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@decrispell
Created September 26, 2019 19:11
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Compute surface normals from 3-plane "xyz" image data
import numpy as np
def normals_from_xyz(xyz, smooth_sigma=None):
"""
Given a 3-plane float image containing x,y,z coordinates,
compute the surface normals at each pixel.
Returns a 3-plane floating point image with nx,ny,nz per pixel.
"""
if smooth_sