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<article id="content">
<header>
<h1 class="title">Module <code>pymskt.statistics.pca</code></h1>
</header>
<section id="section-intro">
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">from tracemalloc import start
import numpy as np
from scipy.linalg import svd
import vtk
from vtk.util.numpy_support import numpy_to_vtk
from pymskt.mesh.utils import GIF
def pca_svd(data):
"""
Calculate eigenvalues & eigenvectors of `data` using Singular Value Decomposition (SVD)
Parameters
----------
data : numpy.ndarray
MxN matrix
M = # of features / dimensions of data
N = # of trials / participants in dataset
Returns
-------
tuple (PC = numpy.ndarray, V = numpy.ndarray)
PC - each volumn is a principal component (eigenvector)
V - Mx1 matrix of variances (coinciding with each PC)
Notes
-----
Adapted from:
"A Tutorial on Principal Component Analysis by Jonathon Shlens"
https://arxiv.org/abs/1404.1100
Inputs
data = MxN matrix (M dimensions, N trials)
Returns
PC - each column is a PC
V - Mx1 matrix of variances
"""
M, N = data.shape
mn = np.mean(data, axis=1)
data = data - mn[:, None] # produce centered data. If already centered this shouldnt be harmful.
Y = data.T / np.sqrt(N - 1)
U, S, V = svd(Y, full_matrices=False)
PC = V.T # V are the principle components (PC)
V = S ** 2 # The squared singular values are the variances (V)
return PC, V
def get_ssm_deformation(PCs, Vs, mean_coords, pc=0, n_sds=3):
"""
Function to Statistical Shape Model (SSM) deformed along given Principal Component.
Parameters
----------
PCs : numpy.ndarray
NxM ndarray; N = number of points on surface, M = number of principal components in model
Each column is a principal component.
Vs : numpy.ndarray
M ndarray; M = number of principal components in model
Each entry is the variance for the coinciding principal component in PCs
mean_coords : numpy.ndarray
3xN ndarray; N = number of points on surface.
pc : int, optional
The principal component of the SSM to deform, by default 0
n_sds : int, optional
The number of standard deviations (sd) to deform the SSM.
This can be positive or negative to scale the model in either direction. , by default 3
Returns
-------
numpy.ndarray
3xN ndarray; N=number of points on mesh surface.
This includes the x/y/z position of each surface node after deformation using the SSM and
the specified characteristics (pc, n_sds)
"""
pc_vector = PCs[:, pc]
pc_vector_scale = np.sqrt(Vs[pc]) * n_sds # convert Variances to SDs & multiply by n_sds (negative/positive important)
coords_deformation = pc_vector * pc_vector_scale
deformed_coords = (mean_coords.flatten() + coords_deformation).reshape(mean_coords.shape)
return deformed_coords
def get_rand_bone_shape(PCs, Vs, mean_coords, n_pcs=100, n_samples=1, mean_=0., sd_=1.0):
"""
Function to get random bones using a Statistical Shape Model (SSM).
Parameters
----------
PCs : numpy.ndarray
NxM ndarray; N = number of points on surface, M = number of principal components in model
Each column is a principal component.
Vs : numpy.ndarray
M ndarray; M = number of principal components in model
Each entry is the variance for the coinciding principal component in PCs
mean_coords : numpy.ndarray
3xN ndarray; N = number of points on surface.
n_pcs : int, optional
Number of PCs to randomly sample from (sequentially), by default 100
n_samples : int, optional
number of bones to create, by default 1
mean_ : float, optional
Mean of the normal distribution to sample PCs from, by default 0.
sd_ : float, optional
Standard deviation of the normal distribution to sample PCs from, by default 1.0
Returns
-------
numpy.ndarray
nx(3xN) ndarray; N=number of points on mesh surface, n=number of new meshes
This includes the x/y/z position of each surface node(N) for the random bones(n).
"""
rand_pc_scores = np.random.normal(mean_, sd_, size=[n_samples, n_pcs])
rand_pc_weights = rand_pc_scores * np.sqrt(Vs[:n_pcs])
rand_data = rand_pc_weights @ PCs[:, :n_pcs].T
rand_data = mean_coords.flatten() + rand_data
return rand_data
def create_vtk_mesh_from_deformed_points(mean_mesh, new_points):
"""
Create new vtk mesh (polydata) from a set of points (ndarray) deformed using the SSM.
