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***********************************************************************************
Maximal Self-Dissimilarity (MSD) Interest Point Detector

This is an implementation of the MSD interest point detector
presented in the scientific publication:

[1] F. Tombari, L. Di Stefano
"Interest Points via Maximal Self-Dissimilarities"
12th Asian Conference on Computer Vision (ACCV), 2014

The code is ported from the stand-alone implementation available
at this repository:
www.github.com/fedassa/msdDetector

AUTHORS:  Federico Tombari (fedassa@gmail.com) (original code),
          Daniele De Gregorio (degregorio.daniele@gmail.com) (OpenCV porting)

University of Bologna, Open Perception

 */

#include "precomp.hpp"
#include <limits>

namespace cv
{
    namespace xfeatures2d
    {
        /*!
            MSD Image Pyramid.
         */
        class MSDImagePyramid
        {
            // Multi-threaded construction of the scale-space pyramid
            struct MSDImagePyramidBuilder : ParallelLoopBody
            {

                MSDImagePyramidBuilder(const cv::Mat& _im, std::vector<cv::Mat>* _m_imPyr, float _scaleFactor)
                {
                    im = &_im;
                    m_imPyr = _m_imPyr;
                    scaleFactor = _scaleFactor;

                }

                void operator()(const Range& range) const CV_OVERRIDE
                {
                    for (int lvl = range.start; lvl < range.end; lvl++)
                    {
                        float scale = 1 / std::pow(scaleFactor, (float) lvl);
                        (*m_imPyr)[lvl] = cv::Mat(cv::Size(cvRound(im->cols * scale), cvRound(im->rows * scale)), im->type());
                        cv::resize(*im, (*m_imPyr)[lvl], cv::Size((*m_imPyr)[lvl].cols, (*m_imPyr)[lvl].rows), 0.0, 0.0, cv::INTER_AREA);
                    }
                }
                const cv::Mat* im;
                std::vector<cv::Mat>* m_imPyr;
                float scaleFactor;
            };

        public:

            MSDImagePyramid(const cv::Mat &im, const int nLevels, const float scaleFactor = 1.6f);
            ~MSDImagePyramid();

            const std::vector<cv::Mat> getImPyr() const
            {
                return m_imPyr;
            };

        private:

            std::vector<cv::Mat> m_imPyr;
            int m_nLevels;
            float m_scaleFactor;
        };

        MSDImagePyramid::MSDImagePyramid(const cv::Mat & im, const int nLevels, const float scaleFactor)
        {
            m_nLevels = nLevels;
            m_scaleFactor = scaleFactor;
            m_imPyr.clear();
            m_imPyr.resize(nLevels);

            m_imPyr[0] = im.clone();

            if (m_nLevels > 1)
            {
                parallel_for_(Range(1, nLevels), MSDImagePyramidBuilder(im, &m_imPyr, scaleFactor));
            }
        }

        MSDImagePyramid::~MSDImagePyramid()
        {
        }

        /*!
            MSD Implementation.
         */
        class MSDDetector_Impl : public MSDDetector
        {
        public:

            // Multi-threaded contextualSelfDissimilarity method
            struct MSDSelfDissimilarityScan : ParallelLoopBody
            {

                MSDSelfDissimilarityScan(MSDDetector_Impl& _detector, std::vector< std::vector<float> >* _saliency, cv::Mat& _img, int _level, int _border, int _split)
                {
                    detector = &_detector;
                    saliency = _saliency;
                    img = &_img;
                    split = _split;
                    level = _level;
                    border = _border;
                    int w = img->cols - border * 2;
                    chunkSize = w / split;
                    remains = w - chunkSize*split;
                }

                void operator()(const Range& range) const CV_OVERRIDE
                {
                    for (int i = range.start; i < range.end; i++)
                    {
                        int start = border + i*chunkSize;
                        int end = border + (i + 1) * chunkSize;
                        if (remains > 0)
                            if (i == split - 1)
                            {
                                end = img->cols - border;
                            }
                        detector->contextualSelfDissimilarity(*img, start, end, &saliency->at(level)[0]);
                    }
                }

                MSDDetector_Impl* detector;
                std::vector< std::vector<float> >* saliency;
                cv::Mat* img;
                int level;
                int split;
                int border;
                int chunkSize;
                int remains;
            };

