with range (-1, 1)
         * @return True, if succeeded
         * @tparam TFloat The floating point data type to be used for calculation, either 'float' or 'double'
         */
        template <typename TFloat>
        static bool determinePrecisePeakLocation1(const T& leftValue, const T& middleValue, const T& rightValue, TFloat& location);
 
        /**
         * Determines the precise peak location in 2D space for nine discrete neighboring measurements at location x == 0, y == 0.
         * The precise peak is determined based on the first and second derivatives of the measurement values.
         * @param topValues The three discrete values in the top row, must be valid
         * @param centerValues The three discrete values in the center row, must be valid
         * @param bottomValues The three discrete values in the bottom row, must be valid
         * @param location The location of the precise peak of all values, with range (-1, 1)
         * @return True, if succeeded
         * @tparam TFloat The floating point data type to be used for calculation, either 'float' or 'double'
         */
        template <typename TFloat>
        static bool determinePrecisePeakLocation2(const T* const topValues, const T* const centerValues, const T* const bottomValues, VectorT2<TFloat>& location);
 
    private:
 
        /**
         * Adds new candidates to this object from a subset of a given buffer providing one value for each bin/pixel of this object.
         * @param values The from which candidates will be added, must be width() * height() elements
         * @param valuesStrideElements The number of elements between two values rows, in elements, with range [0, infinity)
         * @param minimalThreshold The minimal threshold so that a value counts as candidate
         * @param firstColumn First column to be handled, with range [0, width() - 1]
         * @param numberColumns Number of columns to be handled, with range [1, width() - firstColumn]
         * @param firstRow The first row in the buffer from which the candidates will be added, with range [yOffset(), height())
         * @param numberRows The number of rows to be handled, with range [1, height() - firstRow]
         * @see addCandidates().
         */
        void addCandidatesSubset(const T* values, const unsigned int valuesStrideElements, const unsigned int firstColumn, const unsigned int numberColumns, const T* minimalThreshold, const unsigned int firstRow, const unsigned int numberRows);
 
        /**
         * Applies a non-maximum-suppression search on a subset of a given 2D frame in a 3x3 neighborhood (eight neighbors).
         * This function allows to determine the precise position of the individual maximum value positions by application of a callback function determining the individual positions.<br>
         * @param strengthPositions Resulting non maximum suppressed positions including the strength parameters
         * @param firstColumn First column to be handled
         * @param numberColumns Number of columns to be handled
         * @param lock The lock object that must be defined if this function is executed in parallel on several threads
         * @param positionCallback Optional callback function allowing to determine the precise position of the individual maximum value positions
         * @param firstRow First row to be handled
         * @param numberRows Number of rows to be handled
         * @tparam tStrictMaximum True, to search for a strict maximum (larger than all eight neighbors); False, to allow equal values in the upper left neighborhood
         */
        template <typename TCoordinate, typename TStrength, bool tStrictMaximum>
        void suppressNonMaximumSubset(StrengthPositions<TCoordinate, TStrength>* strengthPositions, const unsigned int firstColumn, const unsigned int firstRow, Lock* lock, const PositionCallback<TCoordinate, TStrength>* positionCallback, const unsigned int numberColumns, const unsigned int numberRows) const;
 
    private:
 
        /// Width of this object.
        unsigned int width_ = 0u;
 
        /// All candidate rows.
        StrengthCandidateRows rows_;
};
 
template <typename T>
template <typename TCoordinate, typename TStrength>
inline NonMaximumSuppression<T>::StrengthPosition<TCoordinate, TStrength>::StrengthPosition(const TCoordinate x, const TCoordinate y, const TStrength& strength) :
    VectorT2<TCoordinate>(x, y),
    strength_(strength)
{
    // nothing to do here
}
 
template <typename T>
template <typename TCoordinate, typename TStrength>
inline const TStrength& NonMaximumSuppression<T>::StrengthPosition<TCoordinate, TStrength>::strength() const
{
    return strength_;
}
 