Parameters
----------
mean_mesh : vtk.PolyData
vtk polydata of the mean mesh
new_points : numpy.ndarray
3xN ndarray; N=number of points on mesh surface (same as number of points on mean_mesh).
This includes the x/y/z position of each surface node should be deformed to.
Returns
-------
vtk.PolyData
vtk polydata of the deformed mesh
"""
new_mesh = vtk.vtkPolyData()
new_mesh.DeepCopy(mean_mesh)
new_mesh.GetPoints().SetData(numpy_to_vtk(new_points))
return new_mesh
def save_gif(
path_save,
PCs,
Vs,
mean_coords, # mean_coords could be extracted from mean mesh...?
mean_mesh,
pc=0,
min_sd=-3.,
max_sd=3.,
step=0.25,
color='orange',
show_edges=True,
edge_color='black',
camera_position='xz',
window_size=[3000, 4000],
background_color='white',
verbose=False,
):
"""
Function to save a gif of the SSM deformation.
Parameters
----------
path_save : str
Path to save the gif to.
PCs : numpy.ndarray
SSM Principal Components.
Vs : numpy.ndarray
SSM Variances.
mean_coords : numpy.ndarray
NxM ndarray; N = number of meshes, M = number of points x n_dimensions
mean_mesh : vtk.PolyData
vtk polydata of the mean mesh
pc : int, optional
The principal component of the SSM to deform, by default 0
min_sd : float, optional
The lower bound (minimum) standard deviations (sd) to deform the SSM from
This can be positive or negative to scale the model in either direction. , by default -3.
max_sd : float, optional
The upper bound (maximum) standard deviations (sd) to deform the SSM from
This can be positive or negative to scale the model in either direction. , by default 3.
step : float, optional
The step size (sd) to deform the SSM by, by default 0.25
color : str, optional
The color of the SSM surface during rendering, by default 'orange'
show_edges : bool, optional
Whether to show the edges of the SSM surface during rendering, by default True
edge_color : str, optional
The color of the edges of the SSM surface during rendering, by default 'black'
camera_position : str, optional
The camera position to use during rendering, by default 'xz'
window_size : list, optional
The window size to use during rendering, by default [3000, 4000]
background_color : str, optional
The background color to use during rendering, by default 'white'
verbose : bool, optional
Whether to print progress to console, by default False
"""
# ALTERNATIVELY... could pass a bunch of the above parameters as kwargs..?? but thats less clear
gif = GIF(
path_save=path_save,
color=color,
show_edges=show_edges,
edge_color=edge_color,
camera_position=camera_position,
window_size=window_size,
background_color=background_color,
)
for idx, sd in enumerate(np.arange(min_sd, max_sd + step, step)):
if verbose is True:
print(f'Deforming SSM with idx={idx} sd={sd}')
pts = get_ssm_deformation(PCs, Vs, mean_coords, pc=pc, n_sds=sd)
if type(mean_mesh) == dict:
mesh = []
start_idx = 0
for mesh_name, mesh_params in mean_mesh.items():
mesh.append(
create_vtk_mesh_from_deformed_points(
mesh_params['mesh'],
pts[start_idx:start_idx+mesh_params['n_points'], :],
)
)
start_idx += mesh_params['n_points']
if type(mean_mesh) in (list, tuple):
mesh = []
start_idx = 0
for mesh_ in mean_mesh:
n_pts = mesh_.GetNumberOfPoints()
mesh.append(
create_vtk_mesh_from_deformed_points(
mesh_,
pts[start_idx:start_idx+n_pts, :],
)
)
start_idx += n_pts
else:
mesh = create_vtk_mesh_from_deformed_points(mean_mesh, pts)
gif.add_mesh_frame(mesh)
gif.done()</code></pre>
</details>
</section>
<section>
</section>
<section>
</section>
<section>
<h2 class="section-title" id="header-functions">Functions</h2>
<dl>
<dt id="pymskt.statistics.pca.create_vtk_mesh_from_deformed_points"><code class="name flex">
<span>def <span class="ident">create_vtk_mesh_from_deformed_points</span></span>(<span>mean_mesh, new_points)</span>
</code></dt>
<dd>
<div class="desc"><p>Create new vtk mesh (polydata) from a set of points (ndarray) deformed using the SSM. </p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>mean_mesh</code></strong> : <code>vtk.PolyData</code></dt>
<dd>vtk polydata of the mean mesh</dd>
<dt><strong><code>new_points</code></strong> : <code>numpy.ndarray</code></dt>
<dd>3xN ndarray; N=number of points on mesh surface (same as number of points on mean_mesh).
