githubmirror/tesseract

src/ccstruct/coutln.cpp
1 062 строки34 KB
Yulv-git
Fix some typos.
05 июн 2022, 11:48
05 июн 2022, 11:488bc7a95
/**********************************************************************
 * File:        coutln.cpp  (Formerly coutline.c)
 * Description: Code for the C_OUTLINE class.
 * 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.
 *
 **********************************************************************/

// Include automatically generated configuration file if running autoconf.
#ifdef HAVE_CONFIG_H
#  include "config_auto.h"
#endif

#include "coutln.h"

#include "arrayaccess.h" // for GET_DATA_BYTE
#include "blobs.h"       // for TPOINT
#include "crakedge.h"    // for CRACKEDGE
#include "environ.h"     // for l_uint32
#include "errcode.h"     // for ASSERT_HOST
#include "normalis.h"    // for DENORM

#include "helpers.h" // for ClipToRange, IntCastRounded, Modulo

#include <allheaders.h> // for pixSetPixel, pixGetData, pixRasterop, pixGe...
#include "pix.h"        // for Pix (ptr only), PIX_DST, PIX_NOT

#include <algorithm> // for max, min
#include <cmath>     // for abs
#include <cstdlib>   // for abs
#include <cstring>   // for memset, memcpy, memmove

namespace tesseract {

ICOORD C_OUTLINE::step_coords[4] = {ICOORD(-1, 0), ICOORD(0, -1), ICOORD(1, 0), ICOORD(0, 1)};

/**
 * @name C_OUTLINE::C_OUTLINE
 *
 * Constructor to build a C_OUTLINE from a CRACKEDGE LOOP.
 * @param startpt outline to convert
 * @param bot_left bounding box
 * @param top_right bounding box
 * @param length length of loop
 */

C_OUTLINE::C_OUTLINE(CRACKEDGE *startpt, ICOORD bot_left, ICOORD top_right, int16_t length)
    : box(bot_left, top_right), start(startpt->pos), offsets(nullptr) {
  int16_t stepindex; // index to step
  CRACKEDGE *edgept; // current point

  stepcount = length; // no of steps
  if (length == 0) {
    return;
  }
  // get memory
  steps.resize(step_mem());
  edgept = startpt;

  for (stepindex = 0; stepindex < length; stepindex++) {
    // set compact step
    set_step(stepindex, edgept->stepdir);
    edgept = edgept->next;
  }
}

/**
 * @name C_OUTLINE::C_OUTLINE
 *
 * Constructor to build a C_OUTLINE from a C_OUTLINE_FRAG.
 */
C_OUTLINE::C_OUTLINE(
    // constructor
    // steps to copy
    ICOORD startpt, DIR128 *new_steps,
    int16_t length // length of loop
    )
    : start(startpt), offsets(nullptr) {
  int8_t dirdiff;    // direction difference
  DIR128 prevdir;    // previous direction
  DIR128 dir;        // current direction
  DIR128 lastdir;    // dir of last step
  TBOX new_box;      // easy bounding
  int16_t stepindex; // index to step
  int16_t srcindex;  // source steps
  ICOORD pos;        // current position

  pos = startpt;
  stepcount = length; // No. of steps.
  ASSERT_HOST(length >= 0);
  steps.resize(step_mem()); // Get memory.

  lastdir = new_steps[length - 1];
  prevdir = lastdir;
  for (stepindex = 0, srcindex = 0; srcindex < length; stepindex++, srcindex++) {
    new_box = TBOX(pos, pos);
    box += new_box;
    // copy steps
    dir = new_steps[srcindex];
    set_step(stepindex, dir);
    dirdiff = dir - prevdir;
    pos += step(stepindex);
    if ((dirdiff == 64 || dirdiff == -64) && stepindex > 0) {
      stepindex -= 2; // cancel there-and-back
      prevdir = stepindex >= 0 ? step_dir(stepindex) : lastdir;
    } else {
      prevdir = dir;
    }
  }
  ASSERT_HOST(pos.x() == startpt.x() && pos.y() == startpt.y());
  do {
    dirdiff = step_dir(stepindex - 1) - step_dir(0);
    if (dirdiff == 64 || dirdiff == -64) {
      start += step(0);
      stepindex -= 2; // cancel there-and-back
      for (int i = 0; i < stepindex; ++i) {
        set_step(i, step_dir(i + 1));
      }
    }
  } while (stepindex > 1 && (dirdiff == 64 || dirdiff == -64));
  stepcount = stepindex;
  ASSERT_HOST(stepcount >= 4);
}

/**
 * @name C_OUTLINE::C_OUTLINE
 *
 * Constructor to build a C_OUTLINE from a rotation of a C_OUTLINE.
 * @param srcline outline to rotate
 * @param rotation rotate to coord
 */

