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detlinefit.cpp
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detlinefit.cpp
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///////////////////////////////////////////////////////////////////////
// File: detlinefit.cpp
// Description: Deterministic least median squares line fitting.
// Author: Ray Smith
// Created: Thu Feb 28 14:45:01 PDT 2008
//
// (C) Copyright 2008, Google Inc.
// 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.
//
///////////////////////////////////////////////////////////////////////
#include "detlinefit.h"
#include "statistc.h"
#include "ndminx.h"
#include "tprintf.h"
#include <algorithm>
namespace tesseract {
// The number of points to consider at each end.
const int kNumEndPoints = 3;
// The minimum number of points at which to switch to number of points
// for badly fitted lines.
// To ensure a sensible error metric, kMinPointsForErrorCount should be at
// least kMaxRealDistance / (1 - %ile) where %ile is the fractile used in
// ComputeUpperQuartileError.
const int kMinPointsForErrorCount = 16;
// The maximum real distance to use before switching to number of
// mis-fitted points, which will get square-rooted for true distance.
const int kMaxRealDistance = 2.0;
DetLineFit::DetLineFit() : square_length_(0.0) {
}
DetLineFit::~DetLineFit() {
}
// Delete all Added points.
void DetLineFit::Clear() {
pts_.clear();
distances_.clear();
}
// Add a new point. Takes a copy - the pt doesn't need to stay in scope.
void DetLineFit::Add(const ICOORD& pt) {
pts_.push_back(PointWidth(pt, 0));
}
// Associates a half-width with the given point if a point overlaps the
// previous point by more than half the width, and its distance is further
// than the previous point, then the more distant point is ignored in the
// distance calculation. Useful for ignoring i dots and other diacritics.
void DetLineFit::Add(const ICOORD& pt, int halfwidth) {
pts_.push_back(PointWidth(pt, halfwidth));
}
// Fits a line to the points, ignoring the skip_first initial points and the
// skip_last final points, returning the fitted line as a pair of points,
// and the upper quartile error.
double DetLineFit::Fit(int skip_first, int skip_last,
ICOORD* pt1, ICOORD* pt2) {
// Do something sensible with no points.
if (pts_.empty()) {
pt1->set_x(0);
pt1->set_y(0);
*pt2 = *pt1;
return 0.0;
}
// Count the points and find the first and last kNumEndPoints.
int pt_count = pts_.size();
ICOORD* starts[kNumEndPoints];
if (skip_first >= pt_count) skip_first = pt_count - 1;
int start_count = 0;
int end_i = std::min(skip_first + kNumEndPoints, pt_count);
for (int i = skip_first; i < end_i; ++i) {
starts[start_count++] = &pts_[i].pt;
}
ICOORD* ends[kNumEndPoints];
if (skip_last >= pt_count) skip_last = pt_count - 1;
int end_count = 0;
end_i = std::max(0, pt_count - kNumEndPoints - skip_last);
for (int i = pt_count - 1 - skip_last; i >= end_i; --i) {
ends[end_count++] = &pts_[i].pt;
}
// 1 or 2 points need special treatment.
if (pt_count <= 2) {
*pt1 = *starts[0];
if (pt_count > 1)
*pt2 = *ends[0];
else
*pt2 = *pt1;
return 0.0;
}
// Although with between 2 and 2*kNumEndPoints-1 points, there will be
// overlap in the starts, ends sets, this is OK and taken care of by the
// if (*start != *end) test below, which also tests for equal input points.
double best_uq = -1.0;
// Iterate each pair of points and find the best fitting line.
for (int i = 0; i < start_count; ++i) {
ICOORD* start = starts[i];
for (int j = 0; j < end_count; ++j) {
ICOORD* end = ends[j];
if (*start != *end) {
ComputeDistances(*start, *end);
// Compute the upper quartile error from the line.
double dist = EvaluateLineFit();
if (dist < best_uq || best_uq < 0.0) {
best_uq = dist;
*pt1 = *start;
*pt2 = *end;
}
}
}
}
// Finally compute the square root to return the true distance.
return best_uq > 0.0 ? sqrt(best_uq) : best_uq;
}
// Constrained fit with a supplied direction vector. Finds the best line_pt,
// that is one of the supplied points having the median cross product with
// direction, ignoring points that have a cross product outside of the range
// [min_dist, max_dist]. Returns the resulting error metric using the same
// reduced set of points.
// *Makes use of floating point arithmetic*
double DetLineFit::ConstrainedFit(const FCOORD& direction,
double min_dist, double max_dist,
bool debug, ICOORD* line_pt) {
ComputeConstrainedDistances(direction, min_dist, max_dist);
// Do something sensible with no points or computed distances.
if (pts_.empty() || distances_.empty()) {
line_pt->set_x(0);
line_pt->set_y(0);
return 0.0;
}
int median_index = distances_.choose_nth_item(distances_.size() / 2);
*line_pt = distances_[median_index].data;
if (debug) {
tprintf("Constrained fit to dir %g, %g = %d, %d :%d distances:\n",
direction.x(), direction.y(),
line_pt->x(), line_pt->y(), distances_.size());
for (int i = 0; i < distances_.size(); ++i) {
tprintf("%d: %d, %d -> %g\n", i, distances_[i].data.x(),
distances_[i].data.y(), distances_[i].key);
}
tprintf("Result = %d\n", median_index);
}
// Center distances on the fitted point.
double dist_origin = direction * *line_pt;
for (int i = 0; i < distances_.size(); ++i) {
distances_[i].key -= dist_origin;
}
return sqrt(EvaluateLineFit());
}
// Returns true if there were enough points at the last call to Fit or
// ConstrainedFit for the fitted points to be used on a badly fitted line.
bool DetLineFit::SufficientPointsForIndependentFit() const {
return distances_.size() >= kMinPointsForErrorCount;
}
// Backwards compatible fit returning a gradient and constant.
