点云关键点、对应关系、热力图可视化总结

点云可视化常用的库是open3d，其中关于关键点、对应关系、热力图的可视化却几乎没有博客讲解，本文填补这一空缺，为点云配准的研究工作提供便利

关键点可视化

关键点可以在显著图上采样得到，使用keypoints_to_spheres函数可以可以绘制出球状的关键点，其中radius参数控制球的半径

import torch
import open3d as o3d
import numpy as npdef sample_interest_points(method, scores, N):"""We can do random sampling, probabilistic sampling, or top-k sampling"""assert method in ['prob', 'topk', 'random']n = scores.sizeif n < N:choice = np.random.choice(n, N)else:if method == 'random':choice = np.random.permutation(n)[:N]elif method == 'topk':choice = torch.topk(torch.from_numpy(scores), N, dim=0)[1].numpy()elif method == 'prob':idx = np.arange(n)probs = (scores / scores.sum()).flatten()choice = np.random.choice(idx, size=N, replace=False, p=probs)return choicedef keypoints_to_spheres(keypoints, color):spheres = o3d.geometry.TriangleMesh()for keypoint in keypoints.points:sphere = o3d.geometry.TriangleMesh.create_sphere(radius=0.015)sphere.translate(keypoint)spheres += sphereif color == 1:spheres.paint_uniform_color([1, 0, 0])else:spheres.paint_uniform_color([0, 0, 1])return spheresif __name__ == '__main__':src_raw = np.load('../src_raw_19.npy')# scores = np.load('../scores.npy')M, _ = src_raw.shapescores = np.random.uniform(0,1,M)src_idx = sample_interest_points('prob', scores, 500)src_keypts = src_raw[src_idx]raw1 = o3d.geometry.PointCloud()raw1.points = o3d.utility.Vector3dVector(src_raw)raw1.estimate_normals()radii = [0.005, 0.01, 0.02, 0.04]rec_mesh1 = o3d.geometry.TriangleMesh.create_from_point_cloud_ball_pivoting(raw1, o3d.utility.DoubleVector(radii))raw1.paint_uniform_color([107/255, 175/255, 214/255])keypts1 = o3d.geometry.PointCloud()keypts1.points = o3d.utility.Vector3dVector(src_keypts)mesh_box1 = keypoints_to_spheres(keypts1, 1)o3d.visualization.draw_geometries([raw1, rec_mesh1, mesh_box1])

对应关系可视化

建立对应关系（correspondences）是点云配准的重要步骤，可以通过匹配算法（如最近邻匹配，ransac, sinkhorn）等方法得到对应关系。我们通常希望直观看到我们预测的对应关系有哪些是正确的，哪些是错误的。真值可以根据变换矩阵变换点云之后判断对应点，下图中绿色线代表正确对应关系，红色线代表错误对应关系。

