se2_l2.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2020, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */

#include "tfest-precomp.h"  // Precompiled headers

#include <mrpt/math/TPose2D.h>
#include <mrpt/poses/CPosePDFGaussian.h>
#include <mrpt/random.h>
#include <mrpt/tfest/se2.h>

#if MRPT_HAS_SSE2
#include <mrpt/core/SSE_types.h>
#endif

using namespace mrpt;
using namespace mrpt::tfest;
using namespace mrpt::poses;
using namespace mrpt::math;
using namespace std;

// Wrapper:
bool tfest::se2_l2(
    const TMatchingPairList& in_correspondences,
    CPosePDFGaussian& out_transformation)
{
    mrpt::math::TPose2D p;
    const bool ret =
        tfest::se2_l2(in_correspondences, p, &out_transformation.cov);
    out_transformation.mean = CPose2D(p);
    return ret;
}

/*---------------------------------------------------------------
            leastSquareErrorRigidTransformation

   Compute the best transformation (x,y,phi) given a set of
    correspondences between 2D points in two different maps.
   This method is intensively used within ICP.
  ---------------------------------------------------------------*/
bool tfest::se2_l2(
    const TMatchingPairList& in_correspondences, TPose2D& out_transformation,
    CMatrixDouble33* out_estimateCovariance)
{
    MRPT_START

    const size_t N = in_correspondences.size();

    if (N < 2) return false;

    const float N_inv = 1.0f / N;  // For efficiency, keep this value.

// ----------------------------------------------------------------------
// Compute the estimated pose. Notation from the paper:
// "Mobile robot motion estimation by 2d scan matching with genetic and
// iterative
// closest point algorithms", J.L. Martinez Rodriguez, A.J. Gonzalez, J. Morales
// Rodriguez, A. Mandow Andaluz, A. J. Garcia Cerezo,
// Journal of Field Robotics, 2006.
// ----------------------------------------------------------------------

// ----------------------------------------------------------------------
//  For the formulas of the covariance, see:
//   https://www.mrpt.org/Paper:Occupancy_Grid_Matching
//   and Jose Luis Blanco's PhD thesis.
// ----------------------------------------------------------------------
#if MRPT_HAS_SSE2
    // SSE vectorized version:

    //{
    //  TMatchingPair dumm;
    //  static_assert(sizeof(dumm.this_x)==sizeof(float));
    //  static_assert(sizeof(dumm.other_x)==sizeof(float));
    //}

    __m128 sum_a_xyz = _mm_setzero_ps();  // All 4 zeros (0.0f)
    __m128 sum_b_xyz = _mm_setzero_ps();  // All 4 zeros (0.0f)

    //   [ f0     f1      f2      f3  ]
    //    xa*xb  ya*yb   xa*yb  xb*ya
    __m128 sum_ab_xyz = _mm_setzero_ps();  // All 4 zeros (0.0f)

    for (const auto& in_correspondence : in_correspondences)
    {
        // Get the pair of points in the correspondence:
        //   a_xyyx = [   xa     ay   |   xa    ya ]
        //   b_xyyx = [   xb     yb   |   yb    xb ]
        //      (product)
        //            [  xa*xb  ya*yb   xa*yb  xb*ya
        //                LO0    LO1     HI2    HI3
        // Note: _MM_SHUFFLE(hi3,hi2,lo1,lo0)
        const __m128 a_xyz =
            _mm_loadu_ps(&in_correspondence.this_x);  // *Unaligned* load
        const __m128 b_xyz =
            _mm_loadu_ps(&in_correspondence.other_x);  // *Unaligned* load

        const auto a_xyxy =
            _mm_shuffle_ps(a_xyz, a_xyz, _MM_SHUFFLE(1, 0, 1, 0));
        const auto b_xyyx =
            _mm_shuffle_ps(b_xyz, b_xyz, _MM_SHUFFLE(0, 1, 1, 0));

        // Compute the terms:
        sum_a_xyz = _mm_add_ps(sum_a_xyz, a_xyz);
        sum_b_xyz = _mm_add_ps(sum_b_xyz, b_xyz);

        //   [ f0     f1      f2      f3  ]
        //    xa*xb  ya*yb   xa*yb  xb*ya
        sum_ab_xyz = _mm_add_ps(sum_ab_xyz, _mm_mul_ps(a_xyxy, b_xyyx));
    }

    alignas(MRPT_MAX_STATIC_ALIGN_BYTES) float sums_a[4], sums_b[4];
    _mm_store_ps(sums_a, sum_a_xyz);
    _mm_store_ps(sums_b, sum_b_xyz);

    float SumXa = sums_a[0];
    float SumYa = sums_a[1];
    float SumXb = sums_b[0];
    float SumYb = sums_b[1];

    // Compute all four means:
    const __m128 Ninv_4val =
        _mm_set1_ps(N_inv);  // load 4 copies of the same value
    sum_a_xyz = _mm_mul_ps(sum_a_xyz, Ninv_4val);
    sum_b_xyz = _mm_mul_ps(sum_b_xyz, Ninv_4val);