// Deprecated. Prefer Fit(ICOORD*, ICOORD*) where possible, but use this
// function in preference to the LMS class.
double DetLineFit::Fit(float* m, float* c) {
ICOORD start, end;
double error = Fit(&start, &end);
if (end.x() != start.x()) {
*m = static_cast<float>(end.y() - start.y()) / (end.x() - start.x());
*c = start.y() - *m * start.x();
} else {
*m = 0.0f;
*c = 0.0f;
}
return error;
}
// Backwards compatible constrained fit with a supplied gradient.
// Deprecated. Use ConstrainedFit(const FCOORD& direction) where possible
// to avoid potential difficulties with infinite gradients.
double DetLineFit::ConstrainedFit(double m, float* c) {
// Do something sensible with no points.
if (pts_.empty()) {
*c = 0.0f;
return 0.0;
}
double cos = 1.0 / sqrt(1.0 + m * m);
FCOORD direction(cos, m * cos);
ICOORD line_pt;
double error = ConstrainedFit(direction, -MAX_FLOAT32, MAX_FLOAT32, false,
&line_pt);
*c = line_pt.y() - line_pt.x() * m;
return error;
}
// Computes and returns the squared evaluation metric for a line fit.
double DetLineFit::EvaluateLineFit() {
// Compute the upper quartile error from the line.
double dist = ComputeUpperQuartileError();
if (distances_.size() >= kMinPointsForErrorCount &&
dist > kMaxRealDistance * kMaxRealDistance) {
// Use the number of mis-fitted points as the error metric, as this
// gives a better measure of fit for badly fitted lines where more
// than a quarter are badly fitted.
double threshold = kMaxRealDistance * sqrt(square_length_);
dist = NumberOfMisfittedPoints(threshold);
}
return dist;
}
// Computes the absolute error distances of the points from the line,
// and returns the squared upper-quartile error distance.
double DetLineFit::ComputeUpperQuartileError() {
int num_errors = distances_.size();
if (num_errors == 0) return 0.0;
// Get the absolute values of the errors.
for (int i = 0; i < num_errors; ++i) {
if (distances_[i].key < 0) distances_[i].key = -distances_[i].key;
}
// Now get the upper quartile distance.
int index = distances_.choose_nth_item(3 * num_errors / 4);
double dist = distances_[index].key;
// The true distance is the square root of the dist squared / square_length.
// Don't bother with the square root. Just return the square distance.
return square_length_ > 0.0 ? dist * dist / square_length_ : 0.0;
}
// Returns the number of sample points that have an error more than threshold.
int DetLineFit::NumberOfMisfittedPoints(double threshold) const {
int num_misfits = 0;
int num_dists = distances_.size();
// Get the absolute values of the errors.
for (int i = 0; i < num_dists; ++i) {
if (distances_[i].key > threshold)
++num_misfits;
}
return num_misfits;
}
// Computes all the cross product distances of the points from the line,
// storing the actual (signed) cross products in distances.
// Ignores distances of points that are further away than the previous point,
// and overlaps the previous point by at least half.
void DetLineFit::ComputeDistances(const ICOORD& start, const ICOORD& end) {
distances_.truncate(0);
ICOORD line_vector = end;
line_vector -= start;
square_length_ = line_vector.sqlength();
int line_length = IntCastRounded(sqrt(square_length_));
// Compute the distance of each point from the line.
int prev_abs_dist = 0;
int prev_dot = 0;
for (int i = 0; i < pts_.size(); ++i) {
ICOORD pt_vector = pts_[i].pt;
pt_vector -= start;
int dot = line_vector % pt_vector;
// Compute |line_vector||pt_vector|sin(angle between)
int dist = line_vector * pt_vector;
int abs_dist = dist < 0 ? -dist : dist;
if (abs_dist > prev_abs_dist && i > 0) {
// Ignore this point if it overlaps the previous one.
int separation = abs(dot - prev_dot);
if (separation < line_length * pts_[i].halfwidth ||
separation < line_length * pts_[i - 1].halfwidth)
continue;
}
distances_.push_back(DistPointPair(dist, pts_[i].pt));
prev_abs_dist = abs_dist;
prev_dot = dot;
}
}
// Computes all the cross product distances of the points perpendicular to
// the given direction, ignoring distances outside of the give distance range,
// storing the actual (signed) cross products in distances_.
void DetLineFit::ComputeConstrainedDistances(const FCOORD& direction,
double min_dist, double max_dist) {
distances_.truncate(0);
square_length_ = direction.sqlength();
// Compute the distance of each point from the line.
for (int i = 0; i < pts_.size(); ++i) {
FCOORD pt_vector = pts_[i].pt;
// Compute |line_vector||pt_vector|sin(angle between)
double dist = direction * pt_vector;
if (min_dist <= dist && dist <= max_dist)
distances_.push_back(DistPointPair(dist, pts_[i].pt));
}
}
} // namespace tesseract.