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demo_projSH_rotSH.py
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demo_projSH_rotSH.py
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import importlib
import scipy
import scipy.sparse
import numpy as np
import matplotlib.pyplot as plt
import imageio
import cv2
class Rotation(object):
def __init__(self):
super(Rotation, self).__init__()
rows_x = [0, 1, 2, 3, 4, 5, 6, 6, 7, 8, 8]
cols_x = [0, 2, 1, 3, 7, 5, 6, 8, 4, 6, 8]
data_x_p90 = [1,-1,1,1,-1,-1,-1/2,-np.sqrt(3)/2,1,-np.sqrt(3)/2,1/2]
data_x_n90 = [1,1,-1,1,1,-1,-1/2,-np.sqrt(3)/2,-1,-np.sqrt(3)/2,1/2]
self.Rot_X_p90 = scipy.sparse.coo_matrix((data_x_p90,(rows_x,cols_x)), shape=(9,9)).toarray()
self.Rot_X_n90 = scipy.sparse.coo_matrix((data_x_n90,(rows_x,cols_x)), shape=(9,9)).toarray()
self.rows_z = [0, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8]
self.cols_z = [0, 1, 3, 2, 1, 3, 4, 8, 5, 7, 6, 5, 7, 4, 8]
def rot_SH(self, SH, thetaX, thetaY, thetaZ):
Rot_y = []
Rot_x = []
Rot_z = []
# for rot in np.arange(0,2*np.pi,np.pi/18):
for rotx, roty, rotz in zip(thetaX, thetaY, thetaZ):
Rot_z.append(self.rot_z(rotz))
Rot_y.append(self.rot_y(roty))
Rot_x.append(self.rot_x(rotx))
Rot_y = np.stack(Rot_y, axis=0)
Rot_x = np.stack(Rot_x, axis=0)
Rot_z = np.stack(Rot_z, axis=0)
Rot = np.matmul(Rot_z, np.matmul(Rot_y, Rot_x))
rot_SH = np.matmul(Rot, SH)
return rot_SH
def rot_z(self, thetaZ):
data_Z = [1,np.cos(thetaZ),np.sin(thetaZ),1,-np.sin(thetaZ),np.cos(thetaZ),np.cos(2*thetaZ),np.sin(2*thetaZ),np.cos(thetaZ),np.sin(thetaZ),1,-np.sin(thetaZ),np.cos(thetaZ),-np.sin(2*thetaZ),np.cos(2*thetaZ)]
return scipy.sparse.coo_matrix((data_Z,(self.rows_z, self.cols_z)), shape=(9,9)).toarray()
def rot_y(self, thetaY):
data_Z = [1,np.cos(thetaY),np.sin(thetaY),1,-np.sin(thetaY),np.cos(thetaY),np.cos(2*thetaY),np.sin(2*thetaY),np.cos(thetaY),np.sin(thetaY),1,-np.sin(thetaY),np.cos(thetaY),-np.sin(2*thetaY),np.cos(2*thetaY)]
rotM_z = scipy.sparse.coo_matrix((data_Z,(self.rows_z, self.cols_z)), shape=(9,9)).toarray()
return np.matmul(self.Rot_X_p90, np.matmul(rotM_z, self.Rot_X_n90))
def rot_x(self, thetaX):
data_Z = [1,np.cos(thetaX),np.sin(thetaX),1,-np.sin(thetaX),np.cos(thetaX),np.cos(2*thetaX),np.sin(2*thetaX),np.cos(thetaX),np.sin(thetaX),1,-np.sin(thetaX),np.cos(thetaX),-np.sin(2*thetaX),np.cos(2*thetaX)]
rotM_z = scipy.sparse.coo_matrix((data_Z,(self.rows_z, self.cols_z)), shape=(9,9)).toarray()
return np.matmul(self.rot_y(np.pi/2), np.matmul(rotM_z, self.rot_y(-np.pi/2)))
def render_sphere_nm(radius, num):
# nm is a batch of normal maps
nm = []
for i in range(num):
### sphere (projected on circular image just like angular map)
# span the regular grid for computing azimuth and zenith angular map
height = 2*radius
width = 2*radius
centre = radius
h_grid, v_grid = np.meshgrid(np.arange(1.,2*radius+1), np.arange(1.,2*radius+1))
# grids are (-radius, radius)
h_grid -= centre
# v_grid -= centre
v_grid = centre - v_grid
# scale range of h and v grid in (-1,1)
h_grid /= radius
v_grid /= radius
# z_grid is linearly spread along theta/zenith in range (0,pi)
dist_grid = np.sqrt(h_grid**2+v_grid**2)
dist_grid[dist_grid>1] = np.nan
