解决方案是使用分层聚类算法将大型点云划分为几个较小的子集,在每个子集上运行Alphashape算法并将结果合并。该方法可以大大减少内存占用和运行时间,避免出现意外的多边形产生。
代码示例:
import numpy as np
from sklearn.cluster import MiniBatchKMeans
from scipy.spatial import ConvexHull, Delaunay
def alphashape(points, alpha):
tri = Delaunay(points)
edges = set()
edge_points = []
for i, j, k in tri.vertices:
if i < j:
edges.add((i, j))
edge_points.append(points[[i, j]])
if j < k:
edges.add((j, k))
edge_points.append(points[[j, k]])
if k < i:
edges.add((k, i))
edge_points.append(points[[k, i]])
edge_points = np.array(edge_points)
radii = np.sum((points[edge_points[:, 0]] - points[edge_points[:, 1]]) ** 2, axis=1)
too_small = radii < alpha ** 2
edges = np.array(list(edges))
edge_points = edge_points[too_small]
clusters = MiniBatchKMeans(n_clusters=int(len(points) / 500), batch_size=min(len(points) / 5, 10000)).fit_predict(points)
polygon_points = []
for c in np.unique(clusters):
c_points = points[clusters == c]
c_edge_points = edge_points[(clusters[edges[:, 0]] == c) & (clusters[edges[:, 1]] == c)]
hull = ConvexHull(c_points)
for simplex in hull.simplices:
polygon_points.append(c_points[simplex])
if c_edge_points.size > 0:
c_alpha_points = []
for i, j in c_edge_points:
if radii[(edges[:, 0] == i) & (edges[:, 1] == j)][0] < alpha ** 2:
c_alpha_points.append(np.intersect1d(edge_points[(edges[:, 0] == i) & (edges[:, 1] == j)][0], c_points))
if len(c_alpha_points) > 0:
polygon_points.append(np.vstack(c_alpha_points))
return polygon_points
在这里,MiniBatchKMeans类用于将点云划分为多个子集,而ConvexHull和Delaunay类分别用于计算凸包和三角剖分。edges变量包含所有Delaunay三角形的边缘(去重),而edge_points变量包含所有边缘点。最后,通过合并所有多边形可得到完整的Alpha形状。