tesseract/textord/colpartition.cpp

///////////////////////////////////////////////////////////////////////
// File:        colpartition.cpp
// Description: Class to hold partitions of the page that correspond
//              roughly to text lines.
// Author:      Ray Smith
// Created:     Thu Aug 14 10:54:01 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 "colpartition.h"
#include "colpartitionset.h"
#include "workingpartset.h"

namespace tesseract {

ELIST2IZE(ColPartition)
CLISTIZE(ColPartition)

//////////////// ColPartition Implementation ////////////////

// If multiple partners survive the partner depth test beyond this level,
// then arbitrarily pick one.
const int kMaxPartnerDepth = 4;
// Maximum change in spacing (in inches) to ignore.
const double kMaxSpacingDrift = 1.0 / 72;  // 1/72 is one point.
// Maximum fraction of line height used as an additional allowance
// for top spacing.
const double kMaxTopSpacingFraction = 0.25;
// Maximum ratio of sizes for lines to be considered the same size.
const double kMaxSizeRatio = 1.5;

// blob_type is the blob_region_type_ of the blobs in this partition.
// Vertical is the direction of logical vertical on the possibly skewed image.
ColPartition::ColPartition(BlobRegionType blob_type, const ICOORD& vertical)
  : left_margin_(MIN_INT32), right_margin_(MAX_INT32),
    median_bottom_(MAX_INT32), median_top_(MIN_INT32), median_size_(0),
    blob_type_(blob_type),
    good_width_(false), good_column_(false),
    left_key_tab_(false), right_key_tab_(false),
    left_key_(0), right_key_(0), type_(PT_UNKNOWN), vertical_(vertical),
    working_set_(NULL), block_owned_(false),
    first_column_(-1), last_column_(-1), column_set_(NULL),
    side_step_(0), top_spacing_(0), bottom_spacing_(0),
    type_before_table_(PT_UNKNOWN), inside_table_column_(false),
    nearest_neighbor_above_(NULL), nearest_neighbor_below_(NULL),
    space_above_(0), space_below_(0), space_to_left_(0), space_to_right_(0) {
}

// Constructs a fake ColPartition with a single fake BLOBNBOX, all made
// from a single TBOX.
// WARNING: Despite being on C_LISTs, the BLOBNBOX owns the C_BLOB and
// the ColPartition owns the BLOBNBOX!!!
// Call DeleteBoxes before deleting the ColPartition.
ColPartition* ColPartition::FakePartition(const TBOX& box) {
  ColPartition* part = new ColPartition(BRT_UNKNOWN, ICOORD(0, 1));
  part->AddBox(new BLOBNBOX(C_BLOB::FakeBlob(box)));
  part->set_left_margin(box.left());
  part->set_right_margin(box.right());
  part->ComputeLimits();
  return part;
}

ColPartition::~ColPartition() {
  // Remove this as a partner of all partners, as we don't want them
  // referring to a deleted object.
  ColPartition_C_IT it(&upper_partners_);
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    it.data()->RemovePartner(false, this);
  }
  it.set_to_list(&lower_partners_);
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    it.data()->RemovePartner(true, this);
  }
}

// Constructs a fake ColPartition with no BLOBNBOXes.
// Used for making horizontal line ColPartitions and types it accordingly.
ColPartition::ColPartition(const ICOORD& vertical,
                           int left, int bottom, int right, int top)
  : left_margin_(MIN_INT32), right_margin_(MAX_INT32),
    bounding_box_(left, bottom, right, top),
    median_bottom_(bottom), median_top_(top), median_size_(top - bottom),
    blob_type_(BRT_HLINE),
    good_width_(false), good_column_(false),
    left_key_tab_(false), right_key_tab_(false),
    type_(PT_UNKNOWN), vertical_(vertical),
    working_set_(NULL), block_owned_(false),
    first_column_(-1), last_column_(-1), column_set_(NULL),
    side_step_(0), top_spacing_(0), bottom_spacing_(0),
    type_before_table_(PT_UNKNOWN), inside_table_column_(false),
    nearest_neighbor_above_(NULL), nearest_neighbor_below_(NULL),
    space_above_(0), space_below_(0), space_to_left_(0), space_to_right_(0) {
  left_key_ = BoxLeftKey();
  right_key_ = BoxRightKey();
}


// Adds the given box to the partition, updating the partition bounds.
// The list of boxes in the partition is updated, ensuring that no box is
// recorded twice, and the boxes are kept in increasing left position.
void ColPartition::AddBox(BLOBNBOX* bbox) {
  boxes_.add_sorted(SortByBoxLeft<BLOBNBOX>, true, bbox);
  TBOX box = bbox->bounding_box();
  // Update the partition limits.
  bounding_box_ += box;
  if (!left_key_tab_)
    left_key_ = BoxLeftKey();
  if (!right_key_tab_)
    right_key_ = BoxRightKey();
  if (TabFind::WithinTestRegion(2, box.left(), box.bottom()))
    tprintf("Added box (%d,%d)->(%d,%d) left_blob_x_=%d, right_blob_x_ = %d\n",
            box.left(), box.bottom(), box.right(), box.top(),
            bounding_box_.left(), bounding_box_.right());
}

// Claims the boxes in the boxes_list by marking them with a this owner
// pointer. If a box is already owned, then run Unique on it.
void ColPartition::ClaimBoxes(WidthCallback* cb) {
  bool completed = true;
  do {
    completed = true;
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      BLOBNBOX* bblob = bb_it.data();
      ColPartition* other = bblob->owner();
      if (other == NULL) {
        // Normal case: ownership is available.
        bblob->set_owner(this);
      } else if (other != this) {
        // bblob already has an owner, so resolve the dispute with Unique.
        // Null everything owned by this upto, but not including bblob, as
        // they will all be up for grabs in Unique.
        for (bb_it.move_to_first(); bb_it.data() != bblob; bb_it.forward()) {
          ASSERT_HOST(bb_it.data()->owner() == this);
          bb_it.data()->set_owner(NULL);
        }
        // Null the owners of all other's blobs. They should all be
        // still owned by other.
        BLOBNBOX_C_IT other_it(&other->boxes_);
        for (other_it.mark_cycle_pt(); !other_it.cycled_list();
             other_it.forward()) {
          ASSERT_HOST(other_it.data()->owner() == other);
          other_it.data()->set_owner(NULL);
        }
        Unique(other, cb);
        // Now we need to run ClaimBoxes on other, as it may have obtained
        // a box from this (beyond bbox) that is owned by a third party.
        other->ClaimBoxes(cb);
        // Scan our own list for bblob. If bblob is still in it and owned by
        // other, there is trouble. Otherwise we can just restart to finish
        // the blob list.
        bb_it.set_to_list(&boxes_);
        for (bb_it.mark_cycle_pt();
             !bb_it.cycled_list() && bb_it.data() != bblob;
             bb_it.forward());
        ASSERT_HOST(bb_it.cycled_list() || bblob->owner() == NULL);
        completed = false;
        break;
      }
    }
  } while (!completed);
}

// Delete the boxes that this partition owns.
void ColPartition::DeleteBoxes() {
  // Although the boxes_ list is a C_LIST, in some cases it owns the
  // BLOBNBOXes, as the ColPartition takes ownership from the grid,
  // and the BLOBNBOXes own the underlying C_BLOBs.
  for (BLOBNBOX_C_IT bb_it(&boxes_); !bb_it.empty(); bb_it.forward()) {
    BLOBNBOX* bblob = bb_it.extract();
    delete bblob->cblob();
    delete bblob;
  }
}

// Returns true if this is a legal partition - meaning that the conditions
// left_margin <= bounding_box left
// left_key <= bounding box left key
// bounding box left <= bounding box right
// and likewise for right margin and key
// are all met.
bool ColPartition::IsLegal() {
  if (bounding_box_.left() > bounding_box_.right()) {
    if (textord_debug_bugs) {
      tprintf("Bounding box invalid\n");
      Print();
    }
    return false;  // Bounding box invalid.
  }
  if (left_margin_ > bounding_box_.left() ||
      right_margin_ < bounding_box_.right()) {
    if (textord_debug_bugs) {
      tprintf("Margins invalid\n");
      Print();
    }
    return false;  // Margins invalid.
  }
  if (left_key_ > BoxLeftKey() || right_key_ < BoxRightKey()) {
    if (textord_debug_bugs) {
      tprintf("Key inside box: %d v %d or %d v %d\n",
              left_key_, BoxLeftKey(), right_key_, BoxRightKey());
      Print();
    }
    return false;  // Keys inside the box.
  }
  return true;
}

// Returns true if the left and right edges are approximately equal.
bool ColPartition::MatchingColumns(const ColPartition& other) const {
  int y = (MidY() + other.MidY()) / 2;
  if (!NearlyEqual(other.LeftAtY(y) / kColumnWidthFactor,
                   LeftAtY(y) / kColumnWidthFactor, 1))
    return false;
  if (!NearlyEqual(other.RightAtY(y) / kColumnWidthFactor,
                   RightAtY(y) / kColumnWidthFactor, 1))
    return false;
  return true;
}

// Sets the sort key using either the tab vector, or the bounding box if
// the tab vector is NULL. If the tab_vector lies inside the bounding_box,
// use the edge of the box as a key any way.
void ColPartition::SetLeftTab(const TabVector* tab_vector) {
  if (tab_vector != NULL) {
    left_key_ = tab_vector->sort_key();
    left_key_tab_ = left_key_ <= BoxLeftKey();
  } else {
    left_key_tab_ = false;
  }
  if (!left_key_tab_)
    left_key_ = BoxLeftKey();
}

// As SetLeftTab, but with the right.
void ColPartition::SetRightTab(const TabVector* tab_vector) {
  if (tab_vector != NULL) {
    right_key_ = tab_vector->sort_key();
    right_key_tab_ = right_key_ >= BoxRightKey();
  } else {
    right_key_tab_ = false;
  }
  if (!right_key_tab_)
    right_key_ = BoxRightKey();
}

// Copies the left/right tab from the src partition, but if take_box is
// true, copies the box instead and uses that as a key.
void ColPartition::CopyLeftTab(const ColPartition& src, bool take_box) {
  left_key_tab_ = take_box ? false : src.left_key_tab_;
  if (left_key_tab_) {
    left_key_ = src.left_key_;
  } else {
    bounding_box_.set_left(XAtY(src.BoxLeftKey(), MidY()));
    left_key_ = BoxLeftKey();
  }
  if (left_margin_ > bounding_box_.left())
    left_margin_ = src.left_margin_;
}

// As CopyLeftTab, but with the right.
void ColPartition::CopyRightTab(const ColPartition& src, bool take_box) {
  right_key_tab_ = take_box ? false : src.right_key_tab_;
  if (right_key_tab_) {
    right_key_ = src.right_key_;
  } else {
    bounding_box_.set_right(XAtY(src.BoxRightKey(), MidY()));
    right_key_ = BoxRightKey();
  }
  if (right_margin_ < bounding_box_.right())
    right_margin_ = src.right_margin_;
}

// Add a partner above if upper, otherwise below.
// Add them uniquely and keep the list sorted by box left.
// Partnerships are added symmetrically to partner and this.
void ColPartition::AddPartner(bool upper, ColPartition* partner) {
  if (upper) {
    partner->lower_partners_.add_sorted(SortByBoxLeft<ColPartition>,
                                        true, this);
    upper_partners_.add_sorted(SortByBoxLeft<ColPartition>, true, partner);
  } else {
    partner->upper_partners_.add_sorted(SortByBoxLeft<ColPartition>,
                                        true, this);
    lower_partners_.add_sorted(SortByBoxLeft<ColPartition>, true, partner);
  }
}

// Removes the partner from this, but does not remove this from partner.
// This asymmetric removal is so as not to mess up the iterator that is
// working on partner's partner list.
void ColPartition::RemovePartner(bool upper, ColPartition* partner) {
  ColPartition_C_IT it(upper ? &upper_partners_ : &lower_partners_);
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    if (it.data() == partner) {
      it.extract();
      break;
    }
  }
}

// Returns the partner if the given partner is a singleton, otherwise NULL.
ColPartition* ColPartition::SingletonPartner(bool upper) {
  ColPartition_CLIST* partners = upper ? &upper_partners_ : &lower_partners_;
  if (!partners->singleton())
    return NULL;
  ColPartition_C_IT it(partners);
  return it.data();
}

// Merge with the other partition and delete it.
void ColPartition::Absorb(ColPartition* other, WidthCallback* cb) {
  if (TabFind::WithinTestRegion(2, bounding_box_.left(),
                                bounding_box_.bottom()) ||
      TabFind::WithinTestRegion(2, other->bounding_box_.left(),
                                other->bounding_box_.bottom())) {
    tprintf("Merging:");
    Print();
    other->Print();
  }
  // Merge the two sorted lists.
  BLOBNBOX_C_IT it(&boxes_);
  BLOBNBOX_C_IT it2(&other->boxes_);
  for (; !it2.empty(); it2.forward()) {
    BLOBNBOX* bbox2 = it2.extract();
    ColPartition* prev_owner = bbox2->owner();
    ASSERT_HOST(prev_owner == other || prev_owner == NULL);
    if (prev_owner == other)
      bbox2->set_owner(this);
    bbox2->set_region_type(blob_type_);
    TBOX box2 = bbox2->bounding_box();
    int left2 = box2.left();
    while (!it.at_last() && it.data()->bounding_box().left() <= left2) {
      if (it.data() == bbox2)
        break;
      it.forward();
    }
    if (!it.empty() && it.data() == bbox2)
      continue;
    if (it.empty() || (it.at_last() &&
                       it.data()->bounding_box().left() <= left2)) {
      it.add_after_then_move(bbox2);
    } else {
      it.add_before_then_move(bbox2);
    }
  }
  left_margin_ = MIN(left_margin_, other->left_margin_);
  right_margin_ = MAX(right_margin_, other->right_margin_);
  if (other->left_key_ < left_key_) {
    left_key_ = other->left_key_;
    left_key_tab_ = other->left_key_tab_;
  }
  if (other->right_key_ > right_key_) {
    right_key_ = other->right_key_;
    right_key_tab_ = other->right_key_tab_;
  }
  delete other;
  ComputeLimits();
  if (cb != NULL) {
    SetColumnGoodness(cb);
  }
}

// Shares out any common boxes amongst the partitions, ensuring that no
// box stays in both. Returns true if anything was done.
bool ColPartition::Unique(ColPartition* other, WidthCallback* cb) {
  bool debug = TabFind::WithinTestRegion(2, bounding_box_.left(),
                                         bounding_box_.bottom()) ||
               TabFind::WithinTestRegion(2, other->bounding_box_.left(),
                                         other->bounding_box_.bottom());
  if (debug) {
    tprintf("Running Unique:");
    Print();
    other->Print();
  }
  BLOBNBOX_C_IT it(&boxes_);
  BLOBNBOX_C_IT it2(&other->boxes_);
  it.mark_cycle_pt();
  it2.mark_cycle_pt();
  bool any_moved = false;
  while (!it.cycled_list() && !it2.cycled_list()) {
    BLOBNBOX* bbox = it.data();
    BLOBNBOX* bbox2 = it2.data();
    TBOX box = bbox->bounding_box();
    TBOX box2 = bbox2->bounding_box();
    if (box.left() < box2.left()) {
      it.forward();
    } else if (box.left() > box2.left()) {
      it2.forward();
    } else if (bbox == bbox2) {
      // Separate out most frequent case for efficiency.
      if (debug) {
        tprintf("Keeping box (%d,%d)->(%d,%d) only in %s\n",
                box.left(), box.bottom(), box.right(), box.top(),
                ThisPartitionBetter(bbox, *other) ? "This" : "Other");
      }
      if (ThisPartitionBetter(bbox, *other))
        it2.extract();
      else
        it.extract();
      it.forward();
      it2.forward();
      any_moved = true;
    } else {
      // Lefts are equal, but boxes may be in any order.
      BLOBNBOX_C_IT search_it(it2);
      for (search_it.forward(); !search_it.at_first() &&
           search_it.data() != bbox &&
           search_it.data()->bounding_box().left() == box.left();
           search_it.forward());
      if (search_it.data() == bbox) {
        // Found a match.
        if (ThisPartitionBetter(bbox, *other)) {
          search_it.extract();
          // We just (potentially) invalidated it2, so reposition at bbox2.
          it2.move_to_first();
          for (it2.mark_cycle_pt(); it2.data() != bbox2; it2.forward());
        } else {
          it.extract();
        }
        it.forward();
        any_moved = true;
      } else {
        // No match to bbox in list2. Just move first it forward.
        it.forward();
      }
    }
  }
  // Now check to see if there are any in either list that would be better
  // off in the other.
  if (!it.empty()) {
    it.move_to_first();
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      BLOBNBOX* bbox = it.data();
      if (!ThisPartitionBetter(bbox, *other)) {
        other->AddBox(it.extract());
        TBOX box = bbox->bounding_box();
        if (debug) {
          tprintf("Moved box (%d,%d)->(%d,%d) from this to other:\n",
                  box.left(), box.bottom(), box.right(), box.top());
        }
        any_moved = true;
      }
    }
  }
  if (!it2.empty()) {
    it2.move_to_first();
    for (it2.mark_cycle_pt(); !it2.cycled_list(); it2.forward()) {
      BLOBNBOX* bbox2 = it2.data();
      if (ThisPartitionBetter(bbox2, *other)) {
        AddBox(it2.extract());
        TBOX box = bbox2->bounding_box();
        if (debug) {
          tprintf("Moved box (%d,%d)->(%d,%d) from other to this:\n",
                  box.left(), box.bottom(), box.right(), box.top());
        }
        any_moved = true;
      }
    }
  }
  if (any_moved) {
    if (debug)
      tprintf("Unique did something!\n");
    ComputeLimits();
    other->ComputeLimits();
    if (cb != NULL) {
      SetColumnGoodness(cb);
      other->SetColumnGoodness(cb);
    }
  }
  return any_moved;
}

// Split this partition at the given x coordinate, returning the right
// half and keeping the left half in this.
ColPartition* ColPartition::SplitAt(int split_x) {
  if (split_x <= bounding_box_.left() || split_x >= bounding_box_.right())
    return NULL;  // There will be no change.
  ColPartition* split_part = ShallowCopy();
  BLOBNBOX_C_IT it(&boxes_);
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    BLOBNBOX* bbox = it.data();
    ColPartition* prev_owner = bbox->owner();
    ASSERT_HOST(prev_owner == this || prev_owner == NULL);
    const TBOX& box = bbox->bounding_box();
    if (box.left() >= split_x) {
      split_part->AddBox(it.extract());
      if (prev_owner != NULL)
        bbox->set_owner(split_part);
    }
  }
  ASSERT_HOST(!it.empty());
  if (split_part->IsEmpty()) {
    // Split part ended up with nothing. Possible if split_x passes
    // through the last blob.
    delete split_part;
    return NULL;
  }
  right_key_tab_ = false;
  split_part->left_key_tab_ = false;
  right_margin_ = split_x;
  split_part->left_margin_ = split_x;
  ComputeLimits();
  split_part->ComputeLimits();
  return split_part;
}

// Recalculates all the coordinate limits of the partition.
void ColPartition::ComputeLimits() {
  bounding_box_ = TBOX();  // Clear it
  BLOBNBOX_C_IT it(&boxes_);
  BLOBNBOX* bbox = NULL;
  if (it.empty()) {
    bounding_box_.set_left(left_margin_);
    bounding_box_.set_right(right_margin_);
    bounding_box_.set_bottom(0);
    bounding_box_.set_top(0);
  } else {
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      bbox = it.data();
      bounding_box_ += bbox->bounding_box();
    }
  }
  if (!left_key_tab_)
    left_key_ = BoxLeftKey();
  if (left_key_ > BoxLeftKey() && textord_debug_bugs) {
    // TODO(rays) investigate the causes of these error messages, to find
    // out if they are genuinely harmful, or just indicative of junk input.
    tprintf("Computed left-illegal partition\n");
    Print();
  }
  if (!right_key_tab_)
    right_key_ = BoxRightKey();
  if (right_key_ < BoxRightKey() && textord_debug_bugs) {
    tprintf("Computed right-illegal partition\n");
    Print();
  }
  if (it.empty())
    return;
  STATS top_stats(bounding_box_.bottom(), bounding_box_.top() + 1);
  STATS bottom_stats(bounding_box_.bottom(), bounding_box_.top() + 1);
  STATS size_stats(0, bounding_box_.height() + 1);
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    bbox = it.data();
    TBOX box = bbox->bounding_box();
    top_stats.add(box.top(), 1);
    bottom_stats.add(box.bottom(), 1);
    size_stats.add(box.height(), 1);
  }
  median_top_ = static_cast<int>(top_stats.median() + 0.5);
  median_bottom_ = static_cast<int>(bottom_stats.median() + 0.5);
  median_size_ = static_cast<int>(size_stats.median() + 0.5);

  if (right_margin_ < bounding_box_.right() && textord_debug_bugs) {
    tprintf("Made partition with bad right coords");
    Print();
  }
  if (left_margin_ > bounding_box_.left() && textord_debug_bugs) {
    tprintf("Made partition with bad left coords");
    Print();
  }
  if (TabFind::WithinTestRegion(2, bounding_box_.left(),
                                bounding_box_.bottom())) {
    tprintf("Recomputed box for partition %p\n", this);
    Print();
  }
}

// Computes and sets the type_ and first_colum_, last_column_ and column_set_.
void ColPartition::SetPartitionType(ColPartitionSet* columns) {
  int first_spanned_col = -1;
  int last_spanned_col = -1;
  type_ = columns->SpanningType(blob_type_,
                                bounding_box_.left(), bounding_box_.right(),
                                MidY(), left_margin_, right_margin_,
                                &first_column_, &last_column_,
                                &first_spanned_col, &last_spanned_col);
  column_set_ = columns;
  if (first_column_ != last_column_ &&
      (type_ == PT_PULLOUT_TEXT || type_ == PT_PULLOUT_IMAGE ||
       type_ == PT_PULLOUT_LINE)) {
    // Unequal columns may indicate that the pullout spans one of the columns
    // it lies in, so force it to be allocated to just that column.
    if (first_spanned_col >= 0) {
      first_column_ = first_spanned_col;
      last_column_ = first_spanned_col;
    } else {
      if ((first_column_ & 1) == 0)
        last_column_ = first_column_;
      else if ((last_column_ & 1) == 0)
        first_column_ = last_column_;
      else
        first_column_ = last_column_ = (first_column_ + last_column_) / 2;
    }
  }
}

// Returns the first and last column touched by this partition.
void ColPartition::ColumnRange(ColPartitionSet* columns,
                               int* first_col, int* last_col) {
  int first_spanned_col = -1;
  int last_spanned_col = -1;
  type_ = columns->SpanningType(blob_type_,
                                bounding_box_.left(), bounding_box_.right(),
                                MidY(), left_margin_, right_margin_,
                                first_col, last_col,
                                &first_spanned_col, &last_spanned_col);
}

// Sets the internal flags good_width_ and good_column_.
void ColPartition::SetColumnGoodness(WidthCallback* cb) {
  int y = MidY();
  int width = RightAtY(y) - LeftAtY(y);
  good_width_ = cb->Run(width);
  good_column_ = blob_type_ == BRT_TEXT && left_key_tab_ && right_key_tab_;
}

// Adds this ColPartition to a matching WorkingPartSet if one can be found,
// otherwise starts a new one in the appropriate column, ending the previous.
void ColPartition::AddToWorkingSet(const ICOORD& bleft, const ICOORD& tright,
                                   int resolution,
                                   ColPartition_LIST* used_parts,
                                   WorkingPartSet_LIST* working_sets) {
  if (block_owned_)
    return;  // Done it already.
  block_owned_ = true;
  WorkingPartSet_IT it(working_sets);
  // If there is an upper partner use its working_set_ directly.
  ColPartition* partner = SingletonPartner(true);
  if (partner != NULL && partner->working_set_ != NULL) {
    working_set_ = partner->working_set_;
    working_set_->AddPartition(this);
    return;
  }
  if (partner != NULL && textord_debug_bugs) {
    tprintf("Partition with partner has no working set!:");
    Print();
    partner->Print();
  }
  // Search for the column that the left edge fits in.
  WorkingPartSet* work_set = NULL;
  it.move_to_first();
  int col_index = 0;
  for (it.mark_cycle_pt(); !it.cycled_list() &&
       col_index != first_column_;
        it.forward(), ++col_index);
  if (textord_debug_tabfind >= 2) {
    tprintf("Match is %s for:", (col_index & 1) ? "Real" : "Between");
    Print();
  }
  if (it.cycled_list() && textord_debug_bugs) {
    tprintf("Target column=%d, only had %d\n", first_column_, col_index);
  }
  ASSERT_HOST(!it.cycled_list());
  work_set = it.data();
  // If last_column_ != first_column, then we need to scoop up all blocks
  // between here and the last_column_ and put back in work_set.
  if (!it.cycled_list() && last_column_ != first_column_) {
    // Find the column that the right edge falls in.
    BLOCK_LIST completed_blocks;
    TO_BLOCK_LIST to_blocks;
    for (; !it.cycled_list() && col_index <= last_column_;
         it.forward(), ++col_index) {
      WorkingPartSet* end_set = it.data();
      end_set->ExtractCompletedBlocks(bleft, tright, resolution, used_parts,
                                      &completed_blocks, &to_blocks);
    }
    work_set->InsertCompletedBlocks(&completed_blocks, &to_blocks);
  }
  working_set_ = work_set;
  work_set->AddPartition(this);
}

// From the given block_parts list, builds one or more BLOCKs and
// corresponding TO_BLOCKs, such that the line spacing is uniform in each.
// Created blocks are appended to the end of completed_blocks and to_blocks.
// The used partitions are put onto used_parts, as they may still be referred
// to in the partition grid. bleft, tright and resolution are the bounds
// and resolution of the original image.
void ColPartition::LineSpacingBlocks(const ICOORD& bleft, const ICOORD& tright,
                                     int resolution,
                                     ColPartition_LIST* block_parts,
                                     ColPartition_LIST* used_parts,
                                     BLOCK_LIST* completed_blocks,
                                     TO_BLOCK_LIST* to_blocks) {
  int page_height = tright.y() - bleft.y();
  // Compute the initial spacing stats.
  ColPartition_IT it(block_parts);
  int part_count = 0;
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    ColPartition* part = it.data();
    ASSERT_HOST(!part->boxes()->empty());
    STATS side_steps(0, part->bounding_box().height());
    BLOBNBOX_C_IT blob_it(part->boxes());
    int prev_bottom = blob_it.data()->bounding_box().bottom();
    for (blob_it.forward(); !blob_it.at_first(); blob_it.forward()) {
      BLOBNBOX* blob = blob_it.data();
      int bottom = blob->bounding_box().bottom();
      int step = bottom - prev_bottom;
      if (step < 0)
        step = -step;
      side_steps.add(step, 1);
      prev_bottom = bottom;
    }
    part->set_side_step(static_cast<int>(side_steps.median() + 0.5));
    if (!it.at_last()) {
      ColPartition* next_part = it.data_relative(1);
      part->set_bottom_spacing(part->median_bottom() -
                               next_part->median_bottom());
      part->set_top_spacing(part->median_top() - next_part->median_top());
    } else {
      part->set_bottom_spacing(page_height);
      part->set_top_spacing(page_height);
    }
    if (textord_debug_tabfind) {
      part->Print();
      tprintf("side step = %.2f, top spacing = %d, bottom spacing=%d\n",
              side_steps.median(), part->top_spacing(), part->bottom_spacing());
    }
    ++part_count;
  }
  if (part_count == 0)
    return;

  SmoothSpacings(resolution, page_height, block_parts);

  // Move the partitions into individual block lists and make the blocks.
  BLOCK_IT block_it(completed_blocks);
  TO_BLOCK_IT to_block_it(to_blocks);
  ColPartition_LIST spacing_parts;
  ColPartition_IT sp_block_it(&spacing_parts);
  for (it.mark_cycle_pt(); !it.empty();) {
    ColPartition* part = it.extract();
    sp_block_it.add_to_end(part);
    it.forward();
    if (it.empty() || !part->SpacingsEqual(*it.data(), resolution)) {
      // There is a spacing boundary. Check to see if it.data() belongs
      // better in the current block or the next one.
      if (!it.empty()) {
        ColPartition* next_part = it.data();
        // If there is a size match one-way, then the middle line goes with
        // its matched size, otherwise it goes with the smallest spacing.
        ColPartition* third_part = it.at_last() ? NULL : it.data_relative(1);
        if (textord_debug_tabfind)
          tprintf("Spacings unequal: upper:%d/%d, lower:%d/%d,"
                  " sizes %d %d %d\n",
                  part->top_spacing(), part->bottom_spacing(),
                  next_part->top_spacing(), next_part->bottom_spacing(),
                  part->median_size(), next_part->median_size(),
                  third_part != NULL ? third_part->median_size() : 0);
        // If spacing_diff ends up positive, then next_part goes in the
        // current block.
        int spacing_diff = next_part->bottom_spacing() - part->bottom_spacing();
        if (part->SizesSimilar(*next_part) &&
            (third_part == NULL || !next_part->SizesSimilar(*third_part))) {
          // Sizes overrule.
          spacing_diff = 1;
        } else if (!part->SizesSimilar(*next_part) && third_part != NULL &&
                   next_part->SizesSimilar(*third_part)) {
          // Sizes overrule.
          spacing_diff = -1;
        }
        if (spacing_diff > 0) {
          sp_block_it.add_to_end(it.extract());
          it.forward();
        }
      }
      TO_BLOCK* to_block = MakeBlock(bleft, tright, &spacing_parts, used_parts);
      if (to_block != NULL) {
        to_block_it.add_to_end(to_block);
        block_it.add_to_end(to_block->block);
      }
      sp_block_it.set_to_list(&spacing_parts);
    }
  }
}

// Helper function to clip the input pos to the given bleft, tright bounds.
static void ClipCoord(const ICOORD& bleft, const ICOORD& tright, ICOORD* pos) {
  if (pos->x() < bleft.x())
    pos->set_x(bleft.x());
  if (pos->x() > tright.x())
    pos->set_x(tright.x());
  if (pos->y() < bleft.y())
    pos->set_y(bleft.y());
  if (pos->y() > tright.y())
    pos->set_y(tright.y());
}

// Constructs a block from the given list of partitions.
// Arguments are as LineSpacingBlocks above.
TO_BLOCK* ColPartition::MakeBlock(const ICOORD& bleft, const ICOORD& tright,
                                  ColPartition_LIST* block_parts,
                                  ColPartition_LIST* used_parts) {
  if (block_parts->empty())
    return NULL;  // Nothing to do.
  ColPartition_IT it(block_parts);
  ColPartition* part = it.data();
  int line_spacing = part->bottom_spacing();
  if (line_spacing < part->median_size())
    line_spacing = part->bounding_box().height();
  PolyBlockType type = it.data()->type();
  bool text_type = it.data()->IsTextType();
  ICOORDELT_LIST vertices;
  ICOORDELT_IT vert_it(&vertices);
  ICOORD start, end;
  int min_x = MAX_INT32;
  int max_x = MIN_INT32;
  int min_y = MAX_INT32;
  int max_y = MIN_INT32;
  int iteration = 0;
  do {
    if (iteration == 0)
      ColPartition::LeftEdgeRun(&it, &start, &end);
    else
      ColPartition::RightEdgeRun(&it, &start, &end);
    ClipCoord(bleft, tright, &start);
    ClipCoord(bleft, tright, &end);
    vert_it.add_after_then_move(new ICOORDELT(start));
    vert_it.add_after_then_move(new ICOORDELT(end));
    min_x = MIN(min_x, start.x());
    min_x = MIN(min_x, end.x());
    max_x = MAX(max_x, start.x());
    max_x = MAX(max_x, end.x());
    min_y = MIN(min_y, start.y());
    min_y = MIN(min_y, end.y());
    max_y = MAX(max_y, start.y());
    max_y = MAX(max_y, end.y());
    if ((iteration == 0 && it.at_first()) ||
        (iteration == 1 && it.at_last())) {
      ++iteration;
      it.move_to_last();
    }
  } while (iteration < 2);
  if (textord_debug_tabfind)
    tprintf("Making block at (%d,%d)->(%d,%d)\n",
            min_x, min_y, max_x, max_y);
  BLOCK* block = new BLOCK("", true, 0, 0, min_x, min_y, max_x, max_y);
  block->set_poly_block(new POLY_BLOCK(&vertices, type));
  // Make a matching TO_BLOCK and put all the BLOBNBOXes from the parts in it.
  // Move all the parts to a done list as they are no longer needed, except
  // that have have to continue to exist until the part grid is deleted.
  // Compute the median blob size as we go, as the block needs to know.
  STATS heights(0, max_y + 1 - min_y);
  TO_BLOCK* to_block = new TO_BLOCK(block);
  BLOBNBOX_IT blob_it(&to_block->blobs);
  ColPartition_IT used_it(used_parts);
  for (it.move_to_first(); !it.empty(); it.forward()) {
    ColPartition* part = it.extract();
    if (text_type) {
      // Only transfer blobs from text regions to the output blocks.
      // The rest stay behind and get deleted with the ColPartitions.
      for (BLOBNBOX_C_IT bb_it(part->boxes()); !bb_it.empty();
           bb_it.forward()) {
        BLOBNBOX* bblob = bb_it.extract();
        ASSERT_HOST(bblob->owner() == part);
        ASSERT_HOST(bblob->region_type() >= BRT_UNKNOWN);
        C_OUTLINE_IT ol_it(bblob->cblob()->out_list());
        ASSERT_HOST(ol_it.data()->pathlength() > 0);
        heights.add(bblob->bounding_box().height(), 1);
        blob_it.add_after_then_move(bblob);
      }
    }
    used_it.add_to_end(part);
  }
  if (text_type && blob_it.empty()) {
    delete block;
    delete to_block;
    return NULL;
  }
  to_block->line_size = heights.median();
  int block_height = block->bounding_box().height();
  if (block_height < line_spacing)
    line_spacing = block_height;
  to_block->line_spacing = line_spacing;
  to_block->max_blob_size = block_height + 1;
  if (type == PT_VERTICAL_TEXT) {
    // This block will get rotated 90 deg clockwise so record the inverse.
    FCOORD rotation(0.0f, 1.0f);
    block->set_re_rotation(rotation);
  }
  return to_block;
}

// Returns a copy of everything except the list of boxes. The resulting
// ColPartition is only suitable for keeping in a column candidate list.
ColPartition* ColPartition::ShallowCopy() const {
  ColPartition* part = new ColPartition(blob_type_, vertical_);
  part->left_margin_ = left_margin_;
  part->right_margin_ = right_margin_;
  part->bounding_box_ = bounding_box_;
  part->median_bottom_ = median_bottom_;
  part->median_top_ = median_top_;
  part->median_size_ = median_size_;
  part->good_width_ = good_width_;
  part->good_column_ = good_column_;
  part->left_key_tab_ = left_key_tab_;
  part->right_key_tab_ = right_key_tab_;
  part->type_ = type_;
  part->left_key_ = left_key_;
  part->right_key_ = right_key_;
  return part;
}

// Provides a color for BBGrid to draw the rectangle.
// Must be kept in sync with PolyBlockType.
ScrollView::Color  ColPartition::BoxColor() const {
  return POLY_BLOCK::ColorForPolyBlockType(type_);
}

// Keep in sync with BlobRegionType.
static char kBlobTypes[BRT_COUNT + 1] = "NHRIUVT";

// Prints debug information on this.
void ColPartition::Print() {
  int y = MidY();
  tprintf("ColPart:%c(M%d-%c%d-B%d,%d/%d)->(%dB-%d%c-%dM,%d/%d)"
          " w-ok=%d, v-ok=%d, type=%d%c, fc=%d, lc=%d, boxes=%d"
          " ts=%d bs=%d ls=%d rs=%d\n",
          boxes_.empty() ? 'E' : ' ',
          left_margin_, left_key_tab_ ? 'T' : 'B', LeftAtY(y),
          bounding_box_.left(), median_bottom_, bounding_box_.bottom(),
          bounding_box_.right(), RightAtY(y), right_key_tab_ ? 'T' : 'B',
          right_margin_, median_top_, bounding_box_.top(),
          good_width_, good_column_, type_,
          kBlobTypes[blob_type_],
          first_column_, last_column_, boxes_.length(),
          space_above_, space_below_, space_to_left_, space_to_right_);
}

// Sets the types of all partitions in the run to be the max of the types.
void ColPartition::SmoothPartnerRun(int working_set_count) {
  STATS left_stats(0, working_set_count);
  STATS right_stats(0, working_set_count);
  PolyBlockType max_type = type_;
  ColPartition* partner;
  for (partner = SingletonPartner(false); partner != NULL;
       partner = partner->SingletonPartner(false)) {
    if (partner->type_ > max_type)
      max_type = partner->type_;
    if (column_set_ == partner->column_set_) {
      left_stats.add(partner->first_column_, 1);
      right_stats.add(partner->last_column_, 1);
    }
  }
  type_ = max_type;
  first_column_ = left_stats.mode();
  last_column_ = right_stats.mode();
  if (last_column_ < first_column_)
    last_column_ = first_column_;

  for (partner = SingletonPartner(false); partner != NULL;
       partner = partner->SingletonPartner(false)) {
    partner->type_ = max_type;
    if (column_set_ == partner->column_set_) {
      partner->first_column_ = first_column_;
      partner->last_column_ = last_column_;
    }
  }
}

// Cleans up the partners of the given type so that there is at most
// one partner. This makes block creation simpler.
void ColPartition::RefinePartners(PolyBlockType type) {
  if (type_ == type) {
    RefinePartnersInternal(true);
    RefinePartnersInternal(false);
  } else if (type == PT_COUNT) {
    // This is the final pass. Make sure only the correctly typed
    // partners surivive, however many there are.
    RefinePartnersByType(true, &upper_partners_);
    RefinePartnersByType(false, &lower_partners_);
  }
}

////////////////// PRIVATE CODE /////////////////////////////

// Cleans up the partners above if upper is true, else below.
void ColPartition::RefinePartnersInternal(bool upper) {
  ColPartition_CLIST* partners = upper ? &upper_partners_ : &lower_partners_;
  if (!partners->empty() && !partners->singleton()) {
    RefinePartnersByType(upper, partners);
    if (!partners->empty() && !partners->singleton()) {
      // Check for transitive partnerships and break the cycle.
      RefinePartnerShortcuts(upper, partners);
      if (!partners->empty() && !partners->singleton()) {
        // Types didn't fix it. Flowing text keeps the one with the longest
        // sequence of singleton matching partners. All others max overlap.
        if (type_ == PT_FLOWING_TEXT)
          RefineFlowingTextPartners(upper, partners);
        else
          RefinePartnersByOverlap(upper, partners);
      }
    }
  }
}

// Restricts the partners to only desirable types. For text and BRT_HLINE this
// means the same type_ , and for image types it means any image type.
void ColPartition::RefinePartnersByType(bool upper,
                                        ColPartition_CLIST* partners) {
  if (TabFind::WithinTestRegion(2, bounding_box_.left(),
                                bounding_box_.bottom())) {
    tprintf("Refining %s partners by type for:\n", upper ? "Upper" : "Lower");
    Print();
  }
  ColPartition_C_IT it(partners);
  // Purify text by type.
  if (blob_type_ > BRT_UNKNOWN || blob_type_ == BRT_HLINE) {
    // Keep only partners matching type_.
    // Exception: PT_VERTICAL_TEXT is allowed to stay with the other
    // text types if it is the only partner.
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      ColPartition* partner = it.data();
      if (partner->type_ != type_ &&
          (!partners->singleton() ||
           (type_ != PT_VERTICAL_TEXT && partner->type_ != PT_VERTICAL_TEXT) ||
            !IsTextType() || !partner->IsTextType())) {
        partner->RemovePartner(!upper, this);
        it.extract();
      } else if (TabFind::WithinTestRegion(2, bounding_box_.left(),
                                           bounding_box_.bottom())) {
        tprintf("Keeping partner:");
        partner->Print();
      }
    }
  } else {
    // Keep only images with images, but not being fussy about type.
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      ColPartition* partner = it.data();
      if (partner->blob_type_ > BRT_UNKNOWN ||
          partner->blob_type_ == BRT_HLINE) {
        partner->RemovePartner(!upper, this);
        it.extract();
      } else if (TabFind::WithinTestRegion(2, bounding_box_.left(),
                                           bounding_box_.bottom())) {
        tprintf("Keeping partner:");
        partner->Print();
      }
    }
  }
}

// Remove transitive partnerships: this<->a, and a<->b and this<->b.
// Gets rid of this<->b, leaving a clean chain.
// Also if we have this<->a and a<->this, then gets rid of this<->a, as
// this has multiple partners.
void ColPartition::RefinePartnerShortcuts(bool upper,
                                          ColPartition_CLIST* partners) {
  bool done_any = false;
  do {
    done_any = false;
    ColPartition_C_IT it(partners);
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      ColPartition* a = it.data();
      // Check for a match between all of a's partners (it1/b1) and all
      // of this's partners (it2/b2).
      ColPartition_C_IT it1(upper ? &a->upper_partners_ : &a->lower_partners_);
      for (it1.mark_cycle_pt(); !it1.cycled_list(); it1.forward()) {
        ColPartition* b1 = it1.data();
        if (b1 == this) {
          done_any = true;
          it.extract();
          a->RemovePartner(!upper, this);
          break;
        }
        ColPartition_C_IT it2(partners);
        for (it2.mark_cycle_pt(); !it2.cycled_list(); it2.forward()) {
          ColPartition* b2 = it2.data();
          if (b1 == b2) {
            // Jackpot! b2 should not be a partner of this.
            it2.extract();
            b2->RemovePartner(!upper, this);
            done_any = true;
            // That potentially invalidated all the iterators, so break out
            // and start again.
            break;
          }
        }
        if (done_any)
          break;
      }
      if (done_any)
        break;
    }
  } while (done_any && !partners->empty() && !partners->singleton());
}

// Keeps the partner with the longest sequence of singleton matching partners.
// Converts all others to pullout.
void ColPartition::RefineFlowingTextPartners(bool upper,
                                             ColPartition_CLIST* partners) {
  ColPartition_C_IT it(partners);
  ColPartition* best_partner = it.data();
  // Nasty iterative algorithm.
  int depth = 1;
  int survivors = 0;
  do {
    survivors = 0;
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      ColPartition* partner = it.data();
      // See if it survives a chase to depth levels.
      for (int i = 0; i < depth && partner != NULL; ++i) {
        partner = partner->SingletonPartner(upper);
        if (partner != NULL && partner->type_ != PT_FLOWING_TEXT)
          partner = NULL;
      }
      if (partner != NULL) {
        ++survivors;
        best_partner = it.data();
      }
    }
    ++depth;
  } while (survivors > 1 && depth <= kMaxPartnerDepth);
  // Keep only the best partner.
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    ColPartition* partner = it.data();
    if (partner != best_partner) {
      partner->RemovePartner(!upper, this);
      it.extract();
      // Change the types of partner to be PT_PULLOUT_TEXT.
      while (partner != NULL && partner->type_ == PT_FLOWING_TEXT) {
        partner->type_ = PT_PULLOUT_TEXT;
        partner = partner->SingletonPartner(upper);
      }
    }
  }
}

// Keep the partner with the biggest overlap.
void ColPartition::RefinePartnersByOverlap(bool upper,
                                           ColPartition_CLIST* partners) {
  ColPartition_C_IT it(partners);
  ColPartition* best_partner = it.data();
  // Find the partner with the best overlap.
  int best_overlap = 0;
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    ColPartition* partner = it.data();
    int overlap = MIN(bounding_box_.right(), partner->bounding_box_.right())
                - MAX(bounding_box_.left(), partner->bounding_box_.left());
    if (overlap > best_overlap) {
      best_overlap = overlap;
      best_partner = partner;
    }
  }
  // Keep only the best partner.
  for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
    ColPartition* partner = it.data();
    if (partner != best_partner) {
      partner->RemovePartner(!upper, this);
      it.extract();
    }
  }
}

// Return true if bbox belongs better in this than other.
bool ColPartition::ThisPartitionBetter(BLOBNBOX* bbox,
                                       const ColPartition& other) {
  TBOX box = bbox->bounding_box();
  // Margins take priority.
  int left = box.left();
  int right = box.right();
  if (left < left_margin_ || right > right_margin_)
    return false;
  if (left < other.left_margin_ || right > other.right_margin_)
    return true;
  int top = box.top();
  int bottom = box.bottom();
  int this_overlap = MIN(top, median_top_) - MAX(bottom, median_bottom_);
  int other_overlap = MIN(top, other.median_top_) -
                      MAX(bottom, other.median_bottom_);
  int this_miss = median_top_ - median_bottom_ - this_overlap;
  int other_miss = other.median_top_ - other.median_bottom_ - other_overlap;
  if (TabFind::WithinTestRegion(3, box.left(), box.bottom())) {
    tprintf("Unique on (%d,%d)->(%d,%d) overlap %d/%d, miss %d/%d, mt=%d/%d\n",
            box.left(), box.bottom(), box.right(), box.top(),
            this_overlap, other_overlap, this_miss, other_miss,
            median_top_, other.median_top_);
  }
  if (this_miss < other_miss)
    return true;
  if (this_miss > other_miss)
    return false;
  if (this_overlap > other_overlap)
    return true;
  if (this_overlap < other_overlap)
    return false;
  return median_top_ >= other.median_top_;
}