theta_grid = dist_grid * np.pi
z_grid = np.cos(theta_grid)
rho_grid = np.arctan2(v_grid,h_grid)
x_grid = np.sin(theta_grid)*np.cos(rho_grid)
y_grid = np.sin(theta_grid)*np.sin(rho_grid)
# concatenate normal map
nm.append(np.stack([x_grid,y_grid,z_grid],axis=2))
# construct batch
nm = np.stack(nm,axis=0)
return nm
def sh_recon(nm, lighting):
width = nm.shape[1]
x = nm[:,:,:,0]
y = nm[:,:,:,1]
z = nm[:,:,:,2]
# convert light probe to angular map(evenly distributed front and back environment), find light directions by new angular map
azi = np.arctan2(y, x)
zen = np.arccos(z)
c1 = 0.282095
c2 = 0.488603
c3 = 1.092548
c4 = 0.315392
c5 = 0.546274
# domega = 4*np.pi**2/width**2 * sinc(zen)
domega = np.ones_like(zen)
sh_basis = np.stack([c1 * domega, c2*y * domega, c2*z * domega, c2*x * domega, c3*x*y * domega, c3*y*z * domega, c4*(3*z*z-1) * domega, c3*x*z * domega, c5*(x*x-y*y) * domega], axis=1)
sh_basis = np.expand_dims(sh_basis, axis=-1)
lighting_recon = np.expand_dims(np.expand_dims(lighting,axis=-2),axis=-2) * sh_basis
lighting_recon = np.sum(lighting_recon,axis=1)
return lighting_recon
# perform spherical harmonics projection based on Cartesian Coords SH basis
def SH_proj(func,coords,width):
# func and coords have shape (npix, 3[rgb]/[xyz])
c1 = 0.282095
c2 = 0.488603
c3 = 1.092548
c4 = 0.315392
c5 = 0.546274
x = coords[:,0,np.newaxis]
y = coords[:,1,np.newaxis]
z = coords[:,2,np.newaxis]
theta = np.arccos(z)
domega = 4*np.pi**2/width**2 * sinc(theta)
coeffs = []
coeffs.append(np.sum(func * c1 * domega, axis=0))
coeffs.append(np.sum(func * c2*y * domega, axis=0))
coeffs.append(np.sum(func * c2*z * domega, axis=0))
coeffs.append(np.sum(func * c2*x * domega, axis=0))
coeffs.append(np.sum(func * c3*x*y * domega, axis=0))
coeffs.append(np.sum(func * c3*y*z * domega, axis=0))
coeffs.append(np.sum(func * c4*(3*z*z-1) * domega, axis=0))
coeffs.append(np.sum(func * c3*x*z * domega, axis=0))
coeffs.append(np.sum(func * c5*(x*x-y*y) * domega, axis=0))
coeffs = np.stack(coeffs,axis=0)
return coeffs
def sinc(x):
"""Supporting sinc function
"""
output = np.sin(x)/x
output[np.isnan(output)] = 1.
return output
def angularMap_dirs_r2r(em):
# Coordinates following Will's convention
h,w,_ = em.shape
centre_h = h/2.
centre_w = w/2.
h_grid = np.arange(h,0,-1)
# h_grid = np.arange(1,h+1)
w_grid = np.arange(1,w+1)
w_grid, h_grid = np.meshgrid(w_grid, h_grid)
# w_grid and h_grid stand for x and y in range (-1,1)
w_grid = ((w_grid-centre_w)/centre_w)
h_grid = ((h_grid-centre_h)/centre_h)
dis = np.sqrt(w_grid**2+h_grid**2)
lightMask = dis<=1. # flattened mask
# convert light probe to angular map(evenly distributed front and back environment), find light directions by new angular map
azi = np.arctan2(h_grid, w_grid).astype(np.float32)
zen = (dis*np.pi).astype(np.float32)
x = -np.sin(zen)*np.sin(azi)
y = np.cos(zen)
z = -np.sin(zen)*np.cos(azi)
lightDirs = np.stack([x[lightMask],y[lightMask],z[lightMask]], axis=1)
em_r = em[:,:,0]
em_g = em[:,:,1]
em_b = em[:,:,2]
lightColors = np.stack([em_r[lightMask], em_g[lightMask], em_b[lightMask]], axis=1)
return lightDirs, lightColors, lightMask
def angularMap_dirs(em):
h,w,_ = em.shape
centre_h = h/2.
centre_w = w/2.