template <typename T>
template <typename TCoordinate, typename TStrength>
template <bool tLeftLargerThanRight>
inline bool NonMaximumSuppression<T>::StrengthPosition<TCoordinate, TStrength>::compareStrength(const StrengthPosition<TCoordinate, TStrength>& left, const StrengthPosition<TCoordinate, TStrength>& right)
{
    if constexpr (tLeftLargerThanRight)
    {
        return left.strength() > right.strength();
    }
    else
    {
        return left.strength() < right.strength();
    }
}
 
template <typename T>
inline NonMaximumSuppression<T>::StrengthCandidate::StrengthCandidate() :
    positionX_(-1),
    strength_(T())
{
    // nothing to do here
}
 
template <typename T>
inline NonMaximumSuppression<T>::StrengthCandidate::StrengthCandidate(const unsigned int x, const T& strength) :
    positionX_(x),
    strength_(strength)
{
    // nothing to do here
}
 
template <typename T>
inline unsigned int NonMaximumSuppression<T>::StrengthCandidate::x() const
{
    return positionX_;
}
 
template <typename T>
inline const T& NonMaximumSuppression<T>::StrengthCandidate::strength() const
{
    return strength_;
}
 
template <typename T>
NonMaximumSuppression<T>::NonMaximumSuppression(NonMaximumSuppression<T>&& nonMaximumSuppression) noexcept
{
    *this = std::move(nonMaximumSuppression);
}
 
template <typename T>
NonMaximumSuppression<T>::NonMaximumSuppression(const NonMaximumSuppression<T>& nonMaximumSuppression) noexcept :
    width_(nonMaximumSuppression.width_),
    rows_(nonMaximumSuppression.rows_)
{
    // nothing to do here
}
 
template <typename T>
NonMaximumSuppression<T>::NonMaximumSuppression(const unsigned int width, const unsigned int height, const unsigned int yOffset) noexcept :
    width_(width),
    rows_(yOffset, height, StrengthCandidateRow())
{
    // nothing to do here
}
 
template <typename T>
inline unsigned int NonMaximumSuppression<T>::width() const
{
    return width_;
}
 
template <typename T>
inline unsigned int NonMaximumSuppression<T>::height() const
{
    return (unsigned int)rows_.size();
}
 
template <typename T>
inline unsigned int NonMaximumSuppression<T>::yOffset() const
{
    ocean_assert(rows_.firstIndex() >= 0);
 
    return (unsigned int)(rows_.firstIndex());
}
 
template <typename T>
inline void NonMaximumSuppression<T>::addCandidate(const unsigned int x, const unsigned int y, const T& strength)
{
    ocean_assert(x < width_);
 
    ocean_assert(rows_.isValidIndex(y) && y >= (unsigned int)(rows_.firstIndex()) && y <= (unsigned int)(rows_.endIndex()));
 
    if (rows_[y].empty())
    {
        rows_[y].reserve(128);
    }
 
    rows_[y].emplace_back(x, strength);
}
 
template <typename T>
void NonMaximumSuppression<T>::addCandidates(const T* values, const unsigned int valuesPaddingElements, const unsigned int firstColumn, const unsigned int numberColumns, const unsigned int firstRow, const unsigned int numberRows, const T& minimalThreshold, Worker* worker)
{
    ocean_assert(values != nullptr);
 
    ocean_assert(firstColumn + numberColumns <= width_);
    ocean_assert(typename StrengthCandidateRows::Index(firstRow) >= rows_.firstIndex());
    ocean_assert(typename StrengthCandidateRows::Index(firstRow + numberRows) <= rows_.endIndex());
 
    const unsigned int valuesStrideElements = width_ + valuesPaddingElements;
 
    if (worker)
    {
        worker->executeFunction(Worker::Function::create(*this, &NonMaximumSuppression<T>::addCandidatesSubset, values, valuesStrideElements, firstColumn, numberColumns, &minimalThreshold, 0u, 0u), firstRow, numberRows, 5u, 6u, 20u);
    }
    else
    {
        addCandidatesSubset(values, valuesStrideElements, firstColumn, numberColumns, &minimalThreshold, firstRow, numberRows);
    }
}
 
template <typename T>
inline void NonMaximumSuppression<T>::removeCandidatesRightFrom(const unsigned int x, const unsigned int y)
{
    ocean_assert(rows_.isValidIndex(y) && y >= (unsigned int)(rows_.firstIndex()) && y <= (unsigned int)(rows_.endIndex()));
 