import glob,os
import open3d as o3d
import numpy as np
import torch
from matplotlib import cmdef sample_interest_points(method, scores, N):"""We can do random sampling, probabilistic sampling, or top-k sampling"""assert method in ['prob', 'topk', 'random']n = scores.sizeif n < N:choice = np.random.choice(n, N)else:if method == 'random':choice = np.random.permutation(n)[:N]elif method == 'topk':choice = torch.topk(torch.from_numpy(scores), N, dim=0)[1].numpy()elif method == 'prob':idx = np.arange(n)probs = (scores / scores.sum()).flatten()choice = np.random.choice(idx, size=N, replace=False, p=probs)return choicedef keypoints_to_spheres(keypoints, color):spheres = o3d.geometry.TriangleMesh()for keypoint in keypoints.points:sphere = o3d.geometry.TriangleMesh.create_sphere(radius=0.050)sphere.translate(keypoint)# sphere.paint_uniform_color(color[i])spheres += sphere# spheres.vertex_colors = o3d.utility.Vector3dVector(color)spheres.paint_uniform_color(color)return spheressrc_raw = np.load('../src_raw.npy')
tgt_raw = np.load('../tgt_raw.npy')
src_pcd = np.load('../src_pcd.npy')[:70]
tgt_pcd = np.load('../tgt_pcd.npy')[:70]
gt = np.load('../gt.npy')src_raw = src_raw.dot(gt[:3,:3].T) + gt[:3,3]
src_pcd = src_pcd.dot(gt[:3,:3].T) + gt[:3,3]
# 拉大点云距离，方便可视化
delta = [3,0.2,0.5]
src_raw += delta
src_pcd += delta
# 可视化关键点和源点云
pcd1 = o3d.geometry.PointCloud()
pcd1.points = o3d.utility.Vector3dVector(src_raw)
pcd1.estimate_normals()
radii = [0.005, 0.01, 0.02, 0.04]
rec_mesh1 = o3d.geometry.TriangleMesh.create_from_point_cloud_ball_pivoting(pcd1, o3d.utility.DoubleVector(radii))
pcd1.paint_uniform_color([249/255, 180/255, 2/255])pcd2 = o3d.geometry.PointCloud()
pcd2.points = o3d.utility.Vector3dVector(tgt_raw)
pcd2.estimate_normals()
radii = [0.005, 0.01, 0.02, 0.04]
rec_mesh2 = o3d.geometry.TriangleMesh.create_from_point_cloud_ball_pivoting(pcd1, o3d.utility.DoubleVector(radii))
pcd2.paint_uniform_color([107 / 255, 175 / 255, 214 / 255])# 画线
frag = np.concatenate([src_pcd, tgt_pcd], 0)
n = src_pcd.shape[0]
lines = np.zeros([n, 2])
lines[:, 0] = np.linspace(0, n - 1, n)
lines[:, 1] = np.linspace(0, n - 1, n) + n
line_set = o3d.geometry.LineSet(points=o3d.utility.Vector3dVector(frag),lines=o3d.utility.Vector2iVector(lines),
)
# 判断哪些是正确的线
src_points_T = src_pcd - delta
mask = np.sum((src_points_T - tgt_pcd)**2,axis=1) < 0.1
colors = np.zeros((n,3))
colors[mask] = [0,255,0]
colors[~mask] = [255,0,0]
line_set.colors = o3d.utility.Vector3dVector(colors)# 可视化对应关系
o3d.visualization.draw_geometries([pcd1,pcd2,line_set])

热力图可视化

点云热力图即根据每个点的取值赋予其相应的颜色，整体上形成一个颜色分布图。比如当我求得了显著性的分布图(M $\times$ 1维)，则可以使用cm.get_cmap函数计算其颜色，又或者当求得特征图时(M $\times$ 32维)，需要先用tsne降维到(M $\times$ 1)，再用同样流程可视化。

import open3d as o3d
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from sklearn.manifold import TSNEdef make_open3d_point_cloud(xyz, color=None):pcd = o3d.geometry.PointCloud()pcd.points = o3d.utility.Vector3dVector(xyz)if color is not None:pcd.colors = o3d.utility.Vector3dVector(color)return pcddef get_color_map(x):# colours = plt.cm.Spectral(x)viridis = cm.get_cmap('Oranges', 8)colours = viridis(x).squeeze()return colours[:, :3]def embed_tsne(data):"""N x D np.array data"""tsne = TSNE(n_components=1, verbose=1, perplexity=40, n_iter=300, random_state=1)tsne_results = tsne.fit_transform(data)tsne_results = np.squeeze(tsne_results)tsne_min = np.min(tsne_results)tsne_max = np.max(tsne_results)return (tsne_results - tsne_min) / (tsne_max - tsne_min)if __name__ == '__main__':show_saliency = Trueshow_feature = Falsexyzr0 = np.load('../src_raw_19.npy')M, _ = xyzr0.shapeif show_saliency:# 每个点有一个显著性得分，可视化显著性热力图# scores = np.load('../data/scores.npy')scores = np.random.uniform(0,1,M)elif show_feature:# 每个点有一个特征向量，则先用tsne降维，再可视化# feature = np.load('../data/feature.npy')feature = np.random.rand(M, 32)scores = embed_tsne(feature)else:scores = Noneexit()scores = (scores - np.min(scores)) / (np.max(scores) - np.min(scores))color = get_color_map(scores)pcd = make_open3d_point_cloud(xyzr0, color)o3d.visualization.draw_geometries([pcd])

以下展示随机生成一个显著性图的热力图可视化结果：

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