This includes the x/y/z position of each surface node should be deformed to.</dd>
</dl>
<h2 id="returns">Returns</h2>
<dl>
<dt><code>vtk.PolyData</code></dt>
<dd>vtk polydata of the deformed mesh</dd>
</dl></div>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def create_vtk_mesh_from_deformed_points(mean_mesh, new_points):
"""
Create new vtk mesh (polydata) from a set of points (ndarray) deformed using the SSM.
Parameters
----------
mean_mesh : vtk.PolyData
vtk polydata of the mean mesh
new_points : numpy.ndarray
3xN ndarray; N=number of points on mesh surface (same as number of points on mean_mesh).
This includes the x/y/z position of each surface node should be deformed to.
Returns
-------
vtk.PolyData
vtk polydata of the deformed mesh
"""
new_mesh = vtk.vtkPolyData()
new_mesh.DeepCopy(mean_mesh)
new_mesh.GetPoints().SetData(numpy_to_vtk(new_points))
return new_mesh</code></pre>
</details>
</dd>
<dt id="pymskt.statistics.pca.get_rand_bone_shape"><code class="name flex">
<span>def <span class="ident">get_rand_bone_shape</span></span>(<span>PCs, Vs, mean_coords, n_pcs=100, n_samples=1, mean_=0.0, sd_=1.0)</span>
</code></dt>
<dd>
<div class="desc"><p>Function to get random bones using a Statistical Shape Model (SSM).</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>PCs</code></strong> : <code>numpy.ndarray</code></dt>
<dd>NxM ndarray; N = number of points on surface, M = number of principal components in model
Each column is a principal component.</dd>
<dt><strong><code>Vs</code></strong> : <code>numpy.ndarray</code></dt>
<dd>M ndarray; M = number of principal components in model
Each entry is the variance for the coinciding principal component in PCs</dd>
<dt><strong><code>mean_coords</code></strong> : <code>numpy.ndarray</code></dt>
<dd>3xN ndarray; N = number of points on surface.</dd>
<dt><strong><code>n_pcs</code></strong> : <code>int</code>, optional</dt>
<dd>Number of PCs to randomly sample from (sequentially), by default 100</dd>
<dt><strong><code>n_samples</code></strong> : <code>int</code>, optional</dt>
<dd>number of bones to create, by default 1</dd>
<dt><strong><code>mean_</code></strong> : <code>float</code>, optional</dt>
<dd>Mean of the normal distribution to sample PCs from, by default 0.</dd>
<dt><strong><code>sd_</code></strong> : <code>float</code>, optional</dt>
<dd>Standard deviation of the normal distribution to sample PCs from, by default 1.0</dd>
</dl>
<h2 id="returns">Returns</h2>
<dl>
<dt><code>numpy.ndarray</code></dt>
<dd>nx(3xN) ndarray; N=number of points on mesh surface, n=number of new meshes
This includes the x/y/z position of each surface node(N) for the random bones(n).</dd>
</dl></div>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def get_rand_bone_shape(PCs, Vs, mean_coords, n_pcs=100, n_samples=1, mean_=0., sd_=1.0):
"""
Function to get random bones using a Statistical Shape Model (SSM).
Parameters
----------
PCs : numpy.ndarray
NxM ndarray; N = number of points on surface, M = number of principal components in model
Each column is a principal component.
Vs : numpy.ndarray
M ndarray; M = number of principal components in model
Each entry is the variance for the coinciding principal component in PCs
mean_coords : numpy.ndarray
3xN ndarray; N = number of points on surface.
n_pcs : int, optional
Number of PCs to randomly sample from (sequentially), by default 100
n_samples : int, optional
number of bones to create, by default 1
mean_ : float, optional
Mean of the normal distribution to sample PCs from, by default 0.
sd_ : float, optional
Standard deviation of the normal distribution to sample PCs from, by default 1.0
Returns
-------
numpy.ndarray
nx(3xN) ndarray; N=number of points on mesh surface, n=number of new meshes
This includes the x/y/z position of each surface node(N) for the random bones(n).
