Python實(shí)現(xiàn)曲線點(diǎn)抽稀算法的示例

本文介紹了Python實(shí)現(xiàn)曲線點(diǎn)抽稀算法的示例，分享給大家，具體如下：

目錄

何為抽稀

道格拉斯-普克(Douglas-Peuker)算法

垂距限值法

最后

正文

何為抽稀

在處理矢量化數(shù)據(jù)時(shí)，記錄中往往會(huì)有很多重復(fù)數(shù)據(jù)，對(duì)進(jìn)一步數(shù)據(jù)處理帶來諸多不便。多余的數(shù)據(jù)一方面浪費(fèi)了較多的存儲(chǔ)空間，另一方面造成所要表達(dá)的圖形不光滑或不符合標(biāo)準(zhǔn)。因此要通過某種規(guī)則，在保證矢量曲線形狀不變的情況下， 最大限度地減少數(shù)據(jù)點(diǎn)個(gè)數(shù)，這個(gè)過程稱為抽稀。

通俗的講就是對(duì)曲線進(jìn)行采樣簡(jiǎn)化，即在曲線上取有限個(gè)點(diǎn)，將其變?yōu)檎劬€，并且能夠在一定程度保持原有形狀。比較常用的兩種抽稀算法是：道格拉斯-普克(Douglas-Peuker)算法和垂距限值法。

道格拉斯-普克(Douglas-Peuker)算法

Douglas-Peuker算法(DP算法)過程如下:

1、連接曲線首尾兩點(diǎn)A、B；

2、依次計(jì)算曲線上所有點(diǎn)到A、B兩點(diǎn)所在曲線的距離；

3、計(jì)算最大距離D，如果D小于閾值threshold,則去掉曲線上出A、B外的所有點(diǎn)；如果D大于閾值threshold,則把曲線以最大距離分割成兩段；

4、對(duì)所有曲線分段重復(fù)1-3步驟，知道所有D均小于閾值。即完成抽稀。
這種算法的抽稀精度與閾值有很大關(guān)系，閾值越大，簡(jiǎn)化程度越大，點(diǎn)減少的越多；反之簡(jiǎn)化程度越低，點(diǎn)保留的越多，形狀也越趨于原曲線。

下面是Python代碼實(shí)現(xiàn):

# -*- coding: utf-8 -*-
"""------------------------------------------------- File Name：  DouglasPeuker Description : 道格拉斯-普克抽稀算法 Author :    J_hao date：     2017/8/16------------------------------------------------- Change Activity:         2017/8/16: 道格拉斯-普克抽稀算法-------------------------------------------------"""
from __future__ import division
 
from math import sqrt, pow
 
__author__ = 'J_hao'
 
THRESHOLD = 0.0001 # 閾值
 
 
def point2LineDistance(point_a, point_b, point_c):
  """  計(jì)算點(diǎn)a到點(diǎn)b c所在直線的距離  :param point_a:  :param point_b:  :param point_c:  :return:  """
  # 首先計(jì)算b c 所在直線的斜率和截距
  if point_b[0] == point_c[0]:
    return 9999999
  slope = (point_b[1] - point_c[1]) / (point_b[0] - point_c[0])
  intercept = point_b[1] - slope * point_b[0]
 
  # 計(jì)算點(diǎn)a到b c所在直線的距離
  distance = abs(slope * point_a[0] - point_a[1] + intercept) / sqrt(1 + pow(slope, 2))
  return distance
 
 
class DouglasPeuker(object):
  def__init__(self):
    self.threshold = THRESHOLD
    self.qualify_list = list()
    self.disqualify_list = list()
 
  def diluting(self, point_list):
    """    抽稀    :param point_list:二維點(diǎn)列表    :return:    """
    if len(point_list) < 3:
      self.qualify_list.extend(point_list[::-1])
    else:
      # 找到與收尾兩點(diǎn)連線距離最大的點(diǎn)
      max_distance_index, max_distance = 0, 0
      for index, point in enumerate(point_list):
        if index in [0, len(point_list) - 1]:
          continue
        distance = point2LineDistance(point, point_list[0], point_list[-1])
        if distance > max_distance:
          max_distance_index = index
          max_distance = distance
 