    StrengthCandidateRow& suppressionRow = rows_[y];
 
    while (!suppressionRow.empty())
    {
        if (suppressionRow.back().x() >= x)
        {
            suppressionRow.pop_back();
        }
        else
        {
            break;
        }
    }
}
 
template <typename T>
template <typename TCoordinate, typename TStrength, bool tStrictMaximum>
typename NonMaximumSuppression<T>::template StrengthPositions<TCoordinate, TStrength> NonMaximumSuppression<T>::suppressNonMaximum(const unsigned int firstColumn, const unsigned int numberColumns, const unsigned int firstRow, const unsigned int numberRows, Worker* worker, const PositionCallback<TCoordinate, TStrength>* positionCallback) const
{
    ocean_assert(firstColumn + numberColumns <= width_);
    ocean_assert(firstRow >= (unsigned int)rows_.firstIndex() && firstRow + numberRows <= (unsigned int)rows_.endIndex());
 
    StrengthPositions<TCoordinate, TStrength> result;
    result.reserve(100);
 
    if (worker)
    {
        Lock lock;
        worker->executeFunction(Worker::Function::create(*this, &NonMaximumSuppression<T>::suppressNonMaximumSubset<TCoordinate, TStrength, tStrictMaximum>, &result, firstColumn, numberColumns, &lock, positionCallback, 0u, 0u), firstRow, numberRows, 5u, 6u, 3u);
    }
    else
    {
        suppressNonMaximumSubset<TCoordinate, TStrength, tStrictMaximum>(&result, firstColumn, numberColumns, nullptr, positionCallback, firstRow, numberRows);
    }
 
    return result;
}
 
template <typename T>
void NonMaximumSuppression<T>::reset()
{
    for (ptrdiff_t n = rows_.firstIndex(); n < rows_.endIndex(); ++n)
    {
        rows_[n].clear();
    }
}
 
template <typename T>
NonMaximumSuppression<T>& NonMaximumSuppression<T>::operator=(NonMaximumSuppression<T>&& nonMaximumSuppression)
{
    if (this != &nonMaximumSuppression)
    {
        width_ = nonMaximumSuppression.width_;
        nonMaximumSuppression.width_ = 0u;
 
        rows_ = std::move(nonMaximumSuppression.rows_);
    }
 
    return *this;
}
 
template <typename T>
NonMaximumSuppression<T>& NonMaximumSuppression<T>::operator=(const NonMaximumSuppression<T>& nonMaximumSuppression)
{
    if (this != &nonMaximumSuppression)
    {
        width_ = nonMaximumSuppression.width_;
        rows_ = nonMaximumSuppression.rows_;
    }
 
    return *this;
}
 
template <typename T>
template <typename TCoordinate, typename TStrength, bool tStrictMaximum>
typename NonMaximumSuppression<T>::template StrengthPositions<TCoordinate, TStrength> NonMaximumSuppression<T>::suppressNonMaximum(const unsigned int width, const unsigned int height, const StrengthPositions<TCoordinate, TStrength>& strengthPositions, const TCoordinate radius, Indices32* validIndices)
{
    ocean_assert(width >= 1u && height >= 1u);
    ocean_assert(radius >= TCoordinate(1));
 
    const unsigned int binSize = std::max(10u, (unsigned int)(NumericT<TCoordinate>::ceil(radius)));
 
    const unsigned int horizontalBins = std::max(1u, (width + binSize - 1u) / binSize);
    const unsigned int verticalBins = std::max(1u, (height + binSize - 1u) / binSize);
 
    ocean_assert(binSize * horizontalBins >= width);
    ocean_assert(binSize * verticalBins >= height);
 
    IndexGroups32 indexGroups(horizontalBins * verticalBins);
 