C_OUTLINE::C_OUTLINE(C_OUTLINE *srcline, FCOORD rotation) : offsets(nullptr) {
  TBOX new_box;      // easy bounding
  int16_t stepindex; // index to step
  int16_t dirdiff;   // direction change
  ICOORD pos;        // current position
  ICOORD prevpos;    // previous dest point

  ICOORD destpos;                // destination point
  int16_t destindex = INT16_MAX; // index to step
  DIR128 dir;                    // coded direction
  uint8_t new_step;

  stepcount = srcline->stepcount * 2;
  if (stepcount == 0) {
    box = srcline->box;
    box.rotate(rotation);
    return;
  }
  // get memory
  steps.resize(step_mem());

  for (int iteration = 0; iteration < 2; ++iteration) {
    DIR128 round1 = iteration == 0 ? 32 : 0;
    DIR128 round2 = iteration != 0 ? 32 : 0;
    pos = srcline->start;
    prevpos = pos;
    prevpos.rotate(rotation);
    start = prevpos;
    box = TBOX(start, start);
    destindex = 0;
    for (stepindex = 0; stepindex < srcline->stepcount; stepindex++) {
      pos += srcline->step(stepindex);
      destpos = pos;
      destpos.rotate(rotation);
      //  tprintf("%i %i %i %i ", destpos.x(), destpos.y(), pos.x(), pos.y());
      while (destpos.x() != prevpos.x() || destpos.y() != prevpos.y()) {
        dir = DIR128(FCOORD(destpos - prevpos));
        dir += 64; // turn to step style
        new_step = dir.get_dir();
        //  tprintf(" %i\n", new_step);
        if (new_step & 31) {
          set_step(destindex++, dir + round1);
          prevpos += step(destindex - 1);
          if (destindex < 2 ||
              ((dirdiff = step_dir(destindex - 1) - step_dir(destindex - 2)) != -64 &&
               dirdiff != 64)) {
            set_step(destindex++, dir + round2);
            prevpos += step(destindex - 1);
          } else {
            prevpos -= step(destindex - 1);
            destindex--;
            prevpos -= step(destindex - 1);
            set_step(destindex - 1, dir + round2);
            prevpos += step(destindex - 1);
          }
        } else {
          set_step(destindex++, dir);
          prevpos += step(destindex - 1);
        }
        while (destindex >= 2 &&
               ((dirdiff = step_dir(destindex - 1) - step_dir(destindex - 2)) == -64 ||
                dirdiff == 64)) {
          prevpos -= step(destindex - 1);
          prevpos -= step(destindex - 2);
          destindex -= 2; // Forget u turn
        }
        // ASSERT_HOST(prevpos.x() == destpos.x() && prevpos.y() ==
        // destpos.y());
        new_box = TBOX(destpos, destpos);
        box += new_box;
      }
    }
    ASSERT_HOST(destpos.x() == start.x() && destpos.y() == start.y());
    while (destindex > 1) {
      dirdiff = step_dir(destindex - 1) - step_dir(0);
      if (dirdiff != 64 && dirdiff != -64) {
        break;
      }
      start += step(0);
      destindex -= 2;
      for (int i = 0; i < destindex; ++i) {
        set_step(i, step_dir(i + 1));
      }
    }
    if (destindex >= 4) {
      break;
    }
  }
  ASSERT_HOST(destindex <= stepcount);
  stepcount = destindex;
  destpos = start;
  for (stepindex = 0; stepindex < stepcount; stepindex++) {
    destpos += step(stepindex);
  }
  ASSERT_HOST(destpos.x() == start.x() && destpos.y() == start.y());
}

// Build a fake outline, given just a bounding box and append to the list.
void C_OUTLINE::FakeOutline(const TBOX &box, C_OUTLINE_LIST *outlines) {
  C_OUTLINE_IT ol_it(outlines);
  // Make a C_OUTLINE from the bounds. This is a bit of a hack,
  // as there is no outline, just a bounding box, but it works nicely.
  CRACKEDGE start;
  start.pos = box.topleft();
  auto *outline = new C_OUTLINE(&start, box.topleft(), box.botright(), 0);
  ol_it.add_to_end(outline);
}