// Returns the median line-spacing between the current position and the end
// of the list.
// The iterator is passed by value so the iteration does not modify the
// caller's iterator.
static int MedianSpacing(int page_height, ColPartition_IT it) {
  STATS stats(0, page_height);
  while (!it.cycled_list()) {
    ColPartition* part = it.data();
    it.forward();
    stats.add(part->bottom_spacing(), 1);
    stats.add(part->top_spacing(), 1);
  }
  return static_cast<int>(stats.median() + 0.5);
}

// Smoothes the spacings in the list into groups of equal linespacing.
// resolution is the resolution of the original image, used as a basis
// for thresholds in change of spacing. page_height is in pixels.
void ColPartition::SmoothSpacings(int resolution, int page_height,
                                  ColPartition_LIST* parts) {
  // The task would be trivial if we didn't have to allow for blips -
  // occasional offsets in spacing caused by anomolous text, such as all
  // caps, groups of descenders, joined words, Arabic etc.
  // The neighbourhood stores a consecutive group of partitions so that
  // blips can be detected correctly, yet conservatively enough to not
  // mistake genuine spacing changes for blips. See example below.
  ColPartition* neighbourhood[PN_COUNT];
  ColPartition_IT it(parts);
  it.mark_cycle_pt();
  // Although we know nothing about the spacings is this list, the median is
  // used as an approximation to allow blips.
  // If parts of this block aren't spaced to the median, then we can't
  // accept blips in those parts, but we'll recalculate it each time we
  // split the block, so the median becomes more likely to match all the text.
  int median_space = MedianSpacing(page_height, it);
  ColPartition_IT start_it(it);
  ColPartition_IT end_it(it);
  for (int i = 0; i < PN_COUNT; ++i) {
    if (i < PN_UPPER || it.cycled_list()) {
      neighbourhood[i] = NULL;
    } else {
      if (i == PN_LOWER)
        end_it = it;
      neighbourhood[i] = it.data();
      it.forward();
    }
  }
  while (neighbourhood[PN_UPPER] != NULL) {
    // Test for end of a group. Normally SpacingsEqual is true within a group,
    // but in the case of a blip, it will be false. Here is an example:
    // Line enum   Spacing below (spacing between tops of lines)
    //  1   ABOVE2    20
    //  2   ABOVE1    20
    //  3   UPPER     15
    //  4   LOWER     25
    //  5   BELOW1    20
    //  6   BELOW2    20
    // Line 4 is all in caps (regular caps), so the spacing between line 3
    // and line 4 (looking at the tops) is smaller than normal, and the
    // spacing between line 4 and line 5 is larger than normal, but the
    // two of them add to twice the normal spacing.
    // The following if has to accept unequal spacings 3 times to pass the
    // blip (20/15, 15/25 and 25/20)
    // When the blip is in the middle, OKSpacingBlip tests that one of
    // ABOVE1 and BELOW1 matches the median.
    // The first time, everything is shifted down 1, so we present
    // OKSpacingBlip with neighbourhood+1 and check that PN_UPPER is median.
    // The last time, everything is shifted up 1, so we present OKSpacingBlip
    // with neighbourhood-1 and check that PN_LOWER matches the median.
    if (neighbourhood[PN_LOWER] == NULL ||
        (!neighbourhood[PN_UPPER]->SpacingsEqual(*neighbourhood[PN_LOWER],
                                                 resolution) &&
         !OKSpacingBlip(resolution, median_space, neighbourhood) &&
         (!OKSpacingBlip(resolution, median_space, neighbourhood - 1) ||
          !neighbourhood[PN_LOWER]->SpacingEqual(median_space, resolution)) &&
         (!OKSpacingBlip(resolution, median_space, neighbourhood + 1) ||
          !neighbourhood[PN_UPPER]->SpacingEqual(median_space, resolution)))) {
      // The group has ended. PN_UPPER is the last member.
      // Compute the mean spacing over the group.
      ColPartition_IT sum_it(start_it);
      ColPartition* last_part = neighbourhood[PN_UPPER];
      double total_bottom = 0.0;
      double total_top = 0.0;
      int total_count = 0;
      ColPartition* upper = sum_it.data();
      // We do not process last_part, as its spacing is different.
      while (upper != last_part) {
        total_bottom += upper->bottom_spacing();
        total_top += upper->top_spacing();
        ++total_count;
        sum_it.forward();
        upper = sum_it.data();
      }
      if (total_count > 0) {
        // There were at least 2 lines, so set them all to the mean.
        int top_spacing = static_cast<int>(total_top / total_count + 0.5);
        int bottom_spacing = static_cast<int>(total_bottom / total_count + 0.5);
        if (textord_debug_tabfind) {
          tprintf("Spacing run ended. Cause:");
          if (neighbourhood[PN_LOWER] == NULL) {
            tprintf("No more lines\n");
          } else {
            tprintf("Spacing change. Spacings:\n");
            for (int i = 0; i < PN_COUNT; ++i) {
              if (neighbourhood[i] == NULL) {
                tprintf("NULL\n");
              } else {
                tprintf("Top = %d, bottom = %d\n",
                        neighbourhood[i]->top_spacing(),
                        neighbourhood[i]->bottom_spacing());
              }
            }
          }
          tprintf("Mean spacing = %d/%d\n", top_spacing, bottom_spacing);
        }
        sum_it = start_it;
        upper = sum_it.data();
        while (upper != last_part) {
          upper->set_top_spacing(top_spacing);
          upper->set_bottom_spacing(bottom_spacing);
          if (textord_debug_tabfind) {
            tprintf("Setting mean on:");
            upper->Print();
          }
          sum_it.forward();
          upper = sum_it.data();
        }
      }
      // PN_LOWER starts the next group and end_it is the next start_it.
      start_it = end_it;
      // Recalculate the median spacing to maximize the chances of detecting
      // spacing blips.
      median_space = MedianSpacing(page_height, end_it);
    }
    // Shuffle pointers.
    for (int j = 1; j < PN_COUNT; ++j) {
      neighbourhood[j - 1] = neighbourhood[j];
    }
    if (it.cycled_list()) {
      neighbourhood[PN_COUNT - 1] = NULL;
    } else {
      neighbourhood[PN_COUNT - 1] = it.data();
      it.forward();
    }
    end_it.forward();
  }
}

// Returns true if the parts array of pointers to partitions matches the
// condition for a spacing blip. See SmoothSpacings for what this means
// and how it is used.
bool ColPartition::OKSpacingBlip(int resolution, int median_spacing,
                                 ColPartition** parts) {
  if (parts[PN_UPPER] == NULL || parts[PN_LOWER] == NULL)
    return false;
  // The blip is OK if upper and lower sum to an OK value and at least
  // one of above1 and below1 is equal to the median.
  return parts[PN_UPPER]->SummedSpacingOK(*parts[PN_LOWER],
                                          median_spacing, resolution) &&
         ((parts[PN_ABOVE1] != NULL &&
           parts[PN_ABOVE1]->SpacingEqual(median_spacing, resolution)) ||
          (parts[PN_BELOW1] != NULL &&
           parts[PN_BELOW1]->SpacingEqual(median_spacing, resolution)));
}

