content: # Copyright 2017 The TensorFlow Authors. All Rights Reserved.
  #
  # 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.
  # ==============================================================================
  
  """Operations for [N, 4] numpy arrays representing bounding boxes.
  
  Example box operations that are supported:
    * Areas: compute bounding box areas
    * IOU: pairwise intersection-over-union scores
  """
  from __future__ import (
      absolute_import,
      division,
      print_function,
      unicode_literals,
  )
  import numpy as np
  
  
  def area(boxes):
      """Computes area of boxes.
  
      Args:
        boxes: Numpy array with shape [N, 4] holding N boxes
  
      Returns:
        a numpy array with shape [N*1] representing box areas
      """
      return (boxes[:, 2] - boxes[:, 0]) * (boxes[:, 3] - boxes[:, 1])
  
  
  def intersection(boxes1, boxes2):
      """Compute pairwise intersection areas between boxes.
  
      Args:
        boxes1: a numpy array with shape [N, 4] holding N boxes
        boxes2: a numpy array with shape [M, 4] holding M boxes
  
      Returns:
        a numpy array with shape [N*M] representing pairwise intersection area
      """
      [y_min1, x_min1, y_max1, x_max1] = np.split(boxes1, 4, axis=1)
      [y_min2, x_min2, y_max2, x_max2] = np.split(boxes2, 4, axis=1)
  
      all_pairs_min_ymax = np.minimum(y_max1, np.transpose(y_max2))
      all_pairs_max_ymin = np.maximum(y_min1, np.transpose(y_min2))
      intersect_heights = np.maximum(
          np.zeros(all_pairs_max_ymin.shape),
          all_pairs_min_ymax - all_pairs_max_ymin,
      )
      all_pairs_min_xmax = np.minimum(x_max1, np.transpose(x_max2))
      all_pairs_max_xmin = np.maximum(x_min1, np.transpose(x_min2))
      intersect_widths = np.maximum(
          np.zeros(all_pairs_max_xmin.shape),
          all_pairs_min_xmax - all_pairs_max_xmin,
      )
      return intersect_heights * intersect_widths
  
  
  def iou(boxes1, boxes2):
      """Computes pairwise intersection-over-union between box collections.
  
      Args:
        boxes1: a numpy array with shape [N, 4] holding N boxes.
        boxes2: a numpy array with shape [M, 4] holding N boxes.
  
      Returns:
        a numpy array with shape [N, M] representing pairwise iou scores.
      """
      intersect = intersection(boxes1, boxes2)
      area1 = area(boxes1)
      area2 = area(boxes2)
      union = (
          np.expand_dims(area1, axis=1)
          + np.expand_dims(area2, axis=0)
          - intersect
      )
      return intersect / union
  
  
  def ioa(boxes1, boxes2):
      """Computes pairwise intersection-over-area between box collections.
  
      Intersection-over-area (ioa) between two boxes box1 and box2 is defined as
      their intersection area over box2's area. Note that ioa is not symmetric,
      that is, IOA(box1, box2) != IOA(box2, box1).
  
      Args:
        boxes1: a numpy array with shape [N, 4] holding N boxes.
        boxes2: a numpy array with shape [M, 4] holding N boxes.
  
      Returns:
        a numpy array with shape [N, M] representing pairwise ioa scores.
      """
      intersect = intersection(boxes1, boxes2)
      areas = np.expand_dims(area(boxes2), axis=0)
      return intersect / areas
  