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+<main>
+<article id="content">
+<header>
+<h1 class="title">Module <code>pymskt.statistics.main</code></h1>
+</header>
+<section id="section-intro">
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">from re import sub
+import numpy as np
+from datetime import date
+import os
+import pyvista as pv
+import pyacvd
+from pymskt.mesh.meshRegistration import get_icp_transform, non_rigidly_register
+from pymskt.mesh.meshTools import get_mesh_physical_point_coords, set_mesh_physical_point_coords, resample_surface
+from pymskt.mesh.meshTransform import apply_transform
+from pymskt.mesh.utils import get_symmetric_surface_distance, vtk_deep_copy
+from pymskt.mesh import io
+today = date.today()
+class FindReferenceMeshICP:
+    &#34;&#34;&#34;
+    For list of meshes perform all possible ICP registrations to identify mesh with smallest
+    surface error to all other meshes.
+    Parameters
+    ----------
+    list_meshes : _type_
+        _description_
+    &#34;&#34;&#34;
+    def __init__(
+        self,
+        list_mesh_paths,
+        max_n_iter=1000,
+        n_landmarks=1000,
+        reg_mode=&#39;similarity&#39;,
+        verbose=True
+    ):
+        &#34;&#34;&#34;
+        Perform ICP registration between all pairs of meshes. Calculate
+        symmetric surface distance for all registered meshes. Find target
+        mesh with smallest mean surface error to all other meshes.
+        This smallest error mesh is the refrence mesh for the next step of
+        SSM pipelines (procrustes using non-rigid registration)
+        Parameters
+        ----------
+        list_mesh_paths : _type_
+            _description_
+        max_n_iter : int, optional
+            _description_, by default 1000
+        n_landmarks : int, optional
+            _description_, by default 1000
+        reg_mode : str, optional
+            _description_, by default &#39;similarity&#39;
+        verbose : bool, optional
+            _description_, by default True
+        &#34;&#34;&#34;
+        self.list_mesh_paths = list_mesh_paths
+        self.n_meshes = len(list_mesh_paths)
+        self._symm_surface_distances = np.zeros((self.n_meshes, self.n_meshes), dtype=float)
+        self._mean_errors = None
+        self.max_n_iter = max_n_iter
+        self.n_landmarks = n_landmarks
+        self.reg_mode = reg_mode
+        self.verbose=verbose
+        self._ref_idx = None
+        self._ref_path = None
+    def register_meshes(self, idx1_target, idx2_source):
+        target = io.read_vtk(self.list_mesh_paths[idx1_target])
+        source = io.read_vtk(self.list_mesh_paths[idx2_source])
+        icp_transform = get_icp_transform(
+            source,
+            target,
+            max_n_iter=self.max_n_iter,
+            n_landmarks=self.n_landmarks,
+            reg_mode=self.reg_mode
+        )
+        transformed_source = apply_transform(source, icp_transform)
+        symmetric_surf_distance = get_symmetric_surface_distance(target, transformed_source)
+        self._symm_surface_distances[idx1_target, idx2_source] = symmetric_surf_distance
+    def get_template_idx(self):
+        self._mean_errors = np.mean(self._symm_surface_distances, axis=1)
+        self._ref_idx = np.argmin(self._mean_errors)
+        self._ref_path = self.list_mesh_paths[self._ref_idx]
+    def execute(self):
+        if self.verbose is True:
+            print(f&#39;Starting registrations, there are {len(self.list_mesh_paths)} meshes&#39;)
+        for idx1_target, target_path in enumerate(self.list_mesh_paths):
+            if self.verbose is True:
+                print(f&#39;\tStarting target mesh {idx1_target}&#39;)
+            for idx2_source, source_path in enumerate(self.list_mesh_paths):
+                if self.verbose is True:
+                    print(f&#39;\t\tStarting source mesh {idx2_source}&#39;)
+                # If the target &amp; mesh are same skip, errors = 0
+                if idx1_target == idx2_source:
+                    continue
+                else:
+                    self.register_meshes(idx1_target, idx2_source)
+        if self.verbose is True:
+            print(&#39;Finished all registrations!&#39;)
+        self.get_template_idx()
+    @property
+    def ref_idx(self):
+        return self._ref_idx
+    @property
+    def ref_path(self):
+        return self._ref_path
+    @property
+    def symm_surface_distances(self):
+        return self._symm_surface_distances
+    @property
+    def mean_errors(self):
+        return self._mean_errors
+class ProcrustesRegistration:
+    # https://en.wikipedia.org/wiki/Generalized_Procrustes_analysis
+    def __init__(
+        self,
+        path_ref_mesh,
+        list_mesh_paths,
+        tolerance1=2e-1,
+        tolerance2=1e-2,
+        max_n_registration_steps=10,
+        verbose=True,
+        remesh_each_step=False,
+        patience=2,
+        ref_mesh_eigenmap_as_reference=True,
+        registering_secondary_bone=False,    # True if registering secondary bone of joint, after
+                                             # primary already used for initial registration. E.g.,
+                                             # already did femur for knee, now applying to tibia/patella
+        **kwargs
+    ):
+        self.path_ref_mesh = path_ref_mesh
+        self.list_mesh_paths = list_mesh_paths
+        # Ensure that path_ref_mesh is in list &amp; at index 0
+        if self.path_ref_mesh in self.list_mesh_paths:
+            path_ref_idx = self.list_mesh_paths.index(self.path_ref_mesh)
+            self.list_mesh_paths.pop(path_ref_idx)
+        self.list_mesh_paths.insert(0, self.path_ref_mesh)
+        self._ref_mesh = io.read_vtk(self.path_ref_mesh)
+        self.n_points = self._ref_mesh.GetNumberOfPoints()
+        self.ref_mesh_eigenmap_as_reference = ref_mesh_eigenmap_as_reference
+        self.mean_mesh = None
+        self.tolerance1 = tolerance1
+        self.tolerance2 = tolerance2
+        self.max_n_registration_steps = max_n_registration_steps
+        self.kwargs = kwargs
+        # ORIGINALLY THIS WAS THE LOGIC:
+        # Ensure that the source mesh (mean, or reference) is the base mesh
+        # We want all meshes aligned with this reference. Then we want
+        # to apply a &#34;warp&#34; of the ref/mean mesh to make it
+        # EXCETION - if we are registering a secondary bone in a joint model
+        # E.g., for registering tibia/patella in knee model.