      # 若最大距離小于閾值，則去掉所有中間點(diǎn)。 反之，則將曲線按最大距離點(diǎn)分割
      if max_distance < self.threshold:
        self.qualify_list.append(point_list[-1])
        self.qualify_list.append(point_list[0])
      else:
        # 將曲線按最大距離的點(diǎn)分割成兩段
        sequence_a = point_list[:max_distance_index]
        sequence_b = point_list[max_distance_index:]
 
        for sequence in [sequence_a, sequence_b]:
          if len(sequence) < 3 and sequence == sequence_b:
            self.qualify_list.extend(sequence[::-1])
          else:
            self.disqualify_list.append(sequence)
 
  def main(self, point_list):
    self.diluting(point_list)
    while len(self.disqualify_list) > 0:
      self.diluting(self.disqualify_list.pop())
    print self.qualify_list
    print len(self.qualify_list)
 
 
if __name__ == '__main__':
  d = DouglasPeuker()
  d.main([[104.066228, 30.644527], [104.066279, 30.643528], [104.066296, 30.642528], [104.066314, 30.641529],
      [104.066332, 30.640529], [104.066383, 30.639530], [104.066400, 30.638530], [104.066451, 30.637531],
      [104.066468, 30.636532], [104.066518, 30.635533], [104.066535, 30.634533], [104.066586, 30.633534],
      [104.066636, 30.632536], [104.066686, 30.631537], [104.066735, 30.630538], [104.066785, 30.629539],
      [104.066802, 30.628539], [104.066820, 30.627540], [104.066871, 30.626541], [104.066888, 30.625541],
      [104.066906, 30.624541], [104.066924, 30.623541], [104.066942, 30.622542], [104.066960, 30.621542],
      [104.067011, 30.620543], [104.066122, 30.620086], [104.065124, 30.620021], [104.064124, 30.620022],
      [104.063124, 30.619990], [104.062125, 30.619958], [104.061125, 30.619926], [104.060126, 30.619894],
      [104.059126, 30.619895], [104.058127, 30.619928], [104.057518, 30.620722], [104.057625, 30.621716],
      [104.057735, 30.622710], [104.057878, 30.623700], [104.057984, 30.624694], [104.058094, 30.625688],
      [104.058204, 30.626682], [104.058315, 30.627676], [104.058425, 30.628670], [104.058502, 30.629667],
      [104.058518, 30.630667], [104.058503, 30.631667], [104.058521, 30.632666], [104.057664, 30.633182],
      [104.056664, 30.633174], [104.055664, 30.633166], [104.054672, 30.633289], [104.053758, 30.633694],
      [104.052852, 30.634118], [104.052623, 30.635091], [104.053145, 30.635945], [104.053675, 30.636793],
      [104.054200, 30.637643], [104.054756, 30.638475], [104.055295, 30.639317], [104.055843, 30.640153],
      [104.056387, 30.640993], [104.056933, 30.641830], [104.057478, 30.642669], [104.058023, 30.643507],
      [104.058595, 30.644327], [104.059152, 30.645158], [104.059663, 30.646018], [104.060171, 30.646879],
      [104.061170, 30.646855], [104.062168, 30.646781], [104.063167, 30.646823], [104.064167, 30.646814],
      [104.065163, 30.646725], [104.066157, 30.646618], [104.066231, 30.645620], [104.066247, 30.644621], ])

垂距限值法

垂距限值法其實(shí)和DP算法原理一樣，但是垂距限值不是從整體角度考慮，而是依次掃描每一個(gè)點(diǎn)，檢查是否符合要求。

算法過程如下:

1、以第二個(gè)點(diǎn)開始，計(jì)算第二個(gè)點(diǎn)到前一個(gè)點(diǎn)和后一個(gè)點(diǎn)所在直線的距離d；
2、如果d大于閾值，則保留第二個(gè)點(diǎn)，計(jì)算第三個(gè)點(diǎn)到第二個(gè)點(diǎn)和第四個(gè)點(diǎn)所在直線的距離d;若d小于閾值則舍棄第二個(gè)點(diǎn)，計(jì)算第三個(gè)點(diǎn)到第一個(gè)點(diǎn)和第四個(gè)點(diǎn)所在直線的距離d;
3、依次類推，直線曲線上倒數(shù)第二個(gè)點(diǎn)。

下面是Python代碼實(shí)現(xiàn)：

# -*- coding: utf-8 -*-
"""------------------------------------------------- File Name：  LimitVerticalDistance Description : 垂距限值抽稀算法 Author :    J_hao date：     2017/8/17------------------------------------------------- Change Activity:         2017/8/17:-------------------------------------------------"""
from __future__ import division
 
from math import sqrt, pow
 
__author__ = 'J_hao'
 
THRESHOLD = 0.0001 # 閾值
 
 
def point2LineDistance(point_a, point_b, point_c):
  """  計(jì)算點(diǎn)a到點(diǎn)b c所在直線的距離  :param point_a:  :param point_b:  :param point_c:  :return:  """
  # 首先計(jì)算b c 所在直線的斜率和截距
  if point_b[0] == point_c[0]:
    return 9999999
  slope = (point_b[1] - point_c[1]) / (point_b[0] - point_c[0])
  intercept = point_b[1] - slope * point_b[0]
 
