basalt/include/basalt/optical_flow/patch.h

/**
BSD 3-Clause License

This file is part of the Basalt project.
https://gitlab.com/VladyslavUsenko/basalt.git

Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice,
  this list of conditions and the following disclaimer in the documentation
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* Neither the name of the copyright holder nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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*/
#pragma once

#include <Eigen/Dense>

#include <basalt/image/image.h>
#include <basalt/optical_flow/patterns.h>

namespace basalt {

template <typename Scalar, typename Pattern>
struct OpticalFlowPatch {
  static constexpr int PATTERN_SIZE = Pattern::PATTERN_SIZE;

  typedef Eigen::Matrix<int, 2, 1> Vector2i;

  typedef Eigen::Matrix<Scalar, 2, 1> Vector2;
  typedef Eigen::Matrix<Scalar, 1, 2> Vector2T;
  typedef Eigen::Matrix<Scalar, 3, 1> Vector3;
  typedef Eigen::Matrix<Scalar, 3, 3> Matrix3;
  typedef Eigen::Matrix<Scalar, 4, 4> Matrix4;
  typedef Eigen::Matrix<Scalar, PATTERN_SIZE, 1> VectorP;

  typedef Eigen::Matrix<Scalar, 2, PATTERN_SIZE> Matrix2P;
  typedef Eigen::Matrix<Scalar, PATTERN_SIZE, 2> MatrixP2;
  typedef Eigen::Matrix<Scalar, PATTERN_SIZE, 3> MatrixP3;
  typedef Eigen::Matrix<Scalar, 3, PATTERN_SIZE> Matrix3P;
  typedef Eigen::Matrix<Scalar, PATTERN_SIZE, 4> MatrixP4;
  typedef Eigen::Matrix<int, 2, PATTERN_SIZE> Matrix2Pi;

  static const Matrix2P pattern2;

  EIGEN_MAKE_ALIGNED_OPERATOR_NEW

  OpticalFlowPatch() { mean = 0; }

  OpticalFlowPatch(const Image<const uint16_t> &img, const Vector2 &pos) {
    setFromImage(img, pos);
  }

  void setFromImage(const Image<const uint16_t> &img, const Vector2 &pos) {
    this->pos = pos;

    int num_valid_points = 0;
    Scalar sum = 0;
    Vector2 grad_sum(0, 0);

    MatrixP2 grad;

    for (int i = 0; i < PATTERN_SIZE; i++) {
      Vector2 p = pos + pattern2.col(i);
      if (img.InBounds(p, 2)) {
        Vector3 valGrad = img.interpGrad<Scalar>(p);
        data[i] = valGrad[0];
        sum += valGrad[0];
        grad.row(i) = valGrad.template tail<2>();
        grad_sum += valGrad.template tail<2>();
        num_valid_points++;
      } else {
        data[i] = -1;
      }
    }

    mean = sum / num_valid_points;

    Scalar mean_inv = num_valid_points / sum;

    Eigen::Matrix<Scalar, 2, 3> Jw_se2;
    Jw_se2.template topLeftCorner<2, 2>().setIdentity();

    MatrixP3 J_se2;

    for (int i = 0; i < PATTERN_SIZE; i++) {
      if (data[i] >= 0) {
        data[i] *= mean_inv;
        Vector2 grad_i = grad.row(i);
        grad.row(i) = num_valid_points * (grad_i * sum - grad_sum * data[i]) /
                      (sum * sum);
      } else {
        grad.row(i).setZero();
      }

      // Fill jacobians with respect to SE2 warp
      Jw_se2(0, 2) = -pattern2(1, i);
      Jw_se2(1, 2) = pattern2(0, i);
      J_se2.row(i) = grad.row(i) * Jw_se2;
    }

    Matrix3 H_se2 = J_se2.transpose() * J_se2;
    Matrix3 H_se2_inv;
    H_se2_inv.setIdentity();
    H_se2.ldlt().solveInPlace(H_se2_inv);

    H_se2_inv_J_se2_T = H_se2_inv * J_se2.transpose();
  }

  inline bool residual(const Image<const uint16_t> &img,
                       const Matrix2P &transformed_pattern,
                       VectorP &residual) const {
    Scalar sum = 0;
    Vector2 grad_sum(0, 0);
    int num_valid_points = 0;

    for (int i = 0; i < PATTERN_SIZE; i++) {
      if (img.InBounds(transformed_pattern.col(i), 2)) {
        residual[i] = img.interp<Scalar>(transformed_pattern.col(i));
        sum += residual[i];
        num_valid_points++;
      } else {
        residual[i] = -1;
      }
    }

    int num_residuals = 0;

    for (int i = 0; i < PATTERN_SIZE; i++) {
      if (residual[i] >= 0 && data[i] >= 0) {
        Scalar val = residual[i];
        residual[i] = num_valid_points * val / sum - data[i];
        num_residuals++;

      } else {
        residual[i] = 0;
      }
    }

    return num_residuals > PATTERN_SIZE / 2;
  }

  Vector2 pos;
  VectorP data;  // negative if the point is not valid

  // MatrixP3 J_se2;  // total jacobian with respect to se2 warp
  // Matrix3 H_se2_inv;
  Matrix3P H_se2_inv_J_se2_T;

  Scalar mean;
};

template <typename Scalar, typename Pattern>
const typename OpticalFlowPatch<Scalar, Pattern>::Matrix2P
    OpticalFlowPatch<Scalar, Pattern>::pattern2 = Pattern::pattern2;

}  // namespace basalt