# trimesh.registration

## registration.py

Functions for registering (aligning) point clouds with meshes.

trimesh.registration.icp(a, b, initial=array([[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 1., 0.], [0., 0., 0., 1.]]), threshold=1e-05, max_iterations=20, **kwargs)

Apply the iterative closest point algorithm to align a point cloud with another point cloud or mesh. Will only produce reasonable results if the initial transformation is roughly correct. Initial transformation can be found by applying Procrustes’ analysis to a suitable set of landmark points (often picked manually).

Parameters
• a ((n,3) float) – List of points in space.

• b ((m,3) float or Trimesh) – List of points in space or mesh.

• initial ((4,4) float) – Initial transformation.

• threshold (float) – Stop when change in cost is less than threshold

• max_iterations (int) – Maximum number of iterations

• kwargs (dict) – Args to pass to procrustes

Returns

• matrix ((4,4) float) – The transformation matrix sending a to b

• transformed ((n,3) float) – The image of a under the transformation

• cost (float) – The cost of the transformation

trimesh.registration.mesh_other(mesh, other, samples=500, scale=False, icp_first=10, icp_final=50, **kwargs)

Align a mesh with another mesh or a PointCloud using the principal axes of inertia as a starting point which is refined by iterative closest point.

Parameters
• mesh (trimesh.Trimesh object) – Mesh to align with other

• other (trimesh.Trimesh or (n, 3) float) – Mesh or points in space

• samples (int) – Number of samples from mesh surface to align

• scale (bool) – Allow scaling in transform

• icp_first (int) – How many ICP iterations for the 9 possible combinations of sign flippage

• icp_final (int) – How many ICP iterations for the closest candidate from the wider search

• kwargs (dict) – Passed through to icp, which passes through to procrustes

Returns

• mesh_to_other ((4, 4) float) – Transform to align mesh to the other object

• cost (float) – Average squared distance per point

trimesh.registration.nricp_amberg(source_mesh, target_geometry, source_landmarks=None, target_positions=None, steps=None, eps=0.0001, gamma=1, distance_threshold=0.1, return_records=False, use_faces=True, use_vertex_normals=True, neighbors_count=8)

Non Rigid Iterative Closest Points

Implementation of “Amberg et al. 2007: Optimal Step Nonrigid ICP Algorithms for Surface Registration.” Allows to register non-rigidly a mesh on another or on a point cloud. The core algorithm is explained at the end of page 3 of the paper.

Comparison between nricp_amberg and nricp_sumner: * nricp_amberg fits to the target mesh in less steps * nricp_amberg can generate sharp edges

• only vertices and their neighbors are considered

• nricp_sumner tend to preserve more the original shape

• nricp_sumner parameters are easier to tune

• nricp_sumner solves for triangle positions whereas nricp_amberg solves for vertex transforms

• nricp_sumner is less optimized when wn > 0

Parameters
• source_mesh (Trimesh) – Source mesh containing both vertices and faces.

• target_geometry (Trimesh or PointCloud or (n, 3) float) – Target geometry. It can contain no faces or be a PointCloud.

• source_landmarks ((n,) int or ((n,) int, (n, 3) float)) – n landmarks on the the source mesh. Represented as vertex indices (n,) int. It can also be represented as a tuple of triangle indices and barycentric coordinates ((n,) int, (n, 3) float,).

• target_positions ((n, 3) float) – Target positions assigned to source landmarks

• steps (Core parameters of the algorithm) – Iterable of iterables (ws, wl, wn, max_iter,). ws is smoothness term, wl weights landmark importance, wn normal importance and max_iter is the maximum number of iterations per step.

• eps (float) – If the error decrease if inferior to this value, the current step ends.

• gamma (float) – Weight the translation part against the rotational/skew part. Recommended value : 1.

• distance_threshold (float) – Distance threshold to account for a vertex match or not.

• return_records (bool) – If True, also returns all the intermediate results. It can help debugging and tune the parameters to match a specific case.

• use_faces (bool) – If True and if target geometry has faces, use proximity.closest_point to find matching points. Else use scipy’s cKDTree object.