"""
rand_pc_scores = np.random.normal(mean_, sd_, size=[n_samples, n_pcs])
rand_pc_weights = rand_pc_scores * np.sqrt(Vs[:n_pcs])
rand_data = rand_pc_weights @ PCs[:, :n_pcs].T
rand_data = mean_coords.flatten() + rand_data
return rand_data </code></pre>
</details>
</dd>
<dt id="pymskt.statistics.pca.get_ssm_deformation"><code class="name flex">
<span>def <span class="ident">get_ssm_deformation</span></span>(<span>PCs, Vs, mean_coords, pc=0, n_sds=3)</span>
</code></dt>
<dd>
<div class="desc"><p>Function to Statistical Shape Model (SSM) deformed along given Principal Component.</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>PCs</code></strong> : <code>numpy.ndarray</code></dt>
<dd>NxM ndarray; N = number of points on surface, M = number of principal components in model
Each column is a principal component.</dd>
<dt><strong><code>Vs</code></strong> : <code>numpy.ndarray</code></dt>
<dd>M ndarray; M = number of principal components in model
Each entry is the variance for the coinciding principal component in PCs</dd>
<dt><strong><code>mean_coords</code></strong> : <code>numpy.ndarray</code></dt>
<dd>3xN ndarray; N = number of points on surface.</dd>
<dt><strong><code>pc</code></strong> : <code>int</code>, optional</dt>
<dd>The principal component of the SSM to deform, by default 0</dd>
<dt><strong><code>n_sds</code></strong> : <code>int</code>, optional</dt>
<dd>The number of standard deviations (sd) to deform the SSM.
This can be positive or negative to scale the model in either direction. , by default 3</dd>
</dl>
<h2 id="returns">Returns</h2>
<dl>
<dt><code>numpy.ndarray</code></dt>
<dd>3xN ndarray; N=number of points on mesh surface.
This includes the x/y/z position of each surface node after deformation using the SSM and
the specified characteristics (pc, n_sds)</dd>
</dl></div>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def get_ssm_deformation(PCs, Vs, mean_coords, pc=0, n_sds=3):
"""
Function to Statistical Shape Model (SSM) deformed along given Principal Component.
Parameters
----------
PCs : numpy.ndarray
NxM ndarray; N = number of points on surface, M = number of principal components in model
Each column is a principal component.
Vs : numpy.ndarray
M ndarray; M = number of principal components in model
Each entry is the variance for the coinciding principal component in PCs
mean_coords : numpy.ndarray
3xN ndarray; N = number of points on surface.
pc : int, optional
The principal component of the SSM to deform, by default 0
n_sds : int, optional
The number of standard deviations (sd) to deform the SSM.
This can be positive or negative to scale the model in either direction. , by default 3
Returns
-------
numpy.ndarray
3xN ndarray; N=number of points on mesh surface.
This includes the x/y/z position of each surface node after deformation using the SSM and
the specified characteristics (pc, n_sds)
"""
pc_vector = PCs[:, pc]
pc_vector_scale = np.sqrt(Vs[pc]) * n_sds # convert Variances to SDs & multiply by n_sds (negative/positive important)
coords_deformation = pc_vector * pc_vector_scale
deformed_coords = (mean_coords.flatten() + coords_deformation).reshape(mean_coords.shape)
return deformed_coords</code></pre>
</details>
</dd>
<dt id="pymskt.statistics.pca.pca_svd"><code class="name flex">
<span>def <span class="ident">pca_svd</span></span>(<span>data)</span>
</code></dt>
<dd>
<div class="desc"><p>Calculate eigenvalues & eigenvectors of <code>data</code> using Singular Value Decomposition (SVD)</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>data</code></strong> : <code>numpy.ndarray</code></dt>
<dd>MxN matrix
M = # of features / dimensions of data
N = # of trials / participants in dataset</dd>
</dl>
<h2 id="returns">Returns</h2>
<dl>
<dt><code>tuple (PC = numpy.ndarray, V = numpy.ndarray)</code></dt>
<dd>PC - each volumn is a principal component (eigenvector)
V - Mx1 matrix of variances (coinciding with each PC)</dd>
</dl>
<h2 id="notes">Notes</h2>
<p>Adapted from:
"A Tutorial on Principal Component Analysis by Jonathon Shlens"
<a href="https://arxiv.org/abs/1404.1100">https://arxiv.org/abs/1404.1100</a>
Inputs
data = MxN matrix (M dimensions, N trials)
Returns
PC - each column is a PC
V - Mx1 matrix of variances</p></div>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def pca_svd(data):
"""
Calculate eigenvalues & eigenvectors of `data` using Singular Value Decomposition (SVD)
Parameters
----------
data : numpy.ndarray
MxN matrix
M = # of features / dimensions of data
N = # of trials / participants in dataset
Returns
-------
tuple (PC = numpy.ndarray, V = numpy.ndarray)
PC - each volumn is a principal component (eigenvector)
V - Mx1 matrix of variances (coinciding with each PC)
Notes
-----
Adapted from:
"A Tutorial on Principal Component Analysis by Jonathon Shlens"
https://arxiv.org/abs/1404.1100
Inputs
data = MxN matrix (M dimensions, N trials)
Returns
PC - each column is a PC
V - Mx1 matrix of variances
"""
M, N = data.shape
mn = np.mean(data, axis=1)
data = data - mn[:, None] # produce centered data. If already centered this shouldnt be harmful.