h_grid = np.arange(h,0,-1)
# h_grid = np.arange(1,h+1)
w_grid = np.arange(1,w+1)
w_grid, h_grid = np.meshgrid(w_grid, h_grid)
# w_grid and h_grid stand for x and y in range (-1,1)
w_grid = ((w_grid-centre_w)/centre_w)
h_grid = ((h_grid-centre_h)/centre_h)
dis = np.sqrt(w_grid**2+h_grid**2)
lightMask = dis<=1. # flattened mask
# convert light probe to angular map(evenly distributed front and back environment), find light directions by new angular map
azi = np.arctan2(h_grid, w_grid).astype(np.float32)
zen = (dis*np.pi).astype(np.float32)
# x->right, y->up, z->outward
x = np.sin(zen)*np.cos(azi)
y = np.sin(zen)*np.sin(azi)
z = np.cos(zen)
lightDirs = np.stack([x[lightMask],y[lightMask],z[lightMask]], axis=1)
em_r = em[:,:,0]
em_g = em[:,:,1]
em_b = em[:,:,2]
lightColors = np.stack([em_r[lightMask], em_g[lightMask], em_b[lightMask]], axis=1)
return lightDirs, lightColors, lightMask
def latlongMap_dirs_r2r(em):
# Coordinates following Will's convention
h,w,_ = em.shape
cols, rows = np.meshgrid(np.arange(w), np.arange(h))
theta = -np.pi*((2*cols)/w-1)
phi = (rows*np.pi)/h
x = -np.cos(phi)
y = np.sin(phi)*np.cos(theta)
z = np.sin(phi)*np.sin(theta)
lightDirs = np.stack([x.ravel(), y.ravel(), z.ravel()], axis=1).astype(np.float32)
lightColors = em.reshape(-1, 3).astype(np.float32)
return lightDirs, lightColors
def latlongMap_dirs(em):
h,w,_ = em.shape
azi, zen = np.meshgrid(np.arange(0,2*np.pi,2*np.pi/w), np.arange(np.pi/2,-np.pi/2,-np.pi/h))
# x->right, y->up, z->inward
x = -np.cos(zen)*np.sin(azi)
y = np.sin(zen)
z = np.cos(zen)*np.cos(azi)
lightDirs = np.stack([x.ravel(), y.ravel(), z.ravel()], axis=1).astype(np.float32)
lightColors = em.reshape(-1, 3).astype(np.float32)
return lightDirs, lightColors
def main():
# path to the lat-long hdr image
import ipdb; ipdb.set_trace()
exr_img_paths = 'demo.exr'
# read and resize the hdr image
exr_img = imageio.imread(exr_img_paths, format='EXR-FI')
exr_img = cv2.resize(exr_img, (360, 180), cv2.INTER_CUBIC)
exr_h, exr_w = exr_img.shape[:2]
# project the lat-long map to an angular map
# define the direction for each pixel and interpolate the angular map by the pixels in lat-long map with similar direction
exr_img_angMap = np.zeros((exr_h,exr_h,3), np.float32)
latlongMap_dirs, latlongMap_values = latlongMap_dirs(exr_img)
angularMap_dirs, _, angularMap_mask = angularMap_dirs(exr_img_angMap)
# latlongMap_dirs, latlongMap_values = latlongMap_dirs_r2r(exr_img)
# angularMap_dirs, _, angularMap_mask = angularMap_dirs_r2r(exr_img_angMap)
from sklearn.neighbors import NearestNeighbors
nbrs = NearestNeighbors(n_neighbors=1).fit(latlongMap_dirs)
_, idxs = nbrs.kneighbors(angularMap_dirs)
angularMap_values = latlongMap_values[idxs[:,0]]
exr_img_angMap[angularMap_mask] = angularMap_values
# project the angular hdr map to the spherical harmonics
img_sh = SH_proj(angularMap_values, angularMap_dirs, exr_h)
lighting_recon = sh_recon(np.float32(render_sphere_nm(100,1)), img_sh)
lighting_validPix = lighting_recon[np.logical_not(np.isnan(lighting_recon))]
lighting_recon = (lighting_recon - lighting_validPix.min()) / (lighting_validPix.max() - lighting_validPix.min())
lighting_recon[np.isnan(lighting_recon)] = 0
# rotate the original lighting by -pi/3 about x axis
rotation = Rotation()
rot = np.float32(np.dot(rotation.rot_y(0.), np.dot(rotation.rot_x(-np.pi/3), rotation.rot_z(0.))))
rot_sh = np.matmul(rot, img_sh)[None]
# recontruct the rotated lighting
rot_lighting_recon = sh_recon(np.float32(render_sphere_nm(100,1)), rot_sh)
rot_lighting_validPix = rot_lighting_recon[np.logical_not(np.isnan(rot_lighting_recon))]
rot_lighting_recon = (rot_lighting_recon - rot_lighting_validPix.min()) / (rot_lighting_validPix.max() - rot_lighting_validPix.min())
rot_lighting_recon[np.isnan(rot_lighting_recon)] = 0
plt.figure(); plt.imshow(exr_img)
plt.figure(); plt.imshow(exr_img_angMap)
plt.figure(); plt.imshow(lighting_recon[0])
plt.figure(); plt.imshow(rot_lighting_recon[0])
plt.show()
if __name__ == '__main__':
main()