    // distributing all strength positions into a regular grid to reduce search space later
 
    for (size_t n = 0; n < strengthPositions.size(); ++n)
    {
        const VectorT2<TCoordinate>& position = strengthPositions[n];
 
        ocean_assert((unsigned int)(position.x()) < width);
        ocean_assert((unsigned int)(position.y()) < height);
 
        const unsigned int xBin = (unsigned int)(position.x()) / binSize;
        const unsigned int yBin = (unsigned int)(position.y()) / binSize;
 
        ocean_assert(xBin <= horizontalBins);
        ocean_assert(yBin <= verticalBins);
 
        indexGroups[yBin * horizontalBins + xBin].emplace_back(Index32(n));
    }
 
    std::vector<uint8_t> validPositions(strengthPositions.size(), 1u);
 
    const TCoordinate sqrRadius = radius * radius;
 
    for (size_t nCandidate = 0; nCandidate < strengthPositions.size(); ++nCandidate)
    {
        if (validPositions[nCandidate] == 0u)
        {
            // the positions is already suppressed
            continue;
        }
 
        const StrengthPosition<TCoordinate, TStrength>& candidatePosition = strengthPositions[nCandidate];
 
        const unsigned int xCandidateBin = (unsigned int)(candidatePosition.x()) / binSize;
        const unsigned int yCandidateBin = (unsigned int)(candidatePosition.y()) / binSize;
 
        ocean_assert(xCandidateBin <= horizontalBins);
        ocean_assert(yCandidateBin <= verticalBins);
 
        bool checkNextCandidate = false;
 
        for (unsigned int yBin = (unsigned int)(max(0, int(yCandidateBin) - 1)); !checkNextCandidate && yBin < min(yCandidateBin + 2u, verticalBins); ++yBin)
        {
            for (unsigned int xBin = (unsigned int)(max(0, int(xCandidateBin) - 1)); !checkNextCandidate && xBin < min(xCandidateBin + 2u, horizontalBins); ++xBin)
            {
                const Indices32& indices = indexGroups[yBin * horizontalBins + xBin];
 
                for (const Index32& nTest : indices)
                {
                    if (nTest == Index32(nCandidate))
                    {
                        continue;
                    }
 
                    const StrengthPosition<TCoordinate, TStrength>& testPosition = strengthPositions[nTest];
 
                    // we do not check whether test position is suppressed already (as the test position may still be the reason to suppress the candidate position)
 
                    if (candidatePosition.sqrDistance(testPosition) <= sqrRadius)
                    {
                        if (candidatePosition.strength() > testPosition.strength())
                        {
                            validPositions[nTest] = 0u;
                        }
                        else if (candidatePosition.strength() < testPosition.strength())
                        {
                            validPositions[nCandidate] = 0u;
 
                            checkNextCandidate = true;
                            break;
                        }
                        else
                        {
                            ocean_assert(candidatePosition.strength() == testPosition.strength());
 
                            if constexpr (tStrictMaximum)
                            {
                                // we suppress both elements, as we seek a strict maximum element
 
                                validPositions[nCandidate] = 0u;
                                validPositions[nTest] = 0u;
 
                                checkNextCandidate = true;
                                break;
                            }
                            else
                            {
                                // we will suppress one of both elements, as we accept a non-strict maximum element
 
                                if (candidatePosition.y() < testPosition.y() || (candidatePosition.y() == testPosition.y() && candidatePosition.x() < testPosition.x()))
                                {
                                    // the candidate position will be suppressed as the test position is located to the bottom/right of the candidate position
 
                                    validPositions[nCandidate] = 0u;
 
                                    checkNextCandidate = true;
                                    break;
                                }
                                else
                                {
                                    ocean_assert(testPosition.y() < candidatePosition.y() || (testPosition.y() == candidatePosition.y() && testPosition.x() < candidatePosition.x()));
 
                                    // the test position will be suppressed as the candidate position is located to the bottom/right of the test position
 
                                    validPositions[nTest] = 0u;
                                }
                            }
                        }
                    }
                }
            }
        }
    }
 