+        self.kwargs[&#39;icp_register_first&#39;] = True
+        if registering_secondary_bone is False:
+            self.kwargs[&#39;icp_reg_target_to_source&#39;] = True
+        elif registering_secondary_bone is True:
+            self.kwargs[&#39;icp_reg_target_to_source&#39;] = False
+        self._registered_pt_coords = np.zeros((len(list_mesh_paths), self.n_points, 3), dtype=float)
+        self._registered_pt_coords[0, :, :] = get_mesh_physical_point_coords(self._ref_mesh)
+        self.sym_error = 100
+        self.list_errors = []
+        self.list_ref_meshes = []
+        self.reg_idx = 0
+        self.patience = patience
+        self.patience_idx = 0
+        self._best_score = 100
+        self.verbose = verbose
+        self.remesh_each_step = remesh_each_step
+        self.error_2_error_change = 100
+    def register(self, ref_mesh_source, other_mesh_idx):
+        target_mesh = io.read_vtk(self.list_mesh_paths[other_mesh_idx])
+        registered_mesh = non_rigidly_register(
+            target_mesh=target_mesh,
+            source_mesh=ref_mesh_source,
+            target_eigenmap_as_reference=not self.ref_mesh_eigenmap_as_reference,
+            **self.kwargs
+        )
+        return get_mesh_physical_point_coords(registered_mesh)
+    def execute(self):
+        # create placeholder to store registered point clouds &amp; update inherited one only if also storing
+        registered_pt_coords = np.zeros_like(self._registered_pt_coords)
+        # keep doing registrations until max# is hit, or the minimum error between registrations is hit.
+        while (
+            (self.reg_idx &lt; self.max_n_registration_steps) &amp;
+            (self.sym_error &gt; self.tolerance1) &amp;
+            (self.error_2_error_change &gt; self.tolerance2)
+        ):
+            if self.verbose is True:
+                print(f&#39;Starting registration round {self.reg_idx}&#39;)
+            # If its not the very first iteration - check whether or not we want to re-mesh after every iteration.
+            if (self.reg_idx != 0) &amp; (self.remesh_each_step is True):
+                n_points = self._ref_mesh.GetNumberOfPoints()
+                self._ref_mesh = resample_surface(self._ref_mesh, subdivisions=2, clusters=n_points)
+                if n_points != self.n_points:
+                    print(f&#39;Updating n_points for mesh from {self.n_points} to {self._ref_mesh.GetNumberOfPoints()}&#39;)
+                    # re-create the array to store registered points as the # vertices might change after re-meshing.
+                    # also update n_points.
+                    self.n_points = n_points
+                    registered_pt_coords = np.zeros((len(self.list_mesh_paths), self.n_points, 3), dtype=float)
+            # register the reference mesh to all other meshes
+            for idx, path in enumerate(self.list_mesh_paths):
+                if self.verbose is True:
+                    print(f&#39;\tRegistering to mesh # {idx}&#39;)
+                # skip the first mesh in the list if its the first round (its the reference)
+                if (self.reg_idx == 0) &amp; (idx == 0):
+                    # first iteration &amp; ref mesh, just use points as they are.
+                    registered_pt_coords[idx, :, :] = get_mesh_physical_point_coords(self._ref_mesh)
+                    continue
+                # register &amp; save registered coordinates in the pre-allocated array
+                registered_pt_coords[idx, :, :] = self.register(self._ref_mesh, idx)
+            # Calculate the mean bone shape &amp; create new mean bone shape mesh
+            mean_shape = np.mean(registered_pt_coords, axis=0)
+            mean_mesh = vtk_deep_copy(self._ref_mesh)
+            set_mesh_physical_point_coords(mean_mesh, mean_shape)
+            # store in list of reference meshes
+            self.list_ref_meshes.append(mean_mesh)
+            # Get surface distance between previous reference mesh and the new mean
+            sym_error = get_symmetric_surface_distance(self._ref_mesh, mean_mesh)
+            self.error_2_error_change = np.abs(sym_error - self.sym_error)
+            self.sym_error = sym_error
+            if self.sym_error &gt;= self._best_score:
+                # if the error isnt going down, then keep track of that and done save the
+                # new reference mesh.