// Returns true if both the top and bottom spacings of this match the given
// spacing to within suitable margins dictated by the image resolution.
bool ColPartition::SpacingEqual(int spacing, int resolution) const {
  int bottom_error = BottomSpacingMargin(resolution);
  int top_error = TopSpacingMargin(resolution);
  return NearlyEqual(bottom_spacing_, spacing, bottom_error) &&
         NearlyEqual(top_spacing_, spacing, top_error);
}

// Returns true if both the top and bottom spacings of this and other
// match to within suitable margins dictated by the image resolution.
bool ColPartition::SpacingsEqual(const ColPartition& other,
                                 int resolution) const {
  int bottom_error = MAX(BottomSpacingMargin(resolution),
                         other.BottomSpacingMargin(resolution));
  int top_error = MAX(TopSpacingMargin(resolution),
                      other.TopSpacingMargin(resolution));
  return NearlyEqual(bottom_spacing_, other.bottom_spacing_, bottom_error) &&
         (NearlyEqual(top_spacing_, other.top_spacing_, top_error) ||
          NearlyEqual(top_spacing_ + other.top_spacing_, bottom_spacing_ * 2,
                      bottom_error));
}

// Returns true if the sum spacing of this and other match the given
// spacing (or twice the given spacing) to within a suitable margin dictated
// by the image resolution.
bool ColPartition::SummedSpacingOK(const ColPartition& other,
                                   int spacing, int resolution) const {
  int bottom_error = MAX(BottomSpacingMargin(resolution),
                         other.BottomSpacingMargin(resolution));
  int top_error = MAX(TopSpacingMargin(resolution),
                      other.TopSpacingMargin(resolution));
  int bottom_total = bottom_spacing_ + other.bottom_spacing_;
  int top_total = top_spacing_ + other.top_spacing_;
  return (NearlyEqual(spacing, bottom_total, bottom_error) &&
          NearlyEqual(spacing, top_total, top_error)) ||
         (NearlyEqual(spacing * 2, bottom_total, bottom_error) &&
          NearlyEqual(spacing * 2, top_total, top_error));
}

// Returns a suitable spacing margin that can be applied to bottoms of
// text lines, based on the resolution and the stored side_step_.
int ColPartition::BottomSpacingMargin(int resolution) const {
  return static_cast<int>(kMaxSpacingDrift * resolution + 0.5) + side_step_;
}

// Returns a suitable spacing margin that can be applied to tops of
// text lines, based on the resolution and the stored side_step_.
int ColPartition::TopSpacingMargin(int resolution) const {
  return static_cast<int>(kMaxTopSpacingFraction * median_size_ + 0.5) +
         BottomSpacingMargin(resolution);
}

// Returns true if the median text sizes of this and other agree to within
// a reasonable multiplicative factor.
bool ColPartition::SizesSimilar(const ColPartition& other) const {
  return median_size_ <= other.median_size_ * kMaxSizeRatio &&
         other.median_size_ <= median_size_ * kMaxSizeRatio;
}

// Computes and returns in start, end a line segment formed from a
// forwards-iterated group of left edges of partitions that satisfy the
// condition that the rightmost left margin is to the left of the
// leftmost left bounding box edge.
// TODO(rays) Not good enough. Needs improving to tightly wrap text in both
// directions, and to loosely wrap images.
void ColPartition::LeftEdgeRun(ColPartition_IT* part_it,
                               ICOORD* start, ICOORD* end) {
  ColPartition* part = part_it->data();
  int start_y = part->bounding_box_.top();
  if (!part_it->at_first() &&
      part_it->data_relative(-1)->bounding_box_.bottom() > start_y)
    start_y = (start_y + part_it->data_relative(-1)->bounding_box_.bottom())/2;
  int end_y = part->bounding_box_.bottom();
  int min_right = MAX_INT32;
  int max_left = MIN_INT32;
  do {
    part = part_it->data();
    int top = part->bounding_box_.top();
    int bottom = part->bounding_box_.bottom();
    int tl_key = part->SortKey(part->left_margin_, top);
    int tr_key = part->SortKey(part->bounding_box_.left(), top);
    int bl_key = part->SortKey(part->left_margin_, bottom);
    int br_key = part->SortKey(part->bounding_box_.left(), bottom);
    int left_key = MAX(tl_key, bl_key);
    int right_key = MIN(tr_key, br_key);
    if (left_key <= min_right && right_key >= max_left) {
      // This part is good - let's keep it.
      min_right = MIN(min_right, right_key);
      max_left = MAX(max_left, left_key);
      end_y = bottom;
      part_it->forward();
      if (!part_it->at_first() && part_it->data()->bounding_box_.top() < end_y)
        end_y = (end_y + part_it->data()->bounding_box_.top()) / 2;
    } else {
      if (textord_debug_tabfind)
        tprintf("Sum key %d/%d, new %d/%d\n",
                max_left, min_right, left_key, right_key);
      break;
    }
  } while (!part_it->at_first());
  start->set_y(start_y);
  start->set_x(part->XAtY(min_right, start_y));
  end->set_y(end_y);
  end->set_x(part->XAtY(min_right, end_y));
  if (textord_debug_tabfind && !part_it->at_first())
    tprintf("Left run from y=%d to %d terminated with sum %d-%d, new %d-%d\n",
            start_y, end_y, part->XAtY(max_left, end_y),
            end->x(), part->left_margin_, part->bounding_box_.left());
}

// Computes and returns in start, end a line segment formed from a
// backwards-iterated group of right edges of partitions that satisfy the
// condition that the leftmost right margin is to the right of the
// rightmost right bounding box edge.
// TODO(rays) Not good enough. Needs improving to tightly wrap text in both
// directions, and to loosely wrap images.
void ColPartition::RightEdgeRun(ColPartition_IT* part_it,
                                ICOORD* start, ICOORD* end) {
  ColPartition* part = part_it->data();
  int start_y = part->bounding_box_.bottom();
  if (!part_it->at_first() &&
      part_it->data_relative(1)->bounding_box_.top() < start_y)
    start_y = (start_y + part_it->data_relative(1)->bounding_box_.top()) / 2;
  int end_y = part->bounding_box_.top();
  int min_right = MAX_INT32;
  int max_left = MIN_INT32;
  do {
    part = part_it->data();
    int top = part->bounding_box_.top();
    int bottom = part->bounding_box_.bottom();
    int tl_key = part->SortKey(part->bounding_box_.right(), top);
    int tr_key = part->SortKey(part->right_margin_, top);
    int bl_key = part->SortKey(part->bounding_box_.right(), bottom);
    int br_key = part->SortKey(part->right_margin_, bottom);
    int left_key = MAX(tl_key, bl_key);
    int right_key = MIN(tr_key, br_key);
    if (left_key <= min_right && right_key >= max_left) {
      // This part is good - let's keep it.
      min_right = MIN(min_right, right_key);
      max_left = MAX(max_left, left_key);
      end_y = top;
      part_it->backward();
      if (!part_it->at_last() &&
          part_it->data()->bounding_box_.bottom() > end_y)
        end_y = (end_y + part_it->data()->bounding_box_.bottom()) / 2;
    } else {
      if (textord_debug_tabfind)
        tprintf("Sum cross %d/%d, new %d/%d\n",
                max_left, min_right, left_key, right_key);
      break;
    }
  } while (!part_it->at_last());
  start->set_y(start_y);
  start->set_x(part->XAtY(max_left, start_y));
  end->set_y(end_y);
  end->set_x(part->XAtY(max_left, end_y));
  if (textord_debug_tabfind && !part_it->at_last())
    tprintf("Right run from y=%d to %d terminated with sum %d-%d, new %d-%d\n",
            start_y, end_y, end->x(), part->XAtY(min_right, end_y),
            part->bounding_box_.right(), part->right_margin_);
}

}  // namespace tesseract.