            /**
             * Constructor
             * @param patch_radius Patch radius
             * @param search_area_radius Search Area radius
             * @param nms_radius  Non Maxima Suppression spatial radius
             * @param nms_scale_radius Non Maxima Suppression scale radius
             * @param th_saliency Saliency threshold
             * @param kNN number of nearest neighbors (k)
             * @param scale_factor Scale factor for building up the image pyramid
             * @param n_scales Number of scales number of scales for building up the image pyramid (if set to -1, this number is automatically determined)
             * @param compute_orientation Flag for associating a canoncial orientation to each keypoint
             */
            MSDDetector_Impl(int patch_radius, int search_area_radius,
                    int nms_radius, int nms_scale_radius, float th_saliency, int kNN, float scale_factor,
                    int n_scales, bool compute_orientation)
            : m_patch_radius(patch_radius), m_search_area_radius(search_area_radius), m_nms_radius(nms_radius),
              m_nms_scale_radius(nms_scale_radius), m_th_saliency(th_saliency), m_kNN(kNN), m_scale_factor(scale_factor),
              m_n_scales(n_scales), m_compute_orientation(compute_orientation)

            {
            }

            void detect(InputArray _image, std::vector<KeyPoint>& keypoints, InputArray _mask) CV_OVERRIDE
            {
                m_mask = _mask.getMat();

                int border = m_search_area_radius + m_patch_radius;

                cv::Mat img = _image.getMat();
                if (m_n_scales == -1)
                    m_cur_n_scales = cvFloor(std::log(cv::min(img.cols, img.rows) / ((m_patch_radius + m_search_area_radius)*2.0 + 1)) / std::log(m_scale_factor));
                else
                    m_cur_n_scales = m_n_scales;

                cv::Mat imgG;
                if (img.channels() == 1)
                    imgG = img;
                else
                    cv::cvtColor(img, imgG, cv::COLOR_BGR2GRAY);

                MSDImagePyramid scaleSpacer(imgG, m_cur_n_scales, m_scale_factor);
                m_scaleSpace = scaleSpacer.getImPyr();

                keypoints.clear();
                std::vector< std::vector<float> > saliency;
                saliency.resize(m_cur_n_scales);

                for (int r = 0; r < m_cur_n_scales; r++)
                {
                    saliency[r].resize(m_scaleSpace[r].rows * m_scaleSpace[r].cols);
                    fill(saliency[r].begin(), saliency[r].end(), 0.0f);
                }

                for (int r = 0; r < m_cur_n_scales; r++)
                {
                    int steps = cv::getNumThreads();
                    parallel_for_(Range(0, steps), MSDSelfDissimilarityScan((*this), &saliency, m_scaleSpace[r], r, border, steps));
                }

                nonMaximaSuppression(saliency, keypoints);

                for (int r = 0; r < m_cur_n_scales; r++)
                {
                    saliency[r].clear();
                }

                m_scaleSpace.clear();

            }

        protected:

            // Patch radius
            int m_patch_radius;
            // Search area radius
            int m_search_area_radius;
            // Non Maxima Suppression Spatial Radius
            int m_nms_radius;
            // Non Maxima Suppression Scale Radius
            int m_nms_scale_radius;
            //Saliency threshold
            float m_th_saliency;
            //k nearest neighbors
            int m_kNN;
            //Scale factor
            float m_scale_factor;
            //Number of scales
            int m_n_scales;
            //Current number of scales
            int m_cur_n_scales;
            //Compute orientation flag
            bool m_compute_orientation;

        private:


            // Scale-space image pyramid
            std::vector<cv::Mat> m_scaleSpace;
            // Input binary mask
            cv::Mat m_mask;

            /**
             * Computes the normalized average value of input vector
             * @param minVals input vector
             * @param den normalization factor (pre-multiplied by the number of elements of the input vector, assumed constant)
             * @return normalized average value
             */
            inline float computeAvgDistance(std::vector<int> &minVals, int den)
            {
                float avg_dist = 0.0f;
                for (unsigned int i = 0; i < minVals.size(); i++)
                    avg_dist += minVals[i];

                avg_dist /= den;
                return avg_dist;
            }

            /**
             * Computer the Contextual Self-Dissimilarity (CSD, [1]) for a specific range of image pixels (row-wise)
             * @param img input image
             * @param xmin left-most range limit for the image pixels being processed
             * @param xmax right-most range limit for the image pixels being processed
             * @param saliency output array being filled with the CSD value computed at each input pixel
             */
            void contextualSelfDissimilarity(cv::Mat &img, int xmin, int xmax, float* saliency);