• use_vertex_normals (bool) – If True and if target geometry has faces, interpolate the normals of the target geometry matching points. Else use face normals or estimated normals if target geometry has no faces.

• neighbors_count (int) – number of neighbors used for normal estimation. Only used if target geometry has no faces or if use_faces is False.

Returns

result – The vertices positions of source_mesh such that it is registered non-rigidly onto the target geometry. If return_records is True, it returns the list of the vertex positions at each iteration.

Return type

(n, 3) float or List[(n, 3) float]

trimesh.registration.nricp_sumner(source_mesh, target_geometry, source_landmarks=None, target_positions=None, steps=None, distance_threshold=0.1, return_records=False, use_faces=True, use_vertex_normals=True, neighbors_count=8, face_pairs_type='vertex')

Non Rigid Iterative Closest Points

Implementation of the correspondence computation part of “Sumner and Popovic 2004: Deformation Transfer for Triangle Meshes” Allows to register non-rigidly a mesh on another geometry.

Comparison between nricp_amberg and nricp_sumner: * nricp_amberg fits to the target mesh in less steps * nricp_amberg can generate sharp edges (only vertices and their

neighbors are considered)

• nricp_sumner tend to preserve more the original shape

• nricp_sumner parameters are easier to tune

• nricp_sumner solves for triangle positions whereas nricp_amberg solves for

vertex transforms

• nricp_sumner is less optimized when wn > 0

Parameters
• source_mesh (Trimesh) – Source mesh containing both vertices and faces.

• target_geometry (Trimesh or PointCloud or (n, 3) float) – Target geometry. It can contain no faces or be a PointCloud.

• source_landmarks ((n,) int or ((n,) int, (n, 3) float)) – n landmarks on the the source mesh. Represented as vertex indices (n,) int. It can also be represented as a tuple of triangle indices and barycentric coordinates ((n,) int, (n, 3) float,).

• target_positions ((n, 3) float) – Target positions assigned to source landmarks

• steps (Core parameters of the algorithm) – Iterable of iterables (wc, wi, ws, wl, wn). wc is the correspondence term (strength of fitting), wi is the identity term (recommended value : 0.001), ws is smoothness term, wl weights the landmark importance and wn the normal importance.

• distance_threshold (float) – Distance threshold to account for a vertex match or not.

• return_records (bool) – If True, also returns all the intermediate results. It can help debugging and tune the parameters to match a specific case.

• use_faces (bool) – If True and if target geometry has faces, use proximity.closest_point to find matching points. Else use scipy’s cKDTree object.

• use_vertex_normals (bool) – If True and if target geometry has faces, interpolate the normals of the target geometry matching points. Else use face normals or estimated normals if target geometry has no faces.

• neighbors_count (int) – number of neighbors used for normal estimation. Only used if target geometry has no faces or if use_faces is False.

• face_pairs_type (str 'vertex' or 'edge') – Method to determine face pairs used in the smoothness cost. ‘vertex’ yields smoother results.

Returns

result – The vertices positions of source_mesh such that it is registered non-rigidly onto the target geometry. If return_records is True, it returns the list of the vertex positions at each iteration.

Return type

(n, 3) float or List[(n, 3) float]

trimesh.registration.procrustes(a, b, weights=None, reflection=True, translation=True, scale=True, return_cost=True)

Perform Procrustes’ analysis subject to constraints. Finds the transformation T mapping a to b which minimizes the square sum distances between Ta and b, also called the cost. Optionally specify different weights for the points in a to minimize the weighted square sum distances between Ta and b. This can improve transformation robustness on noisy data if the points’ probability distribution is known.

Parameters
• a ((n,3) float) – List of points in space

• b ((n,3) float) – List of points in space

• weights ((n,) float) – List of floats representing how much weight is assigned to each point of a

• reflection (bool) – If the transformation is allowed reflections

• translation (bool) – If the transformation is allowed translations

• scale (bool) – If the transformation is allowed scaling

• return_cost (bool) – Whether to return the cost and transformed a as well

Returns

• matrix ((4,4) float) – The transformation matrix sending a to b

• transformed ((n,3) float) – The image of a under the transformation

• cost (float) – The cost of the transformation