Y = data.T / np.sqrt(N - 1)
U, S, V = svd(Y, full_matrices=False)
PC = V.T # V are the principle components (PC)
V = S ** 2 # The squared singular values are the variances (V)
return PC, V</code></pre>
</details>
</dd>
<dt id="pymskt.statistics.pca.save_gif"><code class="name flex">
<span>def <span class="ident">save_gif</span></span>(<span>path_save, PCs, Vs, mean_coords, mean_mesh, pc=0, min_sd=-3.0, max_sd=3.0, step=0.25, color='orange', show_edges=True, edge_color='black', camera_position='xz', window_size=[3000, 4000], background_color='white', verbose=False)</span>
</code></dt>
<dd>
<div class="desc"><p>Function to save a gif of the SSM deformation.</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>path_save</code></strong> : <code>str</code></dt>
<dd>Path to save the gif to.</dd>
<dt><strong><code>PCs</code></strong> : <code>numpy.ndarray</code></dt>
<dd>SSM Principal Components.</dd>
<dt><strong><code>Vs</code></strong> : <code>numpy.ndarray</code></dt>
<dd>SSM Variances.</dd>
<dt><strong><code>mean_coords</code></strong> : <code>numpy.ndarray</code></dt>
<dd>NxM ndarray; N = number of meshes, M = number of points x n_dimensions</dd>
<dt><strong><code>mean_mesh</code></strong> : <code>vtk.PolyData</code></dt>
<dd>vtk polydata of the mean mesh</dd>
<dt><strong><code>pc</code></strong> : <code>int</code>, optional</dt>
<dd>The principal component of the SSM to deform, by default 0</dd>
<dt><strong><code>min_sd</code></strong> : <code>float</code>, optional</dt>
<dd>The lower bound (minimum) standard deviations (sd) to deform the SSM from
This can be positive or negative to scale the model in either direction. , by default -3.</dd>
<dt><strong><code>max_sd</code></strong> : <code>float</code>, optional</dt>
<dd>The upper bound (maximum) standard deviations (sd) to deform the SSM from
This can be positive or negative to scale the model in either direction. , by default 3.</dd>
<dt><strong><code>step</code></strong> : <code>float</code>, optional</dt>
<dd>The step size (sd) to deform the SSM by, by default 0.25</dd>
<dt><strong><code>color</code></strong> : <code>str</code>, optional</dt>
<dd>The color of the SSM surface during rendering, by default 'orange'</dd>
<dt><strong><code>show_edges</code></strong> : <code>bool</code>, optional</dt>
<dd>Whether to show the edges of the SSM surface during rendering, by default True</dd>
<dt><strong><code>edge_color</code></strong> : <code>str</code>, optional</dt>
<dd>The color of the edges of the SSM surface during rendering, by default 'black'</dd>
<dt><strong><code>camera_position</code></strong> : <code>str</code>, optional</dt>
<dd>The camera position to use during rendering, by default 'xz'</dd>
<dt><strong><code>window_size</code></strong> : <code>list</code>, optional</dt>
<dd>The window size to use during rendering, by default [3000, 4000]</dd>
<dt><strong><code>background_color</code></strong> : <code>str</code>, optional</dt>
<dd>The background color to use during rendering, by default 'white'</dd>
<dt><strong><code>verbose</code></strong> : <code>bool</code>, optional</dt>
<dd>Whether to print progress to console, by default False</dd>
</dl></div>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def save_gif(
path_save,
PCs,
Vs,
mean_coords, # mean_coords could be extracted from mean mesh...?
