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Example_Frechet_Sphere.py
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Example_Frechet_Sphere.py
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# Geodesic Regression on Sphere Manifold
# Manifolds
import manifolds
import numpy as np
import StatsModel as sm
# Visualization
import vtk
# Parameters
nDimManifold = 3
# Ground Truth
p_interp = manifolds.sphere( nDimManifold )
v_slope = manifolds.sphere_tVec( nDimManifold )
p_interp.SetPoint( [ 0.0, 0.0, 1.0 ] )
v_slope.SetTangentVector( [ 0, np.pi * 0.25, 0 ] )
# Generating sphere manifolds. distributed over time perturbed by Gaussian random
# Time
t0 = 0
t1 = 2.0
# Generate a random point on the manifold
nData = 500
dim = nDimManifold
sigma = 0.1
pt_list = []
t_list = []
for n in range( nData ):
time_pt = np.random.uniform( t0, t1 )
# time_pt = ( t1 - t0 ) * n / nData + t0
# if time_pt > 0.1 and time_pt < 1.5:
# n = n - 1
# continue
# if time_pt <= 0.1:
# sigma = 0.1
# elif time_pt >= 1.5:
# sigma = 0.2
# Generate a random Gaussians with polar Box-Muller Method
rand_pt = np.zeros( nDimManifold ).tolist()
for i in range( dim ):
r2 = 0
x = 0
y = 0
while( r2 > 1.0 or r2 == 0 ):
x = ( 2.0 * np.random.rand() - 1.0 )
y = ( 2.0 * np.random.rand() - 1.0 )
r2 = x * x + y * y
gen_rand_no = sigma * y * np.sqrt( -2.0 * np.log( r2 ) / r2 )
rand_pt[ i ] = gen_rand_no
# print( rand_pt )
# Set Random Vector to Tangent Vector - ListToTangent
rand_tVec = manifolds.sphere_tVec( nDimManifold )
rand_tVec.SetTangentVector( rand_pt )
v_t = manifolds.sphere_tVec( nDimManifold )
for i in range( nDimManifold ):
v_t.tVector[ i ] = v_slope.tVector[ i ] * time_pt
mean = p_interp.ExponentialMap( v_t )
# print( "Mean At Time : " + str( time_pt ) )
# print( mean.pt )
# Projected Tangent to Mean Point
rand_tVec_projected = mean.ProjectTangent( mean, rand_tVec )
# print( "Random Tangent" )
# print( rand_tVec.tVector )
# print( "Projected Random Tangent" )
# print( rand_tVec_projected.tVector )
# Perturbed point at time_pt
pt_perturbed = mean.ExponentialMap( rand_tVec_projected )
# print( "Perturbed pt At Time : " + str( time_pt ) )
# print( pt_perturbed.pt )
pt_list.append( pt_perturbed )
t_list.append( time_pt )
#######################
# Frechet Mean #
#######################
# Gradient Descent Parameters
step_size = 0.01
max_iter = 500
step_tol = 1e-8
mu = sm.FrechetMean( pt_list, max_iter, step_tol )
#######################
# AGReg #
#######################
# Gradient Descent Parameters
step_size = 0.01
max_iter = 600
step_tol = 1e-8
base_lReg, tangent_lReg = sm.LinearizedGeodesicRegression( t_list, pt_list, max_iter, step_size, step_tol, False, True )
#######################
# GReg #
#######################
step_size = 0.01
max_iter = 500
step_tol = 1e-8
base_GReg, tangent_GReg = sm.GeodesicRegression( t_list, pt_list, max_iter, step_size, step_tol, False )
# Linearized Regression Results
print( "=================================================" )
print( " Resulsts : Linearized Geodesic Regression " )
