linlsq.h

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/**********************************************************************
 * File:        linlsq.h  (Formerly llsq.h)
 * Description: Linear Least squares fitting code.
 * Author:      Ray Smith
 *
 * (C) Copyright 1991, Hewlett-Packard Ltd.
 ** Licensed under the Apache License, Version 2.0 (the "License");
 ** you may not use this file except in compliance with the License.
 ** You may obtain a copy of the License at
 ** http://www.apache.org/licenses/LICENSE-2.0
 ** Unless required by applicable law or agreed to in writing, software
 ** distributed under the License is distributed on an "AS IS" BASIS,
 ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 ** See the License for the specific language governing permissions and
 ** limitations under the License.
 *
 **********************************************************************/
 
#ifndef TESSERACT_CCSTRUCT_LINLSQ_H_
#define TESSERACT_CCSTRUCT_LINLSQ_H_
 
#include "points.h" // for FCOORD
 
#include <algorithm> // for std::nth_element
#include <cstdint> // for int32_t
 
namespace tesseract {
 
class TESS_API LLSQ {
public:
  LLSQ() {   // constructor
    clear(); // set to zeros
  }
  void clear(); // initialize
 
  // Adds an element with a weight of 1.
  void add(double x, double y);
  // Adds an element with a specified weight.
  void add(double x, double y, double weight);
  // Adds a whole LLSQ.
  void add(const LLSQ &other);
  // Deletes an element with a weight of 1.
  void remove(double x, double y);
  int32_t count() const { // no of elements
    return static_cast<int>(total_weight + 0.5);
  }
 
  double m() const;                     // get gradient
  double c(double m) const;             // get constant
  double rms(double m, double c) const; // get error
  double pearson() const;               // get correlation coefficient.
 
  // Returns the x,y means as an FCOORD.
  FCOORD mean_point() const;
 
  // Returns the average sum of squared perpendicular error from a line
  // through mean_point() in the direction dir.
  double rms_orth(const FCOORD &dir) const;
 
  // Returns the direction of the fitted line as a unit vector, using the
  // least mean squared perpendicular distance. The line runs through the
  // mean_point, i.e. a point p on the line is given by:
  // p = mean_point() + lambda * vector_fit() for some real number lambda.
  // Note that the result (0<=x<=1, -1<=y<=-1) is directionally ambiguous
  // and may be negated without changing its meaning, since a line is only
  // unique to a range of pi radians.
  // Modernists prefer to think of this as an Eigenvalue problem, but
  // Pearson had the simple solution in 1901.
  //
  // Note that this is equivalent to returning the Principal Component in PCA,
  // or the eigenvector corresponding to the largest eigenvalue in the
  // covariance matrix.
  FCOORD vector_fit() const;
 
  // Returns the covariance.
  double covariance() const {
    if (total_weight > 0.0) {
      return (sigxy - sigx * sigy / total_weight) / total_weight;
    } else {
      return 0.0;
    }
  }
  double x_variance() const {
    if (total_weight > 0.0) {
      return (sigxx - sigx * sigx / total_weight) / total_weight;
    } else {
      return 0.0;
    }
  }
  double y_variance() const {
    if (total_weight > 0.0) {
      return (sigyy - sigy * sigy / total_weight) / total_weight;
    } else {
      return 0.0;
    }
  }
 
private:
  double total_weight; // no of elements or sum of weights.
  double sigx;         // sum of x
  double sigy;         // sum of y
  double sigxx;        // sum x squared
  double sigxy;        // sum of xy
  double sigyy;        // sum y squared
};
 
// Returns the median value of the vector, given that the values are
// circular, with the given modulus. Values may be signed or unsigned,
// eg range from -pi to pi (modulus 2pi) or from 0 to 2pi (modulus 2pi).
// NOTE that the array is shuffled, but the time taken is linear.
// An assumption is made that most of the values are spread over no more than
// half the range, but wrap-around is accounted for if the median is near
// the wrap-around point.
// Cannot be a member of vector, as it makes heavy use of LLSQ.
// T must be an integer or float/double type.
template <typename T>
T MedianOfCircularValues(T modulus, std::vector<T> &v) {
  LLSQ stats;
  T halfrange = static_cast<T>(modulus / 2);
  auto num_elements = v.size();
  for (auto i : v) {
    stats.add(i, i + halfrange);
  }
  bool offset_needed = stats.y_variance() < stats.x_variance();
  if (offset_needed) {
    for (auto i : v) {
      i += halfrange;
    }
  }
  auto median_index = num_elements / 2;
  std::nth_element(v.begin(), v.begin() + median_index, v.end());
  if (offset_needed) {
    for (auto i : v) {
      i -= halfrange;
    }
  }
  return v[median_index];
}
 
} // namespace tesseract
 
#endif // TESSERACT_CCSTRUCT_LINLSQ_H_