/**
 * @name C_OUTLINE::area
 *
 * Compute the area of the outline.
 */

int32_t C_OUTLINE::area() const {
  int stepindex;       // current step
  int32_t total_steps; // steps to do
  int32_t total;       // total area
  ICOORD pos;          // position of point
  ICOORD next_step;    // step to next pix
  // We aren't going to modify the list, or its contents, but there is
  // no const iterator.
  C_OUTLINE_IT it(const_cast<C_OUTLINE_LIST *>(&children));

  pos = start_pos();
  total_steps = pathlength();
  total = 0;
  for (stepindex = 0; stepindex < total_steps; stepindex++) {
    // all intersected
    next_step = step(stepindex);
    if (next_step.x() < 0) {
      total += pos.y();
    } else if (next_step.x() > 0) {
      total -= pos.y();
    }
    pos += next_step;
  }
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    total += it.data()->area(); // add areas of children
  }

  return total;
}

/**
 * @name C_OUTLINE::perimeter
 *
 * Compute the perimeter of the outline and its first level children.
 */

int32_t C_OUTLINE::perimeter() const {
  int32_t total_steps; // Return value.
  // We aren't going to modify the list, or its contents, but there is
  // no const iterator.
  C_OUTLINE_IT it(const_cast<C_OUTLINE_LIST *>(&children));

  total_steps = pathlength();
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    total_steps += it.data()->pathlength(); // Add perimeters of children.
  }

  return total_steps;
}

/**
 * @name C_OUTLINE::outer_area
 *
 * Compute the area of the outline.
 */

int32_t C_OUTLINE::outer_area() const {
  int stepindex;       // current step
  int32_t total_steps; // steps to do
  int32_t total;       // total area
  ICOORD pos;          // position of point
  ICOORD next_step;    // step to next pix

  pos = start_pos();
  total_steps = pathlength();
  if (total_steps == 0) {
    return box.area();
  }
  total = 0;
  for (stepindex = 0; stepindex < total_steps; stepindex++) {
    // all intersected
    next_step = step(stepindex);
    if (next_step.x() < 0) {
      total += pos.y();
    } else if (next_step.x() > 0) {
      total -= pos.y();
    }
    pos += next_step;
  }

  return total;
}

/**
 * @name C_OUTLINE::count_transitions
 *
 * Compute the number of x and y maxes and mins in the outline.
 * @param threshold winding number on size
 */

int32_t C_OUTLINE::count_transitions(int32_t threshold) {
  bool first_was_max_x; // what was first
  bool first_was_max_y;
  bool looking_for_max_x; // what is next
  bool looking_for_min_x;
  bool looking_for_max_y; // what is next
  bool looking_for_min_y;
  int stepindex;       // current step
  int32_t total_steps; // steps to do
                       // current limits
  int32_t max_x, min_x, max_y, min_y;
  int32_t initial_x, initial_y; // initial limits
  int32_t total;                // total changes
  ICOORD pos;                   // position of point
  ICOORD next_step;             // step to next pix

  pos = start_pos();
  total_steps = pathlength();
  total = 0;
  max_x = min_x = pos.x();
  max_y = min_y = pos.y();
  looking_for_max_x = true;
  looking_for_min_x = true;
  looking_for_max_y = true;
  looking_for_min_y = true;
  first_was_max_x = false;
  first_was_max_y = false;
  initial_x = pos.x();
  initial_y = pos.y(); // stop uninit warning
  for (stepindex = 0; stepindex < total_steps; stepindex++) {
    // all intersected
    next_step = step(stepindex);
    pos += next_step;
    if (next_step.x() < 0) {
      if (looking_for_max_x && pos.x() < min_x) {
        min_x = pos.x();
      }
      if (looking_for_min_x && max_x - pos.x() > threshold) {
        if (looking_for_max_x) {
          initial_x = max_x;
          first_was_max_x = false;
        }
        total++;
        looking_for_max_x = true;
        looking_for_min_x = false;
        min_x = pos.x(); // reset min
      }
    } else if (next_step.x() > 0) {
      if (looking_for_min_x && pos.x() > max_x) {
        max_x = pos.x();
      }
      if (looking_for_max_x && pos.x() - min_x > threshold) {
        if (looking_for_min_x) {
          initial_x = min_x; // remember first min
          first_was_max_x = true;
        }
        total++;
        looking_for_max_x = false;
        looking_for_min_x = true;
        max_x = pos.x();
      }
    } else if (next_step.y() < 0) {
      if (looking_for_max_y && pos.y() < min_y) {
        min_y = pos.y();
      }
      if (looking_for_min_y && max_y - pos.y() > threshold) {
        if (looking_for_max_y) {
          initial_y = max_y; // remember first max
          first_was_max_y = false;
        }
        total++;
        looking_for_max_y = true;
        looking_for_min_y = false;
        min_y = pos.y(); // reset min
      }
    } else {
      if (looking_for_min_y && pos.y() > max_y) {
        max_y = pos.y();
      }
      if (looking_for_max_y && pos.y() - min_y > threshold) {
        if (looking_for_min_y) {
          initial_y = min_y; // remember first min
          first_was_max_y = true;
        }
        total++;
        looking_for_max_y = false;
        looking_for_min_y = true;
        max_y = pos.y();
      }
    }
  }
  if (first_was_max_x && looking_for_min_x) {
    if (max_x - initial_x > threshold) {
      total++;
    } else {
      total--;
    }
  } else if (!first_was_max_x && looking_for_max_x) {
    if (initial_x - min_x > threshold) {
      total++;
    } else {
      total--;
    }
  }
  if (first_was_max_y && looking_for_min_y) {
    if (max_y - initial_y > threshold) {
      total++;
    } else {
      total--;
    }
  } else if (!first_was_max_y && looking_for_max_y) {
    if (initial_y - min_y > threshold) {
      total++;
    } else {
      total--;
    }
  }