print( "=================================================" )
print( "True P" )
print( p_interp.pt )
print( "True V" )
print( v_slope.tVector )
print( "Estimated P" )
print( base_lReg.pt )
print( "Estimated V" )
print( tangent_lReg.tVector )
# Geodesic Regression Results
print( "=================================================" )
print( " Resulsts : Geodesic Regression " )
print( "=================================================" )
print( "Estimated P" )
print( base_GReg.pt )
print( "Estimated V" )
print( tangent_GReg.tVector )
########################################
##### Visualization ######
########################################
# Visualize a sphere coordinate
sphere = vtk.vtkSphereSource()
sphere.SetThetaResolution( 30 )
sphere.SetPhiResolution( 30 )
sphere.SetRadius( 1.0 )
sphere.SetCenter( 0.0, 0.0, 0.0 )
sphere.SetLatLongTessellation( True )
sphere.Update()
conMapper = vtk.vtkPolyDataMapper()
conMapper.SetInputData( sphere.GetOutput() )
conMapper.ScalarVisibilityOff()
conMapper.Update()
conActor = vtk.vtkActor()
conActor.SetMapper( conMapper )
conActor.GetProperty().SetOpacity( 1 )
conActor.GetProperty().SetColor( 0.9, 0.9, 0.9 )
conActor.GetProperty().SetEdgeColor( 0.4, 0.4, 0.7 )
conActor.GetProperty().EdgeVisibilityOn()
conActor.GetProperty().SetAmbient(0.3)
conActor.GetProperty().SetDiffuse(0.375)
conActor.GetProperty().SetSpecular(0.0)
# Visualize spherical points
points = vtk.vtkPoints()
for i in range( len( pt_list ) ):
points.InsertNextPoint( pt_list[ i ].pt[0], pt_list[ i ].pt[1], pt_list[ i ].pt[2] )
ptsPolyData = vtk.vtkPolyData()
ptsPolyData.SetPoints( points )
vertFilter = vtk.vtkVertexGlyphFilter()
vertFilter.SetInputData( ptsPolyData )
vertFilter.Update()
ptsMapper = vtk.vtkPolyDataMapper()
ptsMapper.SetInputData( vertFilter.GetOutput() )
ptsActor = vtk.vtkActor()
ptsActor.SetMapper( ptsMapper )
ptsActor.GetProperty().SetPointSize( 8 )
ptsActor.GetProperty().SetColor( 1, 0, 1 )
ptsActor.GetProperty().SetOpacity( 1.0 )
ptsActor.GetProperty().SetRenderPointsAsSpheres( 1 )
# Visualize Frechet Mean
points_mu = vtk.vtkPoints()
points_mu.InsertNextPoint( mu.pt[0], mu.pt[1], mu.pt[2] )
ptsPolyData_mu = vtk.vtkPolyData()
ptsPolyData_mu.SetPoints( points_mu )
vertFilter_mu = vtk.vtkVertexGlyphFilter()
vertFilter_mu.SetInputData( ptsPolyData_mu )
vertFilter_mu.Update()
ptsMapper_mu = vtk.vtkPolyDataMapper()
ptsMapper_mu.SetInputData( vertFilter_mu.GetOutput() )
ptsActor_mu = vtk.vtkActor()
ptsActor_mu.SetMapper( ptsMapper_mu )
ptsActor_mu.GetProperty().SetPointSize( 15 )
ptsActor_mu.GetProperty().SetColor( 0, 1, 1 )
ptsActor_mu.GetProperty().SetOpacity( 1.0 )
ptsActor_mu.GetProperty().SetRenderPointsAsSpheres( 1 )
nTimePt = 100
# Visualize an estimated trend of Linearized Geodesic Regression Model - Red
est_trend_LReg_pt_list = []
est_trend_LReg_t_list = []
for n in range( nTimePt ):
time_pt = ( t1 - t0 ) * n / ( nTimePt - 1 ) + t0
# Generate a random Gaussians with polar Box-Muller Method
v_t = manifolds.sphere_tVec( nDimManifold )