            /**
             * Associates a canonical orientation (computed as in [1]) to each extracted key-point
             * @param img input image
             * @param x column index of the key-point on the input image
             * @param y row index of the key-point on the input image
             * @param circle pre-computed LUT used in the function
             * @return angle of the canonical orientation (in radians)
             */
            float computeOrientation(cv::Mat &img, int x, int y, std::vector<cv::Point2f> circle);

            /**
             * Computes the Non-Maxima Suppression (NMS) over the scale-space as in [1] for all elements of the image pyramid
             * @param saliency input saliency associated to each element of the image pyramid
             * @param keypoints key-points obtained as local maxima of the saliency
             */
            void nonMaximaSuppression(std::vector< std::vector<float> > & saliency, std::vector<cv::KeyPoint> & keypoints);

            /**
             * Computes the floating point interpolation of a key-point coordinates
             * @param x column index of the key-point at its scale of the image pyramid
             * @param yrow index of the key-point at its scale of the image pyramid
             * @param scale scale of the key-point over the image pyramid
             * @param saliency pointer to the saliency array
             * @param p_res interpolated coordinates of the key-point referred to the lowest level of the pyramid (i.e. in the ref. frame of the input image)
             * @return false if the current key-point has to be rejected, true otherwise
             */
            bool rescalePoint(int x, int y, int scale, std::vector< std::vector<float> > & saliency, cv::Point2f & p_res);

        };

        bool MSDDetector_Impl::rescalePoint(int i, int j, int scale, std::vector< std::vector<float> > & saliency, cv::Point2f &p_res)
        {

            const float deriv_scale = 0.5f;
            int width_s = m_scaleSpace[scale].cols;
            //const float second_deriv_scale = 1.0f;
            const float cross_deriv_scale = 0.25f;

            cv::Vec2f dD((saliency[scale][j * width_s + i + 1] - saliency[scale][j * width_s + i - 1]) * deriv_scale,
                    (saliency[scale][(j + 1) * width_s + i] - saliency[scale][(j - 1) * width_s + i]) * deriv_scale);

            float cc = saliency[scale][j * width_s + i] * 2;
            float dxx = (saliency[scale][j * width_s + i + 1] + saliency[scale][j * width_s + i - 1] - cc); // * second_deriv_scale;
            float dyy = (saliency[scale][(j + 1) * width_s + i] + saliency[scale][(j - 1) * width_s + i] - cc); // * second_deriv_scale;
            float dxy = (saliency[scale][(j + 1) * width_s + i + 1] - saliency[scale][(j + 1) * width_s + i - 1] -
                    saliency[scale][(j - 1) * width_s + i + 1] + saliency[scale][(j - 1) * width_s + i - 1]) * cross_deriv_scale;

            cv::Matx22f H(dxx, dxy, dxy, dyy);

            cv::Vec2f X;
            cv::solve(H, dD, X, cv::DECOMP_LU);

            float xr = -X[1];
            float xc = -X[0];

            if (std::abs(xr) > 5 || std::abs(xc) > 5)
                return false;

            if (scale == 0)
            {
                p_res.x = i + xc + 0.5f;
                p_res.y = j + xr + 0.5f;
            } else
            {
                float effectiveScaleFactor = std::pow(m_scale_factor, scale);
                p_res.x = (i + xc + 0.5f) * effectiveScaleFactor;
                p_res.y = (j + xr + 0.5f) * effectiveScaleFactor;

                p_res.x -= 0.5f;
                p_res.y -= 0.5f;

                if (p_res.x < 0 || p_res.x >= m_scaleSpace[0].cols || p_res.y < 0 || p_res.y >= m_scaleSpace[0].rows)
                {
                    return false;
                }
            }

            return true;
        }

        void MSDDetector_Impl::contextualSelfDissimilarity(cv::Mat &img, int xmin, int xmax, float* saliency)
        {
            int r_s = m_patch_radius;
            int r_b = m_search_area_radius;
            int k = m_kNN;

            int w = img.cols;
            int h = img.rows;

            int side_s = 2 * r_s + 1;
            int side_b = 2 * r_b + 1;
            int border = r_s + r_b;
            int temp;
            int den = side_s * side_s * k;

            std::vector<int> minVals(k);
            int *acc = new int[side_b * side_b];
            int **vCol = new int *[w];
            for (int i = 0; i < w; i++)
                vCol[i] = new int[side_b * side_b];