  return total;
}

/**
 * @name C_OUTLINE::operator<
 *
 * @return true if the left operand is inside the right one.
 * @param other other outline
 */

bool C_OUTLINE::operator<(const C_OUTLINE &other) const {
  int16_t count = 0; // winding count
  ICOORD pos;        // position of point
  int32_t stepindex; // index to cstep

  if (!box.overlap(other.box)) {
    return false; // can't be contained
  }
  if (stepcount == 0) {
    return other.box.contains(this->box);
  }

  pos = start;
  for (stepindex = 0; stepindex < stepcount && (count = other.winding_number(pos)) == INTERSECTING;
       stepindex++) {
    pos += step(stepindex); // try all points
  }
  if (count == INTERSECTING) {
    // all intersected
    pos = other.start;
    for (stepindex = 0;
         stepindex < other.stepcount && (count = winding_number(pos)) == INTERSECTING;
         stepindex++) {
      // try other way round
      pos += other.step(stepindex);
    }
    return count == INTERSECTING || count == 0;
  }
  return count != 0;
}

/**
 * @name C_OUTLINE::winding_number
 *
 * @return the winding number of the outline around the given point.
 * @param point point to wind around
 */

int16_t C_OUTLINE::winding_number(ICOORD point) const {
  int16_t stepindex; // index to cstep
  int16_t count;     // winding count
  ICOORD vec;        // to current point
  ICOORD stepvec;    // step vector
  int32_t cross;     // cross product

  vec = start - point; // vector to it
  count = 0;
  for (stepindex = 0; stepindex < stepcount; stepindex++) {
    stepvec = step(stepindex); // get the step
                               // crossing the line
    if (vec.y() <= 0 && vec.y() + stepvec.y() > 0) {
      cross = vec * stepvec; // cross product
      if (cross > 0) {
        count++; // crossing right half
      } else if (cross == 0) {
        return INTERSECTING; // going through point
      }
    } else if (vec.y() > 0 && vec.y() + stepvec.y() <= 0) {
      cross = vec * stepvec;
      if (cross < 0) {
        count--; // crossing back
      } else if (cross == 0) {
        return INTERSECTING; // illegal
      }
    }
    vec += stepvec; // sum vectors
  }
  return count; // winding number
}

/**
 * C_OUTLINE::turn_direction
 *
 * @return the sum direction delta of the outline.
 */

int16_t C_OUTLINE::turn_direction() const { // winding number
  DIR128 prevdir;                           // previous direction
  DIR128 dir;                               // current direction
  int16_t stepindex;                        // index to cstep
  int8_t dirdiff;                           // direction difference
  int16_t count;                            // winding count

  if (stepcount == 0) {
    return 128;
  }
  count = 0;
  prevdir = step_dir(stepcount - 1);
  for (stepindex = 0; stepindex < stepcount; stepindex++) {
    dir = step_dir(stepindex);
    dirdiff = dir - prevdir;
    ASSERT_HOST(dirdiff == 0 || dirdiff == 32 || dirdiff == -32);
    count += dirdiff;
    prevdir = dir;
  }
  ASSERT_HOST(count == 128 || count == -128);
  return count; // winding number
}

/**
 * @name C_OUTLINE::reverse
 *
 * Reverse the direction of an outline.
 */

void C_OUTLINE::reverse() {      // reverse drection
  DIR128 halfturn = MODULUS / 2; // amount to shift
  DIR128 stepdir;                // direction of step
  int16_t stepindex;             // index to cstep
  int16_t farindex;              // index to other side
  int16_t halfsteps;             // half of stepcount

  halfsteps = (stepcount + 1) / 2;
  for (stepindex = 0; stepindex < halfsteps; stepindex++) {
    farindex = stepcount - stepindex - 1;
    stepdir = step_dir(stepindex);
    set_step(stepindex, step_dir(farindex) + halfturn);
    set_step(farindex, stepdir + halfturn);
  }
}

/**
 * @name C_OUTLINE::move
 *
 * Move C_OUTLINE by vector
 * @param vec vector to reposition OUTLINE by
 */

void C_OUTLINE::move(const ICOORD vec) {
  C_OUTLINE_IT it(&children); // iterator

  box.move(vec);
  start += vec;

  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    it.data()->move(vec); // move child outlines
  }
}