v_t.SetTangentVector( [ tangent_lReg.tVector[0] * time_pt, tangent_lReg.tVector[1] * time_pt, tangent_lReg.tVector[2] * time_pt ] )
mean = base_lReg.ExponentialMap( v_t )
est_trend_LReg_pt_list.append( mean )
est_trend_LReg_t_list.append( time_pt )
estLinePolyData_LReg = vtk.vtkPolyData()
estLinePts_LReg = vtk.vtkPoints()
for i in range( len( est_trend_LReg_pt_list ) ):
estLinePts_LReg.InsertNextPoint( est_trend_LReg_pt_list[ i ].pt[0], est_trend_LReg_pt_list[ i ].pt[1], est_trend_LReg_pt_list[ i ].pt[2] )
estLinePolyData_LReg.SetPoints( estLinePts_LReg )
estLines_LReg = vtk.vtkCellArray()
for i in range( len( est_trend_LReg_pt_list ) - 1 ):
line_i = vtk.vtkLine()
line_i.GetPointIds().SetId( 0, i )
line_i.GetPointIds().SetId( 1, i + 1 )
estLines_LReg.InsertNextCell( line_i )
estLinePolyData_LReg.SetLines( estLines_LReg )
estLineMapper_LReg = vtk.vtkPolyDataMapper()
estLineMapper_LReg.SetInputData( estLinePolyData_LReg )
estLineActor_LReg = vtk.vtkActor()
estLineActor_LReg.SetMapper( estLineMapper_LReg )
estLineActor_LReg.GetProperty().SetColor( 1, 0, 0 )
estLineActor_LReg.GetProperty().SetOpacity( 0.5 )
estLineActor_LReg.GetProperty().SetLineWidth( 20 )
estLineActor_LReg.GetProperty().SetRenderLinesAsTubes( 1 )
# Visualize an estimated trend - Geodesic Regression : Green
est_trend_pt_list = []
est_trend_t_list = []
for n in range( nTimePt ):
time_pt = ( t1 - t0 ) * n / ( nTimePt - 1 ) + t0
# Generate a random Gaussians with polar Box-Muller Method
v_t = manifolds.sphere_tVec( nDimManifold )
v_t.SetTangentVector( [ tangent_GReg.tVector[0] * time_pt, tangent_GReg.tVector[1] * time_pt, tangent_GReg.tVector[2] * time_pt ] )
mean = base_GReg.ExponentialMap( v_t )
est_trend_pt_list.append( mean )
est_trend_t_list.append( time_pt )
estLinePolyData = vtk.vtkPolyData()
estLinePts = vtk.vtkPoints()
for i in range( len( est_trend_pt_list ) ):
estLinePts.InsertNextPoint( est_trend_pt_list[ i ].pt[0], est_trend_pt_list[ i ].pt[1], est_trend_pt_list[ i ].pt[2] )
estLinePolyData.SetPoints( estLinePts )
estLines = vtk.vtkCellArray()
for i in range( len( est_trend_pt_list ) - 1 ):
line_i = vtk.vtkLine()
line_i.GetPointIds().SetId( 0, i )
line_i.GetPointIds().SetId( 1, i + 1 )
estLines.InsertNextCell( line_i )
estLinePolyData.SetLines( estLines )
estLineMapper = vtk.vtkPolyDataMapper()
estLineMapper.SetInputData( estLinePolyData )
estLineActor = vtk.vtkActor()
estLineActor.SetMapper( estLineMapper )
estLineActor.GetProperty().SetColor( 0, 1, 0 )
estLineActor.GetProperty().SetOpacity( 0.5 )
estLineActor.GetProperty().SetLineWidth( 12 )
estLineActor.GetProperty().SetRenderLinesAsTubes( 0 )
# Renderer
ren = vtk.vtkRenderer()
renWin = vtk.vtkRenderWindow()
renWin.AddRenderer( ren )
renIn = vtk.vtkRenderWindowInteractor()
renIn.SetRenderWindow( renWin )
ren.AddActor( conActor )
ren.AddActor( ptsActor )
ren.AddActor( ptsActor_mu )
# ren.AddActor( estLineActor_LReg )
ren.AddActor( estLineActor )
light = vtk.vtkLight()
light.SetFocalPoint(1.875,0.6125,0)
light.SetPosition(0.875,1.6125,1)
ren.AddLight( light )
ren.SetBackground( 1.0, 1.0, 1.0 )
renWin.Render()
renIn.Start()