            //first position
            int x = xmin;
            int y = border;

            int ctrInd = 0;
            for (int kk = 0; kk < k; kk++)
                minVals[kk] = std::numeric_limits<int>::max();

            for (int j = y - r_b; j <= y + r_b; j++)
            {

                for (int i = x - r_b; i <= x + r_b; i++)
                {
                    if (j == y && i == x)
                        continue;

                    acc[ctrInd] = 0;
                    for (int u = -r_s; u <= r_s; u++)
                    {
                        vCol[x + u][ctrInd] = 0;
                        for (int v = -r_s; v <= r_s; v++)
                        {

                            temp = img.at<unsigned char>(j + v, i + u) - img.at<unsigned char>(y + v, x + u);
                            vCol[x + u][ctrInd] += (temp * temp);
                        }
                        acc[ctrInd] += vCol[x + u][ctrInd];
                    }

                    if (acc[ctrInd] < minVals[k - 1])
                    {
                        minVals[k - 1] = acc[ctrInd];

                        for (int kk = k - 2; kk >= 0; kk--)
                        {
                            if (minVals[kk] > minVals[kk + 1])
                            {
                                std::swap(minVals[kk], minVals[kk + 1]);
                            } else
                                break;
                        }
                    }

                    ctrInd++;
                }
            }
            saliency[y * w + x] = computeAvgDistance(minVals, den);

            for (x = xmin + 1; x < xmax; x++)
            {
                ctrInd = 0;
                for (int kk = 0; kk < k; kk++)
                    minVals[kk] = std::numeric_limits<int>::max();

                for (int j = y - r_b; j <= y + r_b; j++)
                {
                    for (int i = x - r_b; i <= x + r_b; i++)
                    {
                        if (j == y && i == x)
                            continue;

                        vCol[x + r_s][ctrInd] = 0;
                        for (int v = -r_s; v <= r_s; v++)
                        {
                            temp = img.at<unsigned char>(j + v, i + r_s) - img.at<unsigned char>(y + v, x + r_s);
                            vCol[x + r_s][ctrInd] += (temp * temp);
                        }

                        acc[ctrInd] = acc[ctrInd] + vCol[x + r_s][ctrInd] - vCol[x - r_s - 1][ctrInd];

                        if (acc[ctrInd] < minVals[k - 1])
                        {
                            minVals[k - 1] = acc[ctrInd];
                            for (int kk = k - 2; kk >= 0; kk--)
                            {
                                if (minVals[kk] > minVals[kk + 1])
                                {
                                    std::swap(minVals[kk], minVals[kk + 1]);
                                } else
                                    break;
                            }
                        }

                        ctrInd++;
                    }
                }
                saliency[y * w + x] = computeAvgDistance(minVals, den);
            }

            for (y = border + 1; y < h - border; y++)
            {
                ctrInd = 0;
                for (int kk = 0; kk < k; kk++)
                    minVals[kk] = std::numeric_limits<int>::max();
                x = xmin;

                for (int j = y - r_b; j <= y + r_b; j++)
                {
                    for (int i = x - r_b; i <= x + r_b; i++)
                    {
                        if (j == y && i == x)
                            continue;

                        acc[ctrInd] = 0;
                        for (int u = -r_s; u <= r_s; u++)
                        {
                            temp = img.at<unsigned char>(j + r_s, i + u) - img.at<unsigned char>(y + r_s, x + u);
                            vCol[x + u][ctrInd] += (temp * temp);

                            temp = img.at<unsigned char>(j - r_s - 1, i + u) - img.at<unsigned char>(y - r_s - 1, x + u);
                            vCol[x + u][ctrInd] -= (temp * temp);

                            acc[ctrInd] += vCol[x + u][ctrInd];
                        }

                        if (acc[ctrInd] < minVals[k - 1])
                        {
                            minVals[k - 1] = acc[ctrInd];