/**
 * Returns true if *this and its children are legally nested.
 * The outer area of a child should have the opposite sign to the
 * parent. If not, it means we have discarded an outline in between
 * (probably due to excessive length).
 */
bool C_OUTLINE::IsLegallyNested() const {
  if (stepcount == 0) {
    return true;
  }
  int64_t parent_area = outer_area();
  // We aren't going to modify the list, or its contents, but there is
  // no const iterator.
  C_OUTLINE_IT child_it(const_cast<C_OUTLINE_LIST *>(&children));
  for (child_it.mark_cycle_pt(); !child_it.cycled_list(); child_it.forward()) {
    const C_OUTLINE *child = child_it.data();
    if (child->outer_area() * parent_area > 0 || !child->IsLegallyNested()) {
      return false;
    }
  }
  return true;
}

/**
 * If this outline is smaller than the given min_size, delete this and
 * remove from its list, via *it, after checking that *it points to this.
 * Otherwise, if any children of this are too small, delete them.
 * On entry, *it must be an iterator pointing to this. If this gets deleted
 * then this is extracted from *it, so an iteration can continue.
 * @param min_size minimum size for outline
 * @param it outline iterator
 */
void C_OUTLINE::RemoveSmallRecursive(int min_size, C_OUTLINE_IT *it) {
  if (box.width() < min_size || box.height() < min_size) {
    ASSERT_HOST(this == it->data());
    delete it->extract(); // Too small so get rid of it and any children.
  } else if (!children.empty()) {
    // Search the children of this, deleting any that are too small.
    C_OUTLINE_IT child_it(&children);
    for (child_it.mark_cycle_pt(); !child_it.cycled_list(); child_it.forward()) {
      C_OUTLINE *child = child_it.data();
      child->RemoveSmallRecursive(min_size, &child_it);
    }
  }
}

// Factored out helpers below are used only by ComputeEdgeOffsets to operate
// on data from an 8-bit Pix, and assume that any input x and/or y are already
// constrained to be legal Pix coordinates.

/**
 * Helper computes the local 2-D gradient (dx, dy) from the 2x2 cell centered
 * on the given (x,y). If the cell would go outside the image, it is padded
 * with white.
 */
static void ComputeGradient(const l_uint32 *data, int wpl, int x, int y, int width, int height,
                            ICOORD *gradient) {
  const l_uint32 *line = data + y * wpl;
  int pix_x_y = x < width && y < height ? GET_DATA_BYTE(line, x) : 255;
  int pix_x_prevy = x < width && y > 0 ? GET_DATA_BYTE(line - wpl, x) : 255;
  int pix_prevx_prevy = x > 0 && y > 0 ? GET_DATA_BYTE(line - wpl, x - 1) : 255;
  int pix_prevx_y = x > 0 && y < height ? GET_DATA_BYTE(line, x - 1) : 255;
  gradient->set_x(pix_x_y + pix_x_prevy - (pix_prevx_y + pix_prevx_prevy));
  gradient->set_y(pix_x_prevy + pix_prevx_prevy - (pix_x_y + pix_prevx_y));
}

/**
 * Helper evaluates a vertical difference, (x,y) - (x,y-1), returning true if
 * the difference, matches diff_sign and updating the best_diff, best_sum,
 * best_y if a new max.
 */
static bool EvaluateVerticalDiff(const l_uint32 *data, int wpl, int diff_sign, int x, int y,
                                 int height, int *best_diff, int *best_sum, int *best_y) {
  if (y <= 0 || y >= height) {
    return false;
  }
  const l_uint32 *line = data + y * wpl;
  int pixel1 = GET_DATA_BYTE(line - wpl, x);
  int pixel2 = GET_DATA_BYTE(line, x);
  int diff = (pixel2 - pixel1) * diff_sign;
  if (diff > *best_diff) {
    *best_diff = diff;
    *best_sum = pixel1 + pixel2;
    *best_y = y;
  }
  return diff > 0;
}

/**
 * Helper evaluates a horizontal difference, (x,y) - (x-1,y), where y is implied
 * by the input image line, returning true if the difference matches diff_sign
 * and updating the best_diff, best_sum, best_x if a new max.
 */
static bool EvaluateHorizontalDiff(const l_uint32 *line, int diff_sign, int x, int width,
                                   int *best_diff, int *best_sum, int *best_x) {
  if (x <= 0 || x >= width) {
    return false;
  }
  int pixel1 = GET_DATA_BYTE(line, x - 1);
  int pixel2 = GET_DATA_BYTE(line, x);
  int diff = (pixel2 - pixel1) * diff_sign;
  if (diff > *best_diff) {
    *best_diff = diff;
    *best_sum = pixel1 + pixel2;
    *best_x = x;
  }
  return diff > 0;
}

/**
 * Adds sub-pixel resolution EdgeOffsets for the outline if the supplied
 * pix is 8-bit. Does nothing otherwise.
 * Operation: Consider the following near-horizontal line:
 * @verbatim
 *   _________
 *            |________
 *                     |________
 * @endverbatim
 * At *every* position along this line, the gradient direction will be close
 * to vertical. Extrapoaltion/interpolation of the position of the threshold
 * that was used to binarize the image gives a more precise vertical position
 * for each horizontal step, and the conflict in step direction and gradient
 * direction can be used to ignore the vertical steps.
 */
void C_OUTLINE::ComputeEdgeOffsets(int threshold, Image pix) {
  if (pixGetDepth(pix) != 8) {
    return;
  }
  const l_uint32 *data = pixGetData(pix);
  int wpl = pixGetWpl(pix);
  int width = pixGetWidth(pix);
  int height = pixGetHeight(pix);
  bool negative = flag(COUT_INVERSE);
  delete[] offsets;
  offsets = new EdgeOffset[stepcount];
  ICOORD pos = start;
  ICOORD prev_gradient;
  ComputeGradient(data, wpl, pos.x(), height - pos.y(), width, height, &prev_gradient);
  for (int s = 0; s < stepcount; ++s) {
    ICOORD step_vec = step(s);
    TPOINT pt1(pos);
    pos += step_vec;
    TPOINT pt2(pos);
    ICOORD next_gradient;
    ComputeGradient(data, wpl, pos.x(), height - pos.y(), width, height, &next_gradient);
    // Use the sum of the prev and next as the working gradient.
    ICOORD gradient = prev_gradient + next_gradient;
    // best_diff will be manipulated to be always positive.
    int best_diff = 0;
    // offset will be the extrapolation of the location of the greyscale
    // threshold from the edge with the largest difference, relative to the
    // location of the binary edge.
    int offset = 0;
    if (pt1.y == pt2.y && abs(gradient.y()) * 2 >= abs(gradient.x())) {
      // Horizontal step. diff_sign == 1 indicates black above.
      int diff_sign = (pt1.x > pt2.x) == negative ? 1 : -1;
      int x = std::min(pt1.x, pt2.x);
      int y = height - pt1.y;
      int best_sum = 0;
      int best_y = y;
      EvaluateVerticalDiff(data, wpl, diff_sign, x, y, height, &best_diff, &best_sum, &best_y);
      // Find the strongest edge.
      int test_y = y;
      do {
        ++test_y;
      } while (EvaluateVerticalDiff(data, wpl, diff_sign, x, test_y, height, &best_diff, &best_sum,
                                    &best_y));
      test_y = y;
      do {
        --test_y;
      } while (EvaluateVerticalDiff(data, wpl, diff_sign, x, test_y, height, &best_diff, &best_sum,
                                    &best_y));
      offset = diff_sign * (best_sum / 2 - threshold) + (y - best_y) * best_diff;
    } else if (pt1.x == pt2.x && abs(gradient.x()) * 2 >= abs(gradient.y())) {
      // Vertical step. diff_sign == 1 indicates black on the left.
      int diff_sign = (pt1.y > pt2.y) == negative ? 1 : -1;
      int x = pt1.x;
      int y = height - std::max(pt1.y, pt2.y);
      const l_uint32 *line = pixGetData(pix) + y * wpl;
      int best_sum = 0;
      int best_x = x;
      EvaluateHorizontalDiff(line, diff_sign, x, width, &best_diff, &best_sum, &best_x);
      // Find the strongest edge.
      int test_x = x;
      do {
        ++test_x;
      } while (
          EvaluateHorizontalDiff(line, diff_sign, test_x, width, &best_diff, &best_sum, &best_x));
      test_x = x;
      do {
        --test_x;
      } while (
          EvaluateHorizontalDiff(line, diff_sign, test_x, width, &best_diff, &best_sum, &best_x));
      offset = diff_sign * (threshold - best_sum / 2) + (best_x - x) * best_diff;
    }
    offsets[s].offset_numerator = ClipToRange<int>(offset, -INT8_MAX, INT8_MAX);
    offsets[s].pixel_diff = ClipToRange<int>(best_diff, 0, UINT8_MAX);
    if (negative) {
      gradient = -gradient;
    }
    // Compute gradient angle quantized to 256 directions, rotated by 64 (pi/2)
    // to convert from gradient direction to edge direction.
    offsets[s].direction = Modulo(FCOORD::binary_angle_plus_pi(gradient.angle()) + 64, 256);
    prev_gradient = next_gradient;
  }
}