  # 計(jì)算點(diǎn)a到b c所在直線的距離
  distance = abs(slope * point_a[0] - point_a[1] + intercept) / sqrt(1 + pow(slope, 2))
  return distance
 
 
class LimitVerticalDistance(object):
  def__init__(self):
    self.threshold = THRESHOLD
    self.qualify_list = list()
 
  def diluting(self, point_list):
    """    抽稀    :param point_list:二維點(diǎn)列表    :return:    """
    self.qualify_list.append(point_list[0])
    check_index = 1
    while check_index < len(point_list) - 1:
      distance = point2LineDistance(point_list[check_index],
                     self.qualify_list[-1],
                     point_list[check_index + 1])
 
      if distance < self.threshold:
        check_index += 1
      else:
        self.qualify_list.append(point_list[check_index])
        check_index += 1
    return self.qualify_list
 
 
if __name__ == '__main__':
  l = LimitVerticalDistance()
  diluting = l.diluting([[104.066228, 30.644527], [104.066279, 30.643528], [104.066296, 30.642528], [104.066314, 30.641529],
      [104.066332, 30.640529], [104.066383, 30.639530], [104.066400, 30.638530], [104.066451, 30.637531],
      [104.066468, 30.636532], [104.066518, 30.635533], [104.066535, 30.634533], [104.066586, 30.633534],
      [104.066636, 30.632536], [104.066686, 30.631537], [104.066735, 30.630538], [104.066785, 30.629539],
      [104.066802, 30.628539], [104.066820, 30.627540], [104.066871, 30.626541], [104.066888, 30.625541],
      [104.066906, 30.624541], [104.066924, 30.623541], [104.066942, 30.622542], [104.066960, 30.621542],
      [104.067011, 30.620543], [104.066122, 30.620086], [104.065124, 30.620021], [104.064124, 30.620022],
      [104.063124, 30.619990], [104.062125, 30.619958], [104.061125, 30.619926], [104.060126, 30.619894],
      [104.059126, 30.619895], [104.058127, 30.619928], [104.057518, 30.620722], [104.057625, 30.621716],
      [104.057735, 30.622710], [104.057878, 30.623700], [104.057984, 30.624694], [104.058094, 30.625688],
      [104.058204, 30.626682], [104.058315, 30.627676], [104.058425, 30.628670], [104.058502, 30.629667],
      [104.058518, 30.630667], [104.058503, 30.631667], [104.058521, 30.632666], [104.057664, 30.633182],
      [104.056664, 30.633174], [104.055664, 30.633166], [104.054672, 30.633289], [104.053758, 30.633694],
      [104.052852, 30.634118], [104.052623, 30.635091], [104.053145, 30.635945], [104.053675, 30.636793],
      [104.054200, 30.637643], [104.054756, 30.638475], [104.055295, 30.639317], [104.055843, 30.640153],
      [104.056387, 30.640993], [104.056933, 30.641830], [104.057478, 30.642669], [104.058023, 30.643507],
      [104.058595, 30.644327], [104.059152, 30.645158], [104.059663, 30.646018], [104.060171, 30.646879],
      [104.061170, 30.646855], [104.062168, 30.646781], [104.063167, 30.646823], [104.064167, 30.646814],
      [104.065163, 30.646725], [104.066157, 30.646618], [104.066231, 30.645620], [104.066247, 30.644621], ])
  print len(diluting)
  print(diluting)

最后

其實(shí)DP算法和垂距限值法原理一樣，DP算法是從整體上考慮一條完整的曲線，實(shí)現(xiàn)時(shí)較垂距限值法復(fù)雜，但垂距限值法可能會(huì)在某些情況下導(dǎo)致局部最優(yōu)。另外在實(shí)際使用中發(fā)現(xiàn)采用點(diǎn)到另外兩點(diǎn)所在直線距離的方法來判斷偏離，在曲線弧度比較大的情況下比較準(zhǔn)確。如果在曲線弧度比較小，彎??程度不明顯時(shí)，這種方法抽稀效果不是很理想，建議使用三點(diǎn)所圍成的三角形面積作為判斷標(biāo)準(zhǔn)。下面是抽稀效果:

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