                            for (int kk = k - 2; kk >= 0; kk--)
                            {
                                if (minVals[kk] > minVals[kk + 1])
                                {
                                    std::swap(minVals[kk], minVals[kk + 1]);
                                } else
                                    break;
                            }
                        }

                        ctrInd++;
                    }
                }
                saliency[y * w + x] = computeAvgDistance(minVals, den);

                for (x = xmin + 1; x < xmax; x++)
                {
                    ctrInd = 0;
                    for (int kk = 0; kk < k; kk++)
                        minVals[kk] = std::numeric_limits<int>::max();

                    for (int j = y - r_b; j <= y + r_b; j++)
                    {
                        for (int i = x - r_b; i <= x + r_b; i++)
                        {
                            if (j == y && i == x)
                                continue;

                            temp = img.at<unsigned char>(j + r_s, i + r_s) - img.at<unsigned char>(y + r_s, x + r_s);
                            vCol[x + r_s][ctrInd] += (temp * temp);

                            temp = img.at<unsigned char>(j - r_s - 1, i + r_s) - img.at<unsigned char>(y - r_s - 1, x + r_s);
                            vCol[x + r_s][ctrInd] -= (temp * temp);

                            acc[ctrInd] = acc[ctrInd] + vCol[x + r_s][ctrInd] - vCol[x - r_s - 1][ctrInd];

                            if (acc[ctrInd] < minVals[k - 1])
                            {
                                minVals[k - 1] = acc[ctrInd];

                                for (int kk = k - 2; kk >= 0; kk--)
                                {
                                    if (minVals[kk] > minVals[kk + 1])
                                    {
                                        std::swap(minVals[kk], minVals[kk + 1]);
                                    } else
                                        break;
                                }
                            }
                            ctrInd++;
                        }
                    }
                    saliency[y * w + x] = computeAvgDistance(minVals, den);
                }
            }

            for (int i = 0; i < w; i++)
                delete[] vCol[i];
            delete[] vCol;
            delete[] acc;
        }

        float MSDDetector_Impl::computeOrientation(cv::Mat &img, int x, int y, std::vector<cv::Point2f> circle)
        {
            int temp;

            int nBins = 36;
            float step = float((2 * CV_PI) / nBins);
            std::vector<float> hist(nBins, 0);
            std::vector<int> dists(circle.size(), 0);

            int minDist = std::numeric_limits<int>::max();
            int maxDist = -1;

            for (int k = 0; k < (int) circle.size(); k++)
            {

                int j = y + static_cast<int> (circle[k].y);
                int i = x + static_cast<int> (circle[k].x);

                for (int v = -m_patch_radius; v <= m_patch_radius; v++)
                {
                    for (int u = -m_patch_radius; u <= m_patch_radius; u++)
                    {
                        temp = img.at<unsigned char>(j + v, i + u) - img.at<unsigned char>(y + v, x + u);
                        dists[k] += temp*temp;
                    }
                }

                if (dists[k] > maxDist)
                    maxDist = dists[k];
                if (dists[k] < minDist)
                    minDist = dists[k];
            }

            float deltaAngle = 0.0f;
            for (int k = 0; k < (int) circle.size(); k++)
            {
                float angle = deltaAngle;
                float weight = (1.0f * maxDist - dists[k]) / (maxDist - minDist);

                float binF;
                if (angle >= 2 * CV_PI)
                    binF = 0.0f;
                else
                    binF = angle / step;
                int bin = static_cast<int> (std::floor(binF));

                CV_Assert(bin >= 0 && bin < nBins);
                float binDist = abs(binF - bin - 0.5f);

                float weightA = weight * (1.0f - binDist);
                float weightB = weight * binDist;
                hist[bin] += weightA;

                if (2 * (binF - bin) < step)
                    hist[(bin + nBins - 1) % nBins] += weightB;
                else
                    hist[(bin + 1) % nBins] += weightB;

                deltaAngle += step;
            }

            int bestBin = -1;
            float maxBin = -1;
            for (int i = 0; i < nBins; i++)
            {
                if (hist[i] > maxBin)
                {
                    maxBin = hist[i];
                    bestBin = i;
                }
            }