/**
 * Adds sub-pixel resolution EdgeOffsets for the outline using only
 * a binary image source.
 *
 * Runs a sliding window of 5 edge steps over the outline, maintaining a count
 * of the number of steps in each of the 4 directions in the window, and a
 * sum of the x or y position of each step (as appropriate to its direction.)
 * Ignores single-count steps EXCEPT the sharp U-turn and smoothes out the
 * perpendicular direction. Eg
 * @verbatim
 * ___              ___       Chain code from the left:
 *    |___    ___   ___|      222122212223221232223000
 *        |___|  |_|          Corresponding counts of each direction:
 *                          0   00000000000000000123
 *                          1   11121111001111100000
 *                          2   44434443443333343321
 *                          3   00000001111111112111
 * Count of direction at center 41434143413313143313
 * Step gets used?              YNYYYNYYYNYYNYNYYYyY (y= U-turn exception)
 * Path redrawn showing only the used points:
 * ___              ___
 *     ___    ___   ___|
 *         ___    _
 * @endverbatim
 * Sub-pixel edge position cannot be shown well with ASCII-art, but each
 * horizontal step's y position is the mean of the y positions of the steps
 * in the same direction in the sliding window, which makes a much smoother
 * outline, without losing important detail.
 */
void C_OUTLINE::ComputeBinaryOffsets() {
  delete[] offsets;
  offsets = new EdgeOffset[stepcount];
  // Count of the number of steps in each direction in the sliding window.
  int dir_counts[4];
  // Sum of the positions (y for a horizontal step, x for vertical) in each
  // direction in the sliding window.
  int pos_totals[4];
  memset(dir_counts, 0, sizeof(dir_counts));
  memset(pos_totals, 0, sizeof(pos_totals));
  ICOORD pos = start;
  ICOORD tail_pos = pos;
  // tail_pos is the trailing position, with the next point to be lost from
  // the window.
  tail_pos -= step(stepcount - 1);
  tail_pos -= step(stepcount - 2);
  // head_pos is the leading position, with the next point to be added to the
  // window.
  ICOORD head_pos = tail_pos;
  // Set up the initial window with 4 points in [-2, 2)
  for (int s = -2; s < 2; ++s) {
    increment_step(s, 1, &head_pos, dir_counts, pos_totals);
  }
  for (int s = 0; s < stepcount; pos += step(s++)) {
    // At step s, s in the middle of [s-2, s+2].
    increment_step(s + 2, 1, &head_pos, dir_counts, pos_totals);
    int dir_index = chain_code(s);
    ICOORD step_vec = step(s);
    int best_diff = 0;
    int offset = 0;
    // Use only steps that have a count of >=2 OR the strong U-turn with a
    // single d and 2 at d-1 and 2 at d+1 (mod 4).
    if (dir_counts[dir_index] >= 2 ||
        (dir_counts[dir_index] == 1 && dir_counts[Modulo(dir_index - 1, 4)] == 2 &&
         dir_counts[Modulo(dir_index + 1, 4)] == 2)) {
      // Valid step direction.
      best_diff = dir_counts[dir_index];
      int edge_pos = step_vec.x() == 0 ? pos.x() : pos.y();
      // The offset proposes that the actual step should be positioned at
      // the mean position of the steps in the window of the same direction.
      // See ASCII art above.
      offset = pos_totals[dir_index] - best_diff * edge_pos;
    }
    offsets[s].offset_numerator = ClipToRange<int>(offset, -INT8_MAX, INT8_MAX);
    offsets[s].pixel_diff = ClipToRange<int>(best_diff, 0, UINT8_MAX);
    // The direction is just the vector from start to end of the window.
    FCOORD direction(head_pos.x() - tail_pos.x(), head_pos.y() - tail_pos.y());
    offsets[s].direction = direction.to_direction();
    increment_step(s - 2, -1, &tail_pos, dir_counts, pos_totals);
  }
}

/**
 * Renders the outline to the given pix, with left and top being
 * the coords of the upper-left corner of the pix.
 */
void C_OUTLINE::render(int left, int top, Image pix) const {
  ICOORD pos = start;
  for (int stepindex = 0; stepindex < stepcount; ++stepindex) {
    ICOORD next_step = step(stepindex);
    if (next_step.y() < 0) {
      pixRasterop(pix, 0, top - pos.y(), pos.x() - left, 1, PIX_NOT(PIX_DST), nullptr, 0, 0);
    } else if (next_step.y() > 0) {
      pixRasterop(pix, 0, top - pos.y() - 1, pos.x() - left, 1, PIX_NOT(PIX_DST), nullptr, 0, 0);
    }
    pos += next_step;
  }
}