    // means_a[0]: mean_x_a
    // means_a[1]: mean_y_a
    // means_b[0]: mean_x_b
    // means_b[1]: mean_y_b
    alignas(MRPT_MAX_STATIC_ALIGN_BYTES) float means_a[4], means_b[4];
    _mm_store_ps(means_a, sum_a_xyz);
    _mm_store_ps(means_b, sum_b_xyz);

    float mean_x_a = means_a[0];
    float mean_y_a = means_a[1];
    float mean_x_b = means_b[0];
    float mean_y_b = means_b[1];

    //      Sxx   Syy     Sxy    Syx
    //    xa*xb  ya*yb   xa*yb  xb*ya
    alignas(MRPT_MAX_STATIC_ALIGN_BYTES) float cross_sums[4];
    _mm_store_ps(cross_sums, sum_ab_xyz);

    float Sxx = cross_sums[0];
    float Syy = cross_sums[1];
    float Sxy = cross_sums[2];
    float Syx = cross_sums[3];

    // Auxiliary variables Ax,Ay:
    const float Ax = N * (Sxx + Syy) - SumXa * SumXb - SumYa * SumYb;
    const float Ay = SumXa * SumYb + N * (Syx - Sxy) - SumXb * SumYa;

#else
    // Non vectorized version:
    float SumXa = 0, SumXb = 0, SumYa = 0, SumYb = 0;
    float Sxx = 0, Sxy = 0, Syx = 0, Syy = 0;

    for (TMatchingPairList::const_iterator corrIt = in_correspondences.begin();
         corrIt != in_correspondences.end(); corrIt++)
    {
        // Get the pair of points in the correspondence:
        const float xa = corrIt->this_x;
        const float ya = corrIt->this_y;
        const float xb = corrIt->other_x;
        const float yb = corrIt->other_y;

        // Compute the terms:
        SumXa += xa;
        SumYa += ya;

        SumXb += xb;
        SumYb += yb;

        Sxx += xa * xb;
        Sxy += xa * yb;
        Syx += ya * xb;
        Syy += ya * yb;
    }  // End of "for all correspondences"...

    const float mean_x_a = SumXa * N_inv;
    const float mean_y_a = SumYa * N_inv;
    const float mean_x_b = SumXb * N_inv;
    const float mean_y_b = SumYb * N_inv;

    // Auxiliary variables Ax,Ay:
    const float Ax = N * (Sxx + Syy) - SumXa * SumXb - SumYa * SumYb;
    const float Ay = SumXa * SumYb + N * (Syx - Sxy) - SumXb * SumYa;

#endif

    out_transformation.phi =
        (Ax != 0 || Ay != 0)
            ? atan2(static_cast<double>(Ay), static_cast<double>(Ax))
            : 0.0;

    const double ccos = cos(out_transformation.phi);
    const double csin = sin(out_transformation.phi);

    out_transformation.x = mean_x_a - mean_x_b * ccos + mean_y_b * csin;
    out_transformation.y = mean_y_a - mean_x_b * csin - mean_y_b * ccos;

    if (out_estimateCovariance)
    {
        CMatrixDouble33* C = out_estimateCovariance;  // less typing!

        // Compute the normalized covariance matrix:
        // -------------------------------------------
        double var_x_a = 0, var_y_a = 0, var_x_b = 0, var_y_b = 0;
        const double N_1_inv = 1.0 / (N - 1);

        // 0) Precompute the unbiased variances estimations:
        // ----------------------------------------------------
        for (const auto& in_correspondence : in_correspondences)
        {
            var_x_a += square(in_correspondence.this_x - mean_x_a);
            var_y_a += square(in_correspondence.this_y - mean_y_a);
            var_x_b += square(in_correspondence.other_x - mean_x_b);
            var_y_b += square(in_correspondence.other_y - mean_y_b);
        }
        var_x_a *= N_1_inv;  //  /= (N-1)
        var_y_a *= N_1_inv;
        var_x_b *= N_1_inv;
        var_y_b *= N_1_inv;

        // 1) Compute  BETA = s_Delta^2 / s_p^2
        // --------------------------------
        const double BETA = (var_x_a + var_y_a + var_x_b + var_y_b) *
                            pow(static_cast<double>(N), 2.0) *
                            static_cast<double>(N - 1);

        // 2) And the final covariance matrix:
        //  (remember: this matrix has yet to be
        //   multiplied by var_p to be the actual covariance!)
        // -------------------------------------------------------
        const double D = square(Ax) + square(Ay);

        (*C)(0, 0) =
            2.0 * N_inv + BETA * square((mean_x_b * Ay + mean_y_b * Ax) / D);
        (*C)(1, 1) =
            2.0 * N_inv + BETA * square((mean_x_b * Ax - mean_y_b * Ay) / D);
        (*C)(2, 2) = BETA / D;

        (*C)(0, 1) = (*C)(1, 0) = -BETA * (mean_x_b * Ay + mean_y_b * Ax) *
                                  (mean_x_b * Ax - mean_y_b * Ay) / square(D);

        (*C)(0, 2) = (*C)(2, 0) =
            BETA * (mean_x_b * Ay + mean_y_b * Ax) / pow(D, 1.5);

        (*C)(1, 2) = (*C)(2, 1) =
            BETA * (mean_y_b * Ay - mean_x_b * Ax) / pow(D, 1.5);
    }

    return true;

    MRPT_END
}