    StrengthPositions<TCoordinate, TStrength> remainingPositions;
    remainingPositions.reserve(strengthPositions.size());
 
    if (validIndices)
    {
        ocean_assert(validIndices->empty());
 
        validIndices->clear();
        validIndices->reserve(strengthPositions.size());
 
        for (size_t n = 0; n < validPositions.size(); ++n)
        {
            if (validPositions[n])
            {
                remainingPositions.emplace_back(strengthPositions[n]);
                validIndices->emplace_back(Index32(n));
            }
        }
    }
    else
    {
        for (size_t n = 0; n < validPositions.size(); ++n)
        {
            if (validPositions[n])
            {
                remainingPositions.emplace_back(strengthPositions[n]);
            }
        }
    }
 
    return remainingPositions;
}
 
template <typename T>
template <typename TFloat>
bool NonMaximumSuppression<T>::determinePrecisePeakLocation1(const T& leftValue, const T& middleValue, const T& rightValue, TFloat& location)
{
    static_assert(std::is_floating_point<TFloat>::value, "Invalid floating point data type!");
 
    // f(x) = f(a) + f`(a) * (x - a)
 
    // we expect our middle value to be located at a = 0:
    // f(x) = f(0) + f`(0) * x
 
    // 0 = f'(x)
    //   = f'(0) + f''(0) * x
 
    // x = - f'(0) / f''(0)
 
    //  f`(x) = [-1 0 1] * 1/2
    const TFloat df = (TFloat(rightValue) - TFloat(leftValue)) * TFloat(0.5);
 
    // f``(x) = [1 -2 1] * 1/1
    const TFloat dff = TFloat(leftValue) + TFloat(rightValue) - TFloat(middleValue) * TFloat(2);
 
    if (NumericT<TFloat>::isEqualEps(dff))
    {
        location = TFloat(0);
        return true;
    }
 
    const TFloat x = -df / dff;
 
    if (x < TFloat(-1) || x > TFloat(1))
    {
        return false;
    }
 
    location = x;
    return true;
}
 
template <typename T>
template <typename TFloat>
bool NonMaximumSuppression<T>::determinePrecisePeakLocation2(const T* const topValues, const T* const centerValues, const T* const bottomValues, VectorT2<TFloat>& location)
{
    static_assert(std::is_floating_point<TFloat>::value, "Invalid floating point data type!");
 
    const T& value00 = topValues[0];
    const T& value01 = topValues[1];
    const T& value02 = topValues[2];
 
    const T& value10 = centerValues[0];
    const T& value11 = centerValues[1];
    const T& value12 = centerValues[2];
 
    const T& value20 = bottomValues[0];
    const T& value21 = bottomValues[1];
    const T& value22 = bottomValues[2];
 
#if 0
    // some response values may not perfectly follow the peak criteria so that we do not use the asserts by default
    ocean_assert(value11 >= value00 && value11 >= value01 && value11 >= value02);
    ocean_assert(value11 >= value10 && value11 >= value12);
    ocean_assert(value11 >= value20 && value11 >= value21 && value11 >= value22);
#endif
 
    // [-1 0 1] * 1/2
    const TFloat dx = TFloat(value12 - value10) * TFloat(0.5);
    const TFloat dy = TFloat(value21 - value01) * TFloat(0.5);
 
    // [1 -2 1] * 1/1
    const TFloat dxx = TFloat(value12 + value10 - value11 * TFloat(2));
    const TFloat dyy = TFloat(value21 + value01 - value11 * TFloat(2));
 
    // [ 1  0 -1 ]
    // [ 0  0  0 ] * 1/4
    // [-1  0  1 ]
 
    const TFloat dxy = TFloat(value22 + value00 - value20 - value02) * TFloat(0.25);
 
    const TFloat denominator = dxx * dyy - dxy * dxy;
 
    if (NumericT<TFloat>::isEqualEps(denominator))
    {
        location = VectorT2<TFloat>(0, 0);
        return true;
    }
 
    const TFloat factor = TFloat(1) / denominator;
 
    const TFloat offsetX = -(dyy * dx - dxy * dy) * factor;
    const TFloat offsetY = -(dxx * dy - dxy * dx) * factor;
 
    if (offsetX < TFloat(-1) || offsetX > TFloat(1) || offsetY < TFloat(-1) || offsetY > TFloat(1))
    {
        return false;
    }
 
    location = VectorT2<TFloat>(offsetX, offsetY);
    return true;
}
 
template <typename T>
void NonMaximumSuppression<T>::addCandidatesSubset(const T* values, const unsigned int valuesStrideElements, const unsigned int firstColumn, const unsigned int numberColumns, const T* minimalThreshold, const unsigned int firstRow, const unsigned int numberRows)
{
    ocean_assert(values != nullptr);
    ocean_assert(valuesStrideElements >= width_);
    ocean_assert(firstColumn + numberColumns <= width_);
 
