如何用Python快速提取单个GeoDataFrame中的重叠与孤立几何图形？

问题背景 #

我用geopandas.GeoSeries.buffer给一个包含点几何的大型GeoDataFrame生成了缓冲多边形，现在需要把这些缓冲区分成两个GeoDataFrame：

• 包含所有重叠多边形的GeoDataFrame
• 包含所有孤立多边形的GeoDataFrame

在QGIS里我会用「按位置选择」工具，选择「重叠」几何谓词，让缓冲图层和自身对比，选出重叠的实体，反转选择就是孤立的。但在Python里我用循环遍历每个几何，调用geopandas.GeoSeries.overlaps逐个检查，速度慢得离谱——QGIS只需要40秒，Python跑了1小时20分钟。有没有办法让Python的处理速度接近QGIS？

我之前用的低效代码：

# 生成点缓冲
points = gpd.read_file("path_to_my_layer.gpkg")
buffer = points.copy()
buffer.geometry = points.geometry.buffer(3)

# 检查重叠
overlaps_ids = np.array([], dtype=np.int64)
for geom in buffer.geometry:  # 这里耗时极长
    overlaps = buffer.geometry.overlaps(geom)  # 检查哪些要素和当前几何重叠
    where_overlaps = np.where(overlaps == True)
    overlaps_ids = np.concatenate((overlaps_ids, where_overlaps[0]))
overlaps_ids = np.unique(overlaps_ids)  # 去重得到重叠要素的ID

# 提取重叠的几何
buffer_overlaps = buffer.iloc[overlaps_ids]

# 提取不重叠的几何
buffer_no_overlaps = buffer.drop(overlaps_ids)

低效原因 #

原来的代码是**O(n²)**的全量对比：每个要素都要和整个GeoSeries的所有要素做重叠检查，完全没有利用空间索引过滤候选要素，这也是为什么速度远慢于QGIS——QGIS底层默认用R-tree空间索引先筛选出可能重叠的要素，再做精确检查。

优化方案 #

以下两种方法都基于空间索引优化，性能可以接近QGIS：

方法1：手动利用空间索引筛选候选 #

import geopandas as gpd
import numpy as np

# 读取数据并生成缓冲
points = gpd.read_file("path_to_my_layer.gpkg")
buffer = points.copy()
buffer.geometry = points.geometry.buffer(3)

# 构建R-tree空间索引
sindex = buffer.sindex

# 用集合存储重叠ID（自动去重，比numpy数组拼接高效）
overlapping_ids = set()

for idx, geom in buffer.geometry.items():
    # 用空间索引快速找到可能重叠的候选要素ID（排除自身）
    candidate_ids = list(sindex.query(geom, predicate="overlaps"))
    candidate_ids = [cid for cid in candidate_ids if cid != idx]
    
    if candidate_ids:
        # 将当前ID和候选ID都标记为重叠
        overlapping_ids.add(idx)
        overlapping_ids.update(candidate_ids)

# 转换为numpy数组方便索引
overlapping_ids = np.array(list(overlapping_ids), dtype=np.int64)

# 提取重叠和孤立图层
buffer_overlaps = buffer.loc[overlapping_ids]
buffer_no_overlaps = buffer.drop(overlapping_ids)

方法2：用空间自连接（更简洁） #

Geopandas的gpd.sjoin底层已集成空间索引优化，直接用图层自连接实现QGIS「按位置选择」的逻辑：

import geopandas as gpd
import numpy as np

# 读取数据并生成缓冲
points = gpd.read_file("path_to_my_layer.gpkg")
buffer = points.copy()
buffer.geometry = points.geometry.buffer(3)

# 缓冲图层自连接，只保留重叠的要素对
joined = gpd.sjoin(buffer, buffer, how="inner", predicate="overlaps")

# 提取所有参与重叠的唯一要素ID
overlapping_ids = np.unique(joined.index.unique())

# 提取重叠和孤立图层
buffer_overlaps = buffer.loc[overlapping_ids]
buffer_no_overlaps = buffer.drop(overlapping_ids)

关键优化点 #

1. 空间索引过滤：用R-tree空间索引快速缩小需要检查的要素范围，把复杂度从O(n²)降到O(n log n)
2. 高效去重：用集合存储ID避免重复拼接数组，或者用unique()直接提取连接结果的唯一索引
3. 排除自身对比：提前排除要素和自身的对比（overlaps方法本身也会返回False，但提前排除能减少不必要的计算）

内容的提问来源于stack exchange，提问作者Grobino