/**
 * Renders just the outline to the given pix (no fill), with left and top
 * being the coords of the upper-left corner of the pix.
 * @param left coord
 * @param top coord
 * @param pix the pix to outline
 */
void C_OUTLINE::render_outline(int left, int top, Image pix) const {
  ICOORD pos = start;
  for (int stepindex = 0; stepindex < stepcount; ++stepindex) {
    ICOORD next_step = step(stepindex);
    if (next_step.y() < 0) {
      pixSetPixel(pix, pos.x() - left, top - pos.y(), 1);
    } else if (next_step.y() > 0) {
      pixSetPixel(pix, pos.x() - left - 1, top - pos.y() - 1, 1);
    } else if (next_step.x() < 0) {
      pixSetPixel(pix, pos.x() - left - 1, top - pos.y(), 1);
    } else if (next_step.x() > 0) {
      pixSetPixel(pix, pos.x() - left, top - pos.y() - 1, 1);
    }
    pos += next_step;
  }
}

/**
 * @name C_OUTLINE::plot
 *
 * Draw the outline in the given colour.
 * @param window window to draw in
 * @param colour colour to draw in
 */

#ifndef GRAPHICS_DISABLED
void C_OUTLINE::plot(ScrollView *window, ScrollView::Color colour) const {
  int16_t stepindex; // index to cstep
  ICOORD pos;        // current position
  DIR128 stepdir;    // direction of step

  pos = start; // current position
  window->Pen(colour);
  if (stepcount == 0) {
    window->Rectangle(box.left(), box.top(), box.right(), box.bottom());
    return;
  }
  window->SetCursor(pos.x(), pos.y());

  stepindex = 0;
  while (stepindex < stepcount) {
    pos += step(stepindex); // step to next
    stepdir = step_dir(stepindex);
    stepindex++; // count steps
    // merge straight lines
    while (stepindex < stepcount && stepdir.get_dir() == step_dir(stepindex).get_dir()) {
      pos += step(stepindex);
      stepindex++;
    }
    window->DrawTo(pos.x(), pos.y());
  }
}

/**
 * Draws the outline in the given colour, normalized using the given denorm,
 * making use of sub-pixel accurate information if available.
 */
void C_OUTLINE::plot_normed(const DENORM &denorm, ScrollView::Color colour,
                            ScrollView *window) const {
  window->Pen(colour);
  if (stepcount == 0) {
    window->Rectangle(box.left(), box.top(), box.right(), box.bottom());
    return;
  }
  const DENORM *root_denorm = denorm.RootDenorm();
  ICOORD pos = start; // current position
  FCOORD f_pos = sub_pixel_pos_at_index(pos, 0);
  FCOORD pos_normed;
  denorm.NormTransform(root_denorm, f_pos, &pos_normed);
  window->SetCursor(IntCastRounded(pos_normed.x()), IntCastRounded(pos_normed.y()));
  for (int s = 0; s < stepcount; pos += step(s++)) {
    int edge_weight = edge_strength_at_index(s);
    if (edge_weight == 0) {
      // This point has conflicting gradient and step direction, so ignore it.
      continue;
    }
    FCOORD f_pos = sub_pixel_pos_at_index(pos, s);
    FCOORD pos_normed;
    denorm.NormTransform(root_denorm, f_pos, &pos_normed);
    window->DrawTo(IntCastRounded(pos_normed.x()), IntCastRounded(pos_normed.y()));
  }
}
#endif

/**
 * @name C_OUTLINE::operator=
 *
 * Assignment - deep copy data
 * @param source assign from this
 */

C_OUTLINE &C_OUTLINE::operator=(const C_OUTLINE &source) {
  box = source.box;
  start = source.start;
  if (!children.empty()) {
    children.clear();
  }
  children.deep_copy(&source.children, &deep_copy);
  delete[] offsets;
  offsets = nullptr;
  stepcount = source.stepcount;
  if (stepcount > 0) {
    steps.resize(step_mem());
    memmove(&steps[0], &source.steps[0], step_mem());
    if (source.offsets != nullptr) {
      offsets = new EdgeOffset[stepcount];
      memcpy(offsets, source.offsets, stepcount * sizeof(*offsets));
    }
  }
  return *this;
}

/**
 * Helper for ComputeBinaryOffsets. Increments pos, dir_counts, pos_totals
 * by the step, increment, and vertical step ? x : y position * increment
 * at step s Mod stepcount respectively. Used to add or subtract the
 * direction and position to/from accumulators of a small neighbourhood.
 */
void C_OUTLINE::increment_step(int s, int increment, ICOORD *pos, int *dir_counts,
                               int *pos_totals) const {
  int step_index = Modulo(s, stepcount);
  int dir_index = chain_code(step_index);
  dir_counts[dir_index] += increment;
  ICOORD step_vec = step(step_index);
  if (step_vec.x() == 0) {
    pos_totals[dir_index] += pos->x() * increment;
  } else {
    pos_totals[dir_index] += pos->y() * increment;
  }
  *pos += step_vec;
}

ICOORD C_OUTLINE::chain_step(int chaindir) {
  return step_coords[chaindir % 4];
}

} // namespace tesseract