    ocean_assert(typename StrengthCandidateRows::Index(firstRow) >= rows_.firstIndex());
    ocean_assert(typename StrengthCandidateRows::Index(firstRow + numberRows) <= rows_.endIndex());
 
    const T localThreshold = *minimalThreshold;
 
    values += firstRow * valuesStrideElements;
 
    for (unsigned int y = firstRow; y < firstRow + numberRows; ++y)
    {
        for (unsigned int x = firstColumn; x < firstColumn + numberColumns; ++x)
        {
            if (values[x] >= localThreshold)
            {
                addCandidate(x, y, values[x]);
            }
        }
 
        values += valuesStrideElements;
    }
}
 
template <typename T>
template <typename TCoordinate, typename TStrength, bool tStrictMaximum>
void NonMaximumSuppression<T>::suppressNonMaximumSubset(StrengthPositions<TCoordinate, TStrength>* strengthPositions, const unsigned int firstColumn, const unsigned int numberColumns, Lock* lock, const PositionCallback<TCoordinate, TStrength>* positionCallback, const unsigned int firstRow, const unsigned int numberRows) const
{
    ocean_assert(strengthPositions);
 
    ocean_assert(firstColumn + numberColumns <= width_);
    ocean_assert(firstRow >= (unsigned int)rows_.firstIndex());
    ocean_assert(firstRow + numberRows <= (unsigned int)rows_.endIndex());
 
    if (numberColumns < 3u || numberRows < 3u)
    {
        return;
    }
 
    const unsigned int firstCenterColumn = max(1u, firstColumn);
    const unsigned int endCenterColumn = min(firstColumn + numberColumns, width_ - 1u);
 
    const unsigned int firstCenterRow = max((unsigned int)rows_.firstIndex() + 1u, firstRow);
    const unsigned int endCenterRow = min(firstRow + numberRows, (unsigned int)rows_.lastIndex());
 
    ocean_assert(firstCenterRow >= 1u);
 
    StrengthPositions<TCoordinate, TStrength> localStrengthPositions;
    localStrengthPositions.reserve(100);
 
    for (unsigned int y = firstCenterRow; y < endCenterRow; ++y)
    {
        const StrengthCandidateRow& row0 = rows_[y - 1u];
        const StrengthCandidateRow& row1 = rows_[y + 0u];
        const StrengthCandidateRow& row2 = rows_[y + 1u];
 
        typename StrengthCandidateRow::const_iterator i0 = row0.begin();
        typename StrengthCandidateRow::const_iterator i2 = row2.begin();
 
        typename StrengthCandidateRow::const_iterator i1Minus = row1.end();
        typename StrengthCandidateRow::const_iterator i1Plus = row1.size() > 1 ? row1.begin() + 1 : row1.end();
 
        for (typename StrengthCandidateRow::const_iterator i1 = row1.begin(); i1 != row1.end(); ++i1)
        {
            ocean_assert(i1->x() >= 0u && i1->x() + 1u <= width_);
 
            // check left candidate (west)
            if (i1->x() >= firstCenterColumn && i1->x() < endCenterColumn && (i1Minus == row1.end() || i1Minus->x() + 1u != i1->x() || (tStrictMaximum && i1Minus->strength() < i1->strength()) || (!tStrictMaximum && i1Minus->strength() <= i1->strength())))
            {
                // check right candidate (east)
                if (i1Plus == row1.end() || i1Plus->x() != i1->x() + 1u || i1Plus->strength() < i1->strength())
                {
                    // set the top row iterator to the right position
                    while (i0 != row0.end())
                    {
                        if (i0->x() + 1u < i1->x())
                        {
                            ++i0;
                        }
                        else
                        {
                            break;
                        }
                    }
 
                    // now i0 should point at least to the north west pixel position (or more far east)
                    ocean_assert(i0 == row0.end() || i0->x() + 1u >= i1->x());
 
                    if (i0 != row0.end() && i0->x() <= i1->x() + 1u)
                    {
                        ocean_assert(i0->x() + 1u == i1->x() || i0->x() == i1->x() || i0->x() - 1u == i1->x());
 
