Open3D Intrinsic shape signatures (ISS) 固有形状特征码

Intrinsic shape signatures (ISS) 固有形状特征码

在本教程中，我们将展示如何检测 3D 形状的 ISS 关键点。该实现基于于忠提出的关键点检测模块，“内在形状特征：用于3D对象识别的形状描述符”，2009年。（ Yu Zhong , “Intrinsic Shape Signatures: A Shape Descriptor for 3D Object Recognition）

ISS Keypoints

ISS 显著性测度基于属于$p$的点的散射矩阵$\Sigma (p)$的特征值分解（EVD）。
$$\Sigma (p)=\frac{1}{N}\sum _{q\in N(p)}(q-{\mu }_p)(q-{\mu }_p)Twith{\mu }_p=\frac{1}{N}\sum _{q\in N(p)}q$$
给定$\Sigma (p)$，其数量级数量级递减的特征值在这里表示为 λ1、λ2、λ3。在修剪阶段，保留两个连续特征值之间比率低于阈值的点：
$$\frac{\lambda 2(p)}{\lambda 1(p)}<{\gamma }_{12}\wedge \frac{\lambda 3(p)}{\lambda 2(p)}<{\gamma }_{23}$$
其基本原理是避免在沿主要方向表现出类似扩散的点上检测关键点，在这些点上无法建立可重复的规范参考系，因此，随后的描述阶段很难变得有效。在其余点中，显著性由最小特征值的大小决定
$$\rho (p)\doteq \lambda 3(p)$$
以便仅包括沿每个主方向变化较大的点。

在检测步骤之后，如果某个点在给定邻域上具有最大显著性值，则该点将被视为关键点。

注意：有关更多详细信息，请参考原始出版物或Tombari et.al 的“3D关键点探测器的性能评估”(Performance Evaluation of 3D Keypoint Detectors)。

ISS keypoint detection example ISS 关键点检测示例

#Intrinsic shape siqnatures
import open3d as o3d
import time

# Compute ISS Keypoints on ArmadilloMesh
armadillo_path = r'../data/ArmadilloMesh.ply'
mesh = o3d.io.read_triangle_mesh(armadillo_path)
mesh.compute_vertex_normals()

pcd = o3d.geometry.PointCloud()
pcd.points = mesh.vertices

tic = time.time()
keypoints = o3d.geometry.keypoint.compute_iss_keypoints(pcd)
toc = 1000 * (time.time() - tic)
print("ISS Computation took {:.0f} [ms]".format(toc))

mesh.compute_vertex_normals()
mesh.paint_uniform_color([0.5, 0.5, 0.5])
keypoints.paint_uniform_color([1.0, 0.75, 0.0])
o3d.visualization.draw_geometries([keypoints, mesh])

# This function is only used to make the keypoints look better on the rendering
def keypoints_to_spheres(keypoints):
    spheres = o3d.geometry.TriangleMesh()
    for keypoint in keypoints.points:
        sphere = o3d.geometry.TriangleMesh.create_sphere(radius=0.001)
        sphere.translate(keypoint)
        spheres += sphere
    spheres.paint_uniform_color([1.0, 0.75, 0.0])
    return spheres

# Compute ISS Keypoints on Standford BunnyMesh, changing the default parameters
bunny_path = r'../data/BunnyMesh.ply'
mesh = o3d.io.read_triangle_mesh(bunny_path)
mesh.compute_vertex_normals()

pcd = o3d.geometry.PointCloud()
pcd.points = mesh.vertices

tic = time.time()
keypoints = o3d.geometry.keypoint.compute_iss_keypoints(pcd,
                                                        salient_radius=0.005,
                                                        non_max_radius=0.005,
                                                        gamma_21=0.5,
                                                        gamma_32=0.5)
toc = 1000 * (time.time() - tic)
print("ISS Computation took {:.0f} [ms]".format(toc))

mesh.compute_vertex_normals()
mesh.paint_uniform_color([0.5, 0.5, 0.5])
o3d.visualization.draw_geometries([keypoints_to_spheres(keypoints), mesh])