使用 scipy RBFInterpolate 进行 3D 表面估计

Question

我正在尝试使用 scipy RBFInterpolate 中的 RBFInterpolate 函数对 3D 网格进行表面估计。我认为我遇到了完全错误的事情，但我无法弄清楚它是什么。当我在使用函数后绘制估计数据时，它看起来像这样：

黑色散点图是对网格原始数据的下采样，但正如您所见，该函数显然效果不佳。我尝试使用 scipy 中的函数 CloughTocher2DInterpolator 并获得了一些不错的结果，但是我想看看 RBFInterpolation 是否表现更好。 这是 CloughTocher2DInterpolator 的结果：

我用过的代码在这里：

import open3d as o3d
import numpy as np
from scipy.interpolate import CloughTocher2DInterpolator
from scipy.interpolate import RBFInterpolator
import matplotlib.pyplot as plt

mesh = o3d.io.read_triangle_mesh("..pathToMesh.ply")
#mesh = mesh.subdivide_loop(number_of_iterations=3)
samplingNumber = 3600
pcd = mesh.sample_points_uniformly(number_of_points=samplingNumber)
#pcd = mesh.sample_points_poisson_disk(number_of_points=500, pcl=pcd)

#o3d.visualization.draw_geometries([mesh])

## CONVERTING DATA TO NUMPY ARRAYS
points = np.asarray(pcd.points)
x = points[:, 0]
y = points[:, 1]
z = points[:, 2]

## CREATING GRID  & DOWNSAMLING ##
density = np.sqrt(samplingNumber).astype(int)
X = np.linspace(min(x), max(x), num=density)
Y = np.linspace(min(y), max(y), num=density)
X, Y = np.meshgrid(X, Y)  # 2D grid for interpolation

"""
## USING CloughTocher2DInterpolator FUNCTION ##
interp = CloughTocher2DInterpolator(np.array([x, y]).T, z, fill_value=-1.33, tol=1e-03)
Z = interp.__call__(X, Y)
"""

## USING RBFInterpolator FUNCTION ##
xy_points = np.stack([X.ravel(), Y.ravel()], -1) # shape (N, 2) in 2d

rbf = RBFInterpolator(xy_points, z, kernel='cubic', smoothing=0)
Z = rbf.__call__(xy_points).reshape(X.shape)

fig = plt.figure()
ax = plt.axes(projection='3d')

Z_new = Z.reshape(X.shape)
ax.scatter(x, y, z, marker=".", color='black', s=1)
#ax.contour3D(X, Y, Z, 75, cmap='BrBG_r')
#ax.plot_trisurf(x, y, z, cmap='viridis', edgecolor='none')
#ax.plot_wireframe(X, Y, Z, color='black')
ax.plot_surface(X, Y, Z_new, rstride=1, cstride=1, cmap='viridis', edgecolor='none')

ax.set_title('surface')

ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
plt.show()