                        if ((tStrictMaximum && i0->strength() >= i1->strength()) || (!tStrictMaximum && i0->strength() > i1->strength()))
                        {
                            goto next;
                        }
 
                        // check if there is a further candidate in the north row
 
                        const typename StrengthCandidateRow::const_iterator i0Plus = i0 + 1;
 
                        if (i0Plus != row0.end() && i0Plus->x() <= i1->x() + 1u)
                        {
                            if ((tStrictMaximum && i0Plus->strength() >= i1->strength()) || (!tStrictMaximum && i0Plus->strength() > i1->strength()))
                            {
                                goto next;
                            }
 
                            // check if there is a further candidate in the north row
 
                            const typename StrengthCandidateRow::const_iterator i0PlusPlus = i0Plus + 1;
 
                            if (i0PlusPlus != row0.end() && i0PlusPlus->x() <= i1->x() + 1u)
                            {
                                ocean_assert(i0PlusPlus->x() == i1->x() + 1u);
 
                                if ((tStrictMaximum && i0PlusPlus->strength() >= i1->strength()) || (!tStrictMaximum && i0PlusPlus->strength() > i1->strength()))
                                {
                                    goto next;
                                }
                            }
                        }
                    }
 
 
                    // set the bottom row iterator to the right position
                    while (i2 != row2.end())
                    {
                        if (i2->x() + 1u < i1->x())
                        {
                            ++i2;
                        }
                        else
                        {
                            break;
                        }
                    }
 
                    // now i2 should point at least to the south west pixel position (or more far east)
                    ocean_assert(i2 == row2.end() || i2->x() + 1u >= i1->x());
 
                    if (i2 != row2.end() && i2->x() <= i1->x() + 1u)
                    {
                        ocean_assert(i2->x() + 1u == i1->x() || i2->x() == i1->x() || i2->x() - 1u == i1->x());
 
                        if (i2->x() + 1u == i1->x())
                        {
                            // i2 points to the south west pixel
 
                            if ((tStrictMaximum && i2->strength() >= i1->strength()) || (!tStrictMaximum && i2->strength() > i1->strength()))
                            {
                                goto next;
                            }
                        }
                        else
                        {
                            if (i2->strength() >= i1->strength())
                            {
                                goto next;
                            }
                        }
 
                        // check if there is a further candidate in the south row
 
                        const typename StrengthCandidateRow::const_iterator i2Plus = i2 + 1;
 
                        if (i2Plus != row2.end() && i2Plus->x() <= i1->x() + 1u)
                        {
                            if (i2Plus->strength() >= i1->strength())
                                goto next;
 
                            // check if there is a further candidate in the south row
 
                            const typename StrengthCandidateRow::const_iterator i2PlusPlus = i2Plus + 1;
 
                            if (i2PlusPlus != row2.end() && i2PlusPlus->x() <= i1->x() + 1u)
                            {
                                ocean_assert(i2PlusPlus->x() == i1->x() + 1u);
 
                                if (i2PlusPlus->strength() >= i1->strength())
                                    goto next;
                            }
                        }
                    }
 
                    if (positionCallback)
                    {
                        TCoordinate preciseX, preciseY;
                        TStrength preciseStrength;
                        if ((*positionCallback)(i1->x(), y, i1->strength(), preciseX, preciseY, preciseStrength))
                        {
                            localStrengthPositions.emplace_back(preciseX, preciseY, preciseStrength);
                        }
                    }
                    else
                    {
                        localStrengthPositions.emplace_back(TCoordinate(i1->x()), TCoordinate(y), i1->strength());
                    }
                }
            }
 
next:
 
            i1Minus = i1;
 
            if (i1Plus != row1.end())
                ++i1Plus;
        }
    }
 
    const OptionalScopedLock scopedLock(lock);
 
    strengthPositions->insert(strengthPositions->end(), localStrengthPositions.begin(), localStrengthPositions.end());
}
 
}
 
}
 
#endif // META_OCEAN_CV_NON_MAXIMUM_SUPPRESSION_H