mean_mesh,
pc=0,
min_sd=-3.,
max_sd=3.,
step=0.25,
color='orange',
show_edges=True,
edge_color='black',
camera_position='xz',
window_size=[3000, 4000],
background_color='white',
verbose=False,
):
"""
Function to save a gif of the SSM deformation.
Parameters
----------
path_save : str
Path to save the gif to.
PCs : numpy.ndarray
SSM Principal Components.
Vs : numpy.ndarray
SSM Variances.
mean_coords : numpy.ndarray
NxM ndarray; N = number of meshes, M = number of points x n_dimensions
mean_mesh : vtk.PolyData
vtk polydata of the mean mesh
pc : int, optional
The principal component of the SSM to deform, by default 0
min_sd : float, optional
The lower bound (minimum) standard deviations (sd) to deform the SSM from
This can be positive or negative to scale the model in either direction. , by default -3.
max_sd : float, optional
The upper bound (maximum) standard deviations (sd) to deform the SSM from
This can be positive or negative to scale the model in either direction. , by default 3.
step : float, optional
The step size (sd) to deform the SSM by, by default 0.25
color : str, optional
The color of the SSM surface during rendering, by default 'orange'
show_edges : bool, optional
Whether to show the edges of the SSM surface during rendering, by default True
edge_color : str, optional
The color of the edges of the SSM surface during rendering, by default 'black'
camera_position : str, optional
The camera position to use during rendering, by default 'xz'
window_size : list, optional
The window size to use during rendering, by default [3000, 4000]
background_color : str, optional
The background color to use during rendering, by default 'white'
verbose : bool, optional
Whether to print progress to console, by default False
"""
# ALTERNATIVELY... could pass a bunch of the above parameters as kwargs..?? but thats less clear
gif = GIF(
path_save=path_save,
color=color,
show_edges=show_edges,
edge_color=edge_color,
camera_position=camera_position,
window_size=window_size,
background_color=background_color,
)
for idx, sd in enumerate(np.arange(min_sd, max_sd + step, step)):
if verbose is True:
print(f'Deforming SSM with idx={idx} sd={sd}')
pts = get_ssm_deformation(PCs, Vs, mean_coords, pc=pc, n_sds=sd)
if type(mean_mesh) == dict:
mesh = []
start_idx = 0
for mesh_name, mesh_params in mean_mesh.items():
mesh.append(
create_vtk_mesh_from_deformed_points(
mesh_params['mesh'],
pts[start_idx:start_idx+mesh_params['n_points'], :],
)
)
start_idx += mesh_params['n_points']
if type(mean_mesh) in (list, tuple):
mesh = []
start_idx = 0
for mesh_ in mean_mesh:
n_pts = mesh_.GetNumberOfPoints()
mesh.append(
create_vtk_mesh_from_deformed_points(
mesh_,
pts[start_idx:start_idx+n_pts, :],
)
)
start_idx += n_pts
else:
mesh = create_vtk_mesh_from_deformed_points(mean_mesh, pts)
gif.add_mesh_frame(mesh)
gif.done()</code></pre>
</details>
</dd>
</dl>
</section>
<section>
</section>
</article>
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<div class="toc">
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<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-functions">Functions</a></h3>
<ul class="">
<li><code><a title="pymskt.statistics.pca.create_vtk_mesh_from_deformed_points" href="#pymskt.statistics.pca.create_vtk_mesh_from_deformed_points">create_vtk_mesh_from_deformed_points</a></code></li>
<li><code><a title="pymskt.statistics.pca.get_rand_bone_shape" href="#pymskt.statistics.pca.get_rand_bone_shape">get_rand_bone_shape</a></code></li>
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<li><code><a title="pymskt.statistics.pca.pca_svd" href="#pymskt.statistics.pca.pca_svd">pca_svd</a></code></li>
<li><code><a title="pymskt.statistics.pca.save_gif" href="#pymskt.statistics.pca.save_gif">save_gif</a></code></li>
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