+                self.patience_idx += 1
+            else:
+                self.patience_idx = 0
+                # ONLY UPDATE THE REF_MESH or the REGISTERED_PTS WHEN THE INTER-MESH (REF) ERROR GETS BETTER
+                # NOT SURE IF THIS IS A GOOD IDEA - MIGHT WANT A BETTER CRITERIA?
+                self._ref_mesh = mean_mesh
+                self._registered_pt_coords = registered_pt_coords
+            # Store the symmetric error values so they can be plotted later
+            self.list_errors.append(self.sym_error)
+            if self.verbose is True:
+                print(f&#39;\t\tSymmetric surface error: {self.sym_error}&#39;)
+            if self.patience_idx &gt;= self.patience:
+                print(f&#39;Early stopping initiated - no improvment for {self.patience_idx} iterations, patience is: {self.patience}&#39;)
+                break
+            self.reg_idx += 1
+    def save_meshes(
+        self,
+        mesh_suffix=f&#39;procrustes_registered_{today.strftime(&#34;%b&#34;)}_{today.day}_{today.year}&#39;,
+        folder=None
+    ):
+        if folder is not None:
+            os.makedirs(folder, exist_ok=True)
+        mesh = vtk_deep_copy(self._ref_mesh)
+        for idx, path in enumerate(self.list_mesh_paths):
+            # parse folder / filename for saving
+            orig_folder = os.path.dirname(path)
+            orig_filename = os.path.basename(path)
+            base_filename = orig_filename[: orig_filename.rfind(&#34;.&#34;)]
+            filename = f&#39;{base_filename}_{mesh_suffix}_{idx}.vtk&#39;
+            if folder is None:
+                path_to_save = os.path.join(orig_folder, filename)
+            else:
+                path_to_save = os.path.join(os.path.abspath(folder), filename)
+            # Keep recycling the same base mesh, just move the x/y/z point coords around.
+            set_mesh_physical_point_coords(mesh, self._registered_pt_coords[idx, :, :])
+            # save mesh to disk
+            io.write_vtk(mesh, path_to_save)
+    def save_ref_mesh(self, path):
+        io.write_vtk(self._ref_mesh, path)
+    @property
+    def ref_mesh(self):
+        return self._ref_mesh
+    @property
+    def registered_pt_coords(self):
+        return self._registered_pt_coords
+    </code></pre>
+</details>
+</section>
+<section>
+</section>
+<section>
+</section>
+<section>
+</section>
+<section>
+<h2 class="section-title" id="header-classes">Classes</h2>
+<dl>
+<dt id="pymskt.statistics.main.FindReferenceMeshICP"><code class="flex name class">
+<span>class <span class="ident">FindReferenceMeshICP</span></span>
+<span>(</span><span>list_mesh_paths, max_n_iter=1000, n_landmarks=1000, reg_mode='similarity', verbose=True)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>For list of meshes perform all possible ICP registrations to identify mesh with smallest
+surface error to all other meshes. </p>
+<h2 id="parameters">Parameters</h2>
+<dl>
+<dt><strong><code>list_meshes</code></strong> :&ensp;<code>_type_</code></dt>
+<dd><em>description</em></dd>
+</dl>
+<p>Perform ICP registration between all pairs of meshes. Calculate
+symmetric surface distance for all registered meshes. Find target
+mesh with smallest mean surface error to all other meshes. </p>
+<p>This smallest error mesh is the refrence mesh for the next step of
+SSM pipelines (procrustes using non-rigid registration)</p>
+<h2 id="parameters_1">Parameters</h2>
+<dl>
+<dt><strong><code>list_mesh_paths</code></strong> :&ensp;<code>_type_</code></dt>
+<dd><em>description</em></dd>
+<dt><strong><code>max_n_iter</code></strong> :&ensp;<code>int</code>, optional</dt>
+<dd><em>description</em>, by default 1000</dd>
+<dt><strong><code>n_landmarks</code></strong> :&ensp;<code>int</code>, optional</dt>
+<dd><em>description</em>, by default 1000</dd>
+<dt><strong><code>reg_mode</code></strong> :&ensp;<code>str</code>, optional</dt>
+<dd><em>description</em>, by default 'similarity'</dd>
+<dt><strong><code>verbose</code></strong> :&ensp;<code>bool</code>, optional</dt>
+<dd><em>description</em>, by default True</dd>
+</dl></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">class FindReferenceMeshICP:
+    &#34;&#34;&#34;
+    For list of meshes perform all possible ICP registrations to identify mesh with smallest
+    surface error to all other meshes.
+    Parameters
+    ----------
+    list_meshes : _type_
+        _description_
+    &#34;&#34;&#34;
+    def __init__(
+        self,
+        list_mesh_paths,
+        max_n_iter=1000,
+        n_landmarks=1000,
+        reg_mode=&#39;similarity&#39;,
+        verbose=True
+    ):
+        &#34;&#34;&#34;
+        Perform ICP registration between all pairs of meshes. Calculate
+        symmetric surface distance for all registered meshes. Find target
+        mesh with smallest mean surface error to all other meshes.
+        This smallest error mesh is the refrence mesh for the next step of
+        SSM pipelines (procrustes using non-rigid registration)
+        Parameters
+        ----------
+        list_mesh_paths : _type_
+            _description_
+        max_n_iter : int, optional
+            _description_, by default 1000
+        n_landmarks : int, optional
+            _description_, by default 1000
+        reg_mode : str, optional
+            _description_, by default &#39;similarity&#39;
+        verbose : bool, optional
+            _description_, by default True
+        &#34;&#34;&#34;
+        self.list_mesh_paths = list_mesh_paths
+        self.n_meshes = len(list_mesh_paths)
+        self._symm_surface_distances = np.zeros((self.n_meshes, self.n_meshes), dtype=float)
+        self._mean_errors = None
+        self.max_n_iter = max_n_iter
+        self.n_landmarks = n_landmarks
+        self.reg_mode = reg_mode
+        self.verbose=verbose
+        self._ref_idx = None
+        self._ref_path = None
+    def register_meshes(self, idx1_target, idx2_source):
+        target = io.read_vtk(self.list_mesh_paths[idx1_target])
+        source = io.read_vtk(self.list_mesh_paths[idx2_source])
+        icp_transform = get_icp_transform(
+            source,
+            target,
+            max_n_iter=self.max_n_iter,
+            n_landmarks=self.n_landmarks,
+            reg_mode=self.reg_mode
+        )
+        transformed_source = apply_transform(source, icp_transform)
+        symmetric_surf_distance = get_symmetric_surface_distance(target, transformed_source)
+        self._symm_surface_distances[idx1_target, idx2_source] = symmetric_surf_distance
+    def get_template_idx(self):
+        self._mean_errors = np.mean(self._symm_surface_distances, axis=1)
+        self._ref_idx = np.argmin(self._mean_errors)
+        self._ref_path = self.list_mesh_paths[self._ref_idx]
+    def execute(self):
+        if self.verbose is True:
+            print(f&#39;Starting registrations, there are {len(self.list_mesh_paths)} meshes&#39;)
+        for idx1_target, target_path in enumerate(self.list_mesh_paths):
+            if self.verbose is True:
+                print(f&#39;\tStarting target mesh {idx1_target}&#39;)
+            for idx2_source, source_path in enumerate(self.list_mesh_paths):
+                if self.verbose is True:
+                    print(f&#39;\t\tStarting source mesh {idx2_source}&#39;)
+                # If the target &amp; mesh are same skip, errors = 0
+                if idx1_target == idx2_source:
+                    continue
+                else:
+                    self.register_meshes(idx1_target, idx2_source)
+        if self.verbose is True:
+            print(&#39;Finished all registrations!&#39;)
+        self.get_template_idx()
+    @property
+    def ref_idx(self):
+        return self._ref_idx
+    @property
+    def ref_path(self):
+        return self._ref_path
+    @property
+    def symm_surface_distances(self):
+        return self._symm_surface_distances
+    @property
+    def mean_errors(self):
+        return self._mean_errors</code></pre>
+</details>
+<h3>Instance variables</h3>
+<dl>
+<dt id="pymskt.statistics.main.FindReferenceMeshICP.mean_errors"><code class="name">var <span class="ident">mean_errors</span></code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">@property
+def mean_errors(self):
+    return self._mean_errors</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.FindReferenceMeshICP.ref_idx"><code class="name">var <span class="ident">ref_idx</span></code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">@property
+def ref_idx(self):
+    return self._ref_idx</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.FindReferenceMeshICP.ref_path"><code class="name">var <span class="ident">ref_path</span></code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">@property
+def ref_path(self):
+    return self._ref_path</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.FindReferenceMeshICP.symm_surface_distances"><code class="name">var <span class="ident">symm_surface_distances</span></code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">@property
+def symm_surface_distances(self):
+    return self._symm_surface_distances</code></pre>
+</details>
+</dd>
+</dl>
+<h3>Methods</h3>
+<dl>
+<dt id="pymskt.statistics.main.FindReferenceMeshICP.execute"><code class="name flex">
+<span>def <span class="ident">execute</span></span>(<span>self)</span>
+</code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def execute(self):
+    if self.verbose is True:
+        print(f&#39;Starting registrations, there are {len(self.list_mesh_paths)} meshes&#39;)
+    for idx1_target, target_path in enumerate(self.list_mesh_paths):
+        if self.verbose is True:
+            print(f&#39;\tStarting target mesh {idx1_target}&#39;)
+        for idx2_source, source_path in enumerate(self.list_mesh_paths):
+            if self.verbose is True:
+                print(f&#39;\t\tStarting source mesh {idx2_source}&#39;)
+            # If the target &amp; mesh are same skip, errors = 0
+            if idx1_target == idx2_source:
+                continue
+            else:
+                self.register_meshes(idx1_target, idx2_source)
+    if self.verbose is True:
+        print(&#39;Finished all registrations!&#39;)
+    self.get_template_idx()</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.FindReferenceMeshICP.get_template_idx"><code class="name flex">
+<span>def <span class="ident">get_template_idx</span></span>(<span>self)</span>
+</code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def get_template_idx(self):
+    self._mean_errors = np.mean(self._symm_surface_distances, axis=1)
+    self._ref_idx = np.argmin(self._mean_errors)
+    self._ref_path = self.list_mesh_paths[self._ref_idx]</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.FindReferenceMeshICP.register_meshes"><code class="name flex">
+<span>def <span class="ident">register_meshes</span></span>(<span>self, idx1_target, idx2_source)</span>
+</code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def register_meshes(self, idx1_target, idx2_source):
+    target = io.read_vtk(self.list_mesh_paths[idx1_target])
+    source = io.read_vtk(self.list_mesh_paths[idx2_source])
+    icp_transform = get_icp_transform(
+        source,
+        target,
+        max_n_iter=self.max_n_iter,
+        n_landmarks=self.n_landmarks,
+        reg_mode=self.reg_mode
+    )
+    transformed_source = apply_transform(source, icp_transform)
+    symmetric_surf_distance = get_symmetric_surface_distance(target, transformed_source)
+    self._symm_surface_distances[idx1_target, idx2_source] = symmetric_surf_distance</code></pre>
+</details>
+</dd>
+</dl>
+</dd>
+<dt id="pymskt.statistics.main.ProcrustesRegistration"><code class="flex name class">
+<span>class <span class="ident">ProcrustesRegistration</span></span>
+<span>(</span><span>path_ref_mesh, list_mesh_paths, tolerance1=0.2, tolerance2=0.01, max_n_registration_steps=10, verbose=True, remesh_each_step=False, patience=2, ref_mesh_eigenmap_as_reference=True, registering_secondary_bone=False, **kwargs)</span>
+</code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">class ProcrustesRegistration:
+    # https://en.wikipedia.org/wiki/Generalized_Procrustes_analysis
+    def __init__(
+        self,
+        path_ref_mesh,
+        list_mesh_paths,
+        tolerance1=2e-1,
+        tolerance2=1e-2,
+        max_n_registration_steps=10,
+        verbose=True,
+        remesh_each_step=False,
+        patience=2,
+        ref_mesh_eigenmap_as_reference=True,
+        registering_secondary_bone=False,    # True if registering secondary bone of joint, after
+                                             # primary already used for initial registration. E.g.,
+                                             # already did femur for knee, now applying to tibia/patella
+        **kwargs
+    ):
+        self.path_ref_mesh = path_ref_mesh
+        self.list_mesh_paths = list_mesh_paths
+        # Ensure that path_ref_mesh is in list &amp; at index 0
+        if self.path_ref_mesh in self.list_mesh_paths:
+            path_ref_idx = self.list_mesh_paths.index(self.path_ref_mesh)
+            self.list_mesh_paths.pop(path_ref_idx)
+        self.list_mesh_paths.insert(0, self.path_ref_mesh)
+        self._ref_mesh = io.read_vtk(self.path_ref_mesh)
+        self.n_points = self._ref_mesh.GetNumberOfPoints()
+        self.ref_mesh_eigenmap_as_reference = ref_mesh_eigenmap_as_reference
+        self.mean_mesh = None
+        self.tolerance1 = tolerance1
+        self.tolerance2 = tolerance2
+        self.max_n_registration_steps = max_n_registration_steps
+        self.kwargs = kwargs
+        # ORIGINALLY THIS WAS THE LOGIC:
+        # Ensure that the source mesh (mean, or reference) is the base mesh
+        # We want all meshes aligned with this reference. Then we want
+        # to apply a &#34;warp&#34; of the ref/mean mesh to make it
+        # EXCETION - if we are registering a secondary bone in a joint model
+        # E.g., for registering tibia/patella in knee model.
+        self.kwargs[&#39;icp_register_first&#39;] = True
+        if registering_secondary_bone is False:
+            self.kwargs[&#39;icp_reg_target_to_source&#39;] = True
+        elif registering_secondary_bone is True:
+            self.kwargs[&#39;icp_reg_target_to_source&#39;] = False
+        self._registered_pt_coords = np.zeros((len(list_mesh_paths), self.n_points, 3), dtype=float)
+        self._registered_pt_coords[0, :, :] = get_mesh_physical_point_coords(self._ref_mesh)
+        self.sym_error = 100
+        self.list_errors = []
+        self.list_ref_meshes = []
+        self.reg_idx = 0
+        self.patience = patience
+        self.patience_idx = 0
+        self._best_score = 100
+        self.verbose = verbose
+        self.remesh_each_step = remesh_each_step
+        self.error_2_error_change = 100
+    def register(self, ref_mesh_source, other_mesh_idx):
+        target_mesh = io.read_vtk(self.list_mesh_paths[other_mesh_idx])
+        registered_mesh = non_rigidly_register(
+            target_mesh=target_mesh,
+            source_mesh=ref_mesh_source,
+            target_eigenmap_as_reference=not self.ref_mesh_eigenmap_as_reference,
+            **self.kwargs
+        )
+        return get_mesh_physical_point_coords(registered_mesh)
+    def execute(self):
+        # create placeholder to store registered point clouds &amp; update inherited one only if also storing
+        registered_pt_coords = np.zeros_like(self._registered_pt_coords)
+        # keep doing registrations until max# is hit, or the minimum error between registrations is hit.
+        while (
+            (self.reg_idx &lt; self.max_n_registration_steps) &amp;
+            (self.sym_error &gt; self.tolerance1) &amp;
+            (self.error_2_error_change &gt; self.tolerance2)
+        ):
+            if self.verbose is True:
+                print(f&#39;Starting registration round {self.reg_idx}&#39;)
+            # If its not the very first iteration - check whether or not we want to re-mesh after every iteration.
+            if (self.reg_idx != 0) &amp; (self.remesh_each_step is True):
+                n_points = self._ref_mesh.GetNumberOfPoints()
+                self._ref_mesh = resample_surface(self._ref_mesh, subdivisions=2, clusters=n_points)
+                if n_points != self.n_points:
+                    print(f&#39;Updating n_points for mesh from {self.n_points} to {self._ref_mesh.GetNumberOfPoints()}&#39;)
+                    # re-create the array to store registered points as the # vertices might change after re-meshing.
+                    # also update n_points.
+                    self.n_points = n_points
+                    registered_pt_coords = np.zeros((len(self.list_mesh_paths), self.n_points, 3), dtype=float)
+            # register the reference mesh to all other meshes
+            for idx, path in enumerate(self.list_mesh_paths):
+                if self.verbose is True:
+                    print(f&#39;\tRegistering to mesh # {idx}&#39;)
+                # skip the first mesh in the list if its the first round (its the reference)
+                if (self.reg_idx == 0) &amp; (idx == 0):
+                    # first iteration &amp; ref mesh, just use points as they are.
+                    registered_pt_coords[idx, :, :] = get_mesh_physical_point_coords(self._ref_mesh)
+                    continue
+                # register &amp; save registered coordinates in the pre-allocated array
+                registered_pt_coords[idx, :, :] = self.register(self._ref_mesh, idx)
+            # Calculate the mean bone shape &amp; create new mean bone shape mesh
+            mean_shape = np.mean(registered_pt_coords, axis=0)
+            mean_mesh = vtk_deep_copy(self._ref_mesh)
+            set_mesh_physical_point_coords(mean_mesh, mean_shape)
+            # store in list of reference meshes
+            self.list_ref_meshes.append(mean_mesh)
+            # Get surface distance between previous reference mesh and the new mean
+            sym_error = get_symmetric_surface_distance(self._ref_mesh, mean_mesh)
+            self.error_2_error_change = np.abs(sym_error - self.sym_error)
+            self.sym_error = sym_error
+            if self.sym_error &gt;= self._best_score:
+                # if the error isnt going down, then keep track of that and done save the
+                # new reference mesh.
+                self.patience_idx += 1
+            else:
+                self.patience_idx = 0
+                # ONLY UPDATE THE REF_MESH or the REGISTERED_PTS WHEN THE INTER-MESH (REF) ERROR GETS BETTER
+                # NOT SURE IF THIS IS A GOOD IDEA - MIGHT WANT A BETTER CRITERIA?
+                self._ref_mesh = mean_mesh
+                self._registered_pt_coords = registered_pt_coords
+            # Store the symmetric error values so they can be plotted later
+            self.list_errors.append(self.sym_error)
+            if self.verbose is True:
+                print(f&#39;\t\tSymmetric surface error: {self.sym_error}&#39;)
+            if self.patience_idx &gt;= self.patience:
+                print(f&#39;Early stopping initiated - no improvment for {self.patience_idx} iterations, patience is: {self.patience}&#39;)
+                break
+            self.reg_idx += 1
+    def save_meshes(
+        self,
+        mesh_suffix=f&#39;procrustes_registered_{today.strftime(&#34;%b&#34;)}_{today.day}_{today.year}&#39;,
+        folder=None
+    ):
+        if folder is not None:
+            os.makedirs(folder, exist_ok=True)
+        mesh = vtk_deep_copy(self._ref_mesh)
+        for idx, path in enumerate(self.list_mesh_paths):
+            # parse folder / filename for saving
+            orig_folder = os.path.dirname(path)
+            orig_filename = os.path.basename(path)
+            base_filename = orig_filename[: orig_filename.rfind(&#34;.&#34;)]
+            filename = f&#39;{base_filename}_{mesh_suffix}_{idx}.vtk&#39;
+            if folder is None:
+                path_to_save = os.path.join(orig_folder, filename)
+            else:
+                path_to_save = os.path.join(os.path.abspath(folder), filename)
+            # Keep recycling the same base mesh, just move the x/y/z point coords around.
+            set_mesh_physical_point_coords(mesh, self._registered_pt_coords[idx, :, :])
+            # save mesh to disk
+            io.write_vtk(mesh, path_to_save)
+    def save_ref_mesh(self, path):
+        io.write_vtk(self._ref_mesh, path)
+    @property
+    def ref_mesh(self):
+        return self._ref_mesh
+    @property
+    def registered_pt_coords(self):
+        return self._registered_pt_coords</code></pre>
+</details>
+<h3>Instance variables</h3>
+<dl>
+<dt id="pymskt.statistics.main.ProcrustesRegistration.ref_mesh"><code class="name">var <span class="ident">ref_mesh</span></code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">@property
+def ref_mesh(self):
+    return self._ref_mesh</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.ProcrustesRegistration.registered_pt_coords"><code class="name">var <span class="ident">registered_pt_coords</span></code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">@property
+def registered_pt_coords(self):
+    return self._registered_pt_coords</code></pre>
+</details>
+</dd>
+</dl>
+<h3>Methods</h3>
+<dl>
+<dt id="pymskt.statistics.main.ProcrustesRegistration.execute"><code class="name flex">
+<span>def <span class="ident">execute</span></span>(<span>self)</span>
+</code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def execute(self):
+    # create placeholder to store registered point clouds &amp; update inherited one only if also storing
+    registered_pt_coords = np.zeros_like(self._registered_pt_coords)
+    # keep doing registrations until max# is hit, or the minimum error between registrations is hit.
+    while (
+        (self.reg_idx &lt; self.max_n_registration_steps) &amp;
+        (self.sym_error &gt; self.tolerance1) &amp;
+        (self.error_2_error_change &gt; self.tolerance2)
+    ):
+        if self.verbose is True:
+            print(f&#39;Starting registration round {self.reg_idx}&#39;)
+        # If its not the very first iteration - check whether or not we want to re-mesh after every iteration.
+        if (self.reg_idx != 0) &amp; (self.remesh_each_step is True):
+            n_points = self._ref_mesh.GetNumberOfPoints()
+            self._ref_mesh = resample_surface(self._ref_mesh, subdivisions=2, clusters=n_points)
+            if n_points != self.n_points:
+                print(f&#39;Updating n_points for mesh from {self.n_points} to {self._ref_mesh.GetNumberOfPoints()}&#39;)
+                # re-create the array to store registered points as the # vertices might change after re-meshing.
+                # also update n_points.
+                self.n_points = n_points
+                registered_pt_coords = np.zeros((len(self.list_mesh_paths), self.n_points, 3), dtype=float)
+        # register the reference mesh to all other meshes
+        for idx, path in enumerate(self.list_mesh_paths):
+            if self.verbose is True:
+                print(f&#39;\tRegistering to mesh # {idx}&#39;)
+            # skip the first mesh in the list if its the first round (its the reference)
+            if (self.reg_idx == 0) &amp; (idx == 0):
+                # first iteration &amp; ref mesh, just use points as they are.
+                registered_pt_coords[idx, :, :] = get_mesh_physical_point_coords(self._ref_mesh)
+                continue
+            # register &amp; save registered coordinates in the pre-allocated array
+            registered_pt_coords[idx, :, :] = self.register(self._ref_mesh, idx)
+        # Calculate the mean bone shape &amp; create new mean bone shape mesh
+        mean_shape = np.mean(registered_pt_coords, axis=0)
+        mean_mesh = vtk_deep_copy(self._ref_mesh)
+        set_mesh_physical_point_coords(mean_mesh, mean_shape)
+        # store in list of reference meshes
+        self.list_ref_meshes.append(mean_mesh)
+        # Get surface distance between previous reference mesh and the new mean
+        sym_error = get_symmetric_surface_distance(self._ref_mesh, mean_mesh)
+        self.error_2_error_change = np.abs(sym_error - self.sym_error)
+        self.sym_error = sym_error
+        if self.sym_error &gt;= self._best_score:
+            # if the error isnt going down, then keep track of that and done save the
+            # new reference mesh.
+            self.patience_idx += 1
+        else:
+            self.patience_idx = 0
+            # ONLY UPDATE THE REF_MESH or the REGISTERED_PTS WHEN THE INTER-MESH (REF) ERROR GETS BETTER
+            # NOT SURE IF THIS IS A GOOD IDEA - MIGHT WANT A BETTER CRITERIA?
+            self._ref_mesh = mean_mesh
+            self._registered_pt_coords = registered_pt_coords
+        # Store the symmetric error values so they can be plotted later
+        self.list_errors.append(self.sym_error)
+        if self.verbose is True:
+            print(f&#39;\t\tSymmetric surface error: {self.sym_error}&#39;)
+        if self.patience_idx &gt;= self.patience:
+            print(f&#39;Early stopping initiated - no improvment for {self.patience_idx} iterations, patience is: {self.patience}&#39;)
+            break
+        self.reg_idx += 1</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.ProcrustesRegistration.register"><code class="name flex">
+<span>def <span class="ident">register</span></span>(<span>self, ref_mesh_source, other_mesh_idx)</span>
+</code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def register(self, ref_mesh_source, other_mesh_idx):
+    target_mesh = io.read_vtk(self.list_mesh_paths[other_mesh_idx])
+    registered_mesh = non_rigidly_register(
+        target_mesh=target_mesh,
+        source_mesh=ref_mesh_source,
+        target_eigenmap_as_reference=not self.ref_mesh_eigenmap_as_reference,
+        **self.kwargs
+    )
+    return get_mesh_physical_point_coords(registered_mesh)</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.ProcrustesRegistration.save_meshes"><code class="name flex">
+<span>def <span class="ident">save_meshes</span></span>(<span>self, mesh_suffix='procrustes_registered_Jul_31_2022', folder=None)</span>
+</code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def save_meshes(
+    self,
+    mesh_suffix=f&#39;procrustes_registered_{today.strftime(&#34;%b&#34;)}_{today.day}_{today.year}&#39;,
+    folder=None
+):
+    if folder is not None:
+        os.makedirs(folder, exist_ok=True)
+    mesh = vtk_deep_copy(self._ref_mesh)
+    for idx, path in enumerate(self.list_mesh_paths):
+        # parse folder / filename for saving
+        orig_folder = os.path.dirname(path)
+        orig_filename = os.path.basename(path)
+        base_filename = orig_filename[: orig_filename.rfind(&#34;.&#34;)]
+        filename = f&#39;{base_filename}_{mesh_suffix}_{idx}.vtk&#39;
+        if folder is None:
+            path_to_save = os.path.join(orig_folder, filename)
+        else:
+            path_to_save = os.path.join(os.path.abspath(folder), filename)
+        # Keep recycling the same base mesh, just move the x/y/z point coords around.