            int l = (bestBin == 0) ? nBins - 1 : bestBin - 1;
            int r = (bestBin + 1) % nBins;
            float bestAngle2 = bestBin + 0.5f * ((hist[l]) - (hist[r])) / ((hist[l]) - 2.0f * (hist[bestBin]) + (hist[r]));
            bestAngle2 = (bestAngle2 < 0) ? nBins + bestAngle2 : (bestAngle2 >= nBins) ? bestAngle2 - nBins : bestAngle2;
            bestAngle2 *= step;

            return bestAngle2;
        }

        void MSDDetector_Impl::nonMaximaSuppression(std::vector< std::vector<float> > & saliency, std::vector<cv::KeyPoint> & keypoints)
        {
            cv::KeyPoint kp_temp;
            int border = m_search_area_radius + m_patch_radius;

            std::vector<cv::Point2f> orientPoints;
            if (m_compute_orientation)
            {
                int nBins = 36;
                float step = float((2 * CV_PI) / nBins);
                float deltaAngle = 0.0f;

                for (int i = 0; i < nBins; i++)
                {
                    cv::Point2f pt;
                    pt.x = m_search_area_radius * cos(deltaAngle);
                    pt.y = m_search_area_radius * sin(deltaAngle);

                    orientPoints.push_back(pt);

                    deltaAngle += step;
                }
            }

            for (int r = 0; r < m_cur_n_scales; r++)
            {
                int cW = m_scaleSpace[r].cols;
                int cH = m_scaleSpace[r].rows;

                for (int j = border; j < cH - border; j++)
                {
                    for (int i = border; i < cW - border; i++)
                    {
                        if (saliency[r][j * cW + i] <= m_th_saliency)
                            continue;

                        if (m_mask.rows > 0)
                        {
                            int j_full = cvRound(j * std::pow(m_scale_factor, r));
                            int i_full = cvRound(i * std::pow(m_scale_factor, r));
                            if ((int) m_mask.at<unsigned char>(j_full, i_full) == 0)
                                continue;
                        }

                        bool is_max = true;

                        for (int k = cv::max(0, r - m_nms_scale_radius); k <= cv::min(m_cur_n_scales - 1, r + m_nms_scale_radius); k++)
                        {
                            if (k != r)
                            {
                                int j_sc = cvRound(j * std::pow(m_scale_factor, r - k));
                                int i_sc = cvRound(i * std::pow(m_scale_factor, r - k));

                                if (saliency[r][j * cW + i] < saliency[k][j_sc * cW + i_sc])
                                {
                                    is_max = false;
                                    break;
                                }
                            }
                        }

                        for (int v = cv::max(border, j - m_nms_radius); v <= cv::min(cH - border - 1, j + m_nms_radius); v++)
                        {
                            for (int u = cv::max(border, i - m_nms_radius); u <= cv::min(cW - border - 1, i + m_nms_radius); u++)
                            {
                                if (saliency[r][j * cW + i] < saliency[r][v * cW + u])
                                {
                                    is_max = false;
                                    break;
                                }
                            }

                            if (!is_max)
                                break;
                        }

                        if (is_max)
                        {
                            bool resInt = rescalePoint(i, j, r, saliency, kp_temp.pt);
                            if (!resInt)
                                continue;


                            if (m_mask.rows > 0)
                            {
                                if (m_mask.at<unsigned char>((int) kp_temp.pt.y, (int) kp_temp.pt.x) == 0)
                                    continue;
                            }
                            kp_temp.response = saliency[r][j * cW + i];
                            kp_temp.size = (m_patch_radius * 2.0f + 1) * std::pow(m_scale_factor, r);
                            kp_temp.octave = r;
                            if (m_compute_orientation)
                                kp_temp.angle = computeOrientation(m_scaleSpace[r], i, j, orientPoints);

                            keypoints.push_back(kp_temp);
                        }
                    }
                }
            }

        }

        Ptr<MSDDetector> MSDDetector::create(int m_patch_radius, int m_search_area_radius,
                int m_nms_radius, int m_nms_scale_radius, float m_th_saliency, int m_kNN, float m_scale_factor,
                int m_n_scales, bool m_compute_orientation)
        {
            return makePtr<MSDDetector_Impl>(m_patch_radius, m_search_area_radius,
                    m_nms_radius, m_nms_scale_radius, m_th_saliency, m_kNN, m_scale_factor,
                    m_n_scales, m_compute_orientation);
        }

    }
}