+        set_mesh_physical_point_coords(mesh, self._registered_pt_coords[idx, :, :])
+        # save mesh to disk
+        io.write_vtk(mesh, path_to_save)</code></pre>
+</details>
+</dd>
+<dt id="pymskt.statistics.main.ProcrustesRegistration.save_ref_mesh"><code class="name flex">
+<span>def <span class="ident">save_ref_mesh</span></span>(<span>self, path)</span>
+</code></dt>
+<dd>
+<div class="desc"></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def save_ref_mesh(self, path):
+    io.write_vtk(self._ref_mesh, path)</code></pre>
+</details>
+</dd>
+</dl>
+</dd>
+</dl>
+</section>
+</article>
+<nav id="sidebar">
+<h1>Index</h1>
+<div class="toc">
+<ul></ul>
+</div>
+<ul id="index">
+<li><h3>Super-module</h3>
+<ul>
+<li><code><a title="pymskt.statistics" href="index.html">pymskt.statistics</a></code></li>
+</ul>
+</li>
+<li><h3><a href="#header-classes">Classes</a></h3>
+<ul>
+<li>
+<h4><code><a title="pymskt.statistics.main.FindReferenceMeshICP" href="#pymskt.statistics.main.FindReferenceMeshICP">FindReferenceMeshICP</a></code></h4>
+<ul class="">
+<li><code><a title="pymskt.statistics.main.FindReferenceMeshICP.execute" href="#pymskt.statistics.main.FindReferenceMeshICP.execute">execute</a></code></li>
+<li><code><a title="pymskt.statistics.main.FindReferenceMeshICP.get_template_idx" href="#pymskt.statistics.main.FindReferenceMeshICP.get_template_idx">get_template_idx</a></code></li>
+<li><code><a title="pymskt.statistics.main.FindReferenceMeshICP.mean_errors" href="#pymskt.statistics.main.FindReferenceMeshICP.mean_errors">mean_errors</a></code></li>
+<li><code><a title="pymskt.statistics.main.FindReferenceMeshICP.ref_idx" href="#pymskt.statistics.main.FindReferenceMeshICP.ref_idx">ref_idx</a></code></li>
+<li><code><a title="pymskt.statistics.main.FindReferenceMeshICP.ref_path" href="#pymskt.statistics.main.FindReferenceMeshICP.ref_path">ref_path</a></code></li>
+<li><code><a title="pymskt.statistics.main.FindReferenceMeshICP.register_meshes" href="#pymskt.statistics.main.FindReferenceMeshICP.register_meshes">register_meshes</a></code></li>
+<li><code><a title="pymskt.statistics.main.FindReferenceMeshICP.symm_surface_distances" href="#pymskt.statistics.main.FindReferenceMeshICP.symm_surface_distances">symm_surface_distances</a></code></li>
+</ul>
+</li>
+<li>
+<h4><code><a title="pymskt.statistics.main.ProcrustesRegistration" href="#pymskt.statistics.main.ProcrustesRegistration">ProcrustesRegistration</a></code></h4>
+<ul class="">
+<li><code><a title="pymskt.statistics.main.ProcrustesRegistration.execute" href="#pymskt.statistics.main.ProcrustesRegistration.execute">execute</a></code></li>
+<li><code><a title="pymskt.statistics.main.ProcrustesRegistration.ref_mesh" href="#pymskt.statistics.main.ProcrustesRegistration.ref_mesh">ref_mesh</a></code></li>
+<li><code><a title="pymskt.statistics.main.ProcrustesRegistration.register" href="#pymskt.statistics.main.ProcrustesRegistration.register">register</a></code></li>
+<li><code><a title="pymskt.statistics.main.ProcrustesRegistration.registered_pt_coords" href="#pymskt.statistics.main.ProcrustesRegistration.registered_pt_coords">registered_pt_coords</a></code></li>
+<li><code><a title="pymskt.statistics.main.ProcrustesRegistration.save_meshes" href="#pymskt.statistics.main.ProcrustesRegistration.save_meshes">save_meshes</a></code></li>
+<li><code><a title="pymskt.statistics.main.ProcrustesRegistration.save_ref_mesh" href="#pymskt.statistics.main.ProcrustesRegistration.save_ref_mesh">save_ref_mesh</a></code></li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
+</nav>
+</main>
+<footer id="footer">
+<p>Generated by <a href="https://pdoc3.github.io/pdoc" title="pdoc: Python API documentation generator"><cite>pdoc</cite> 0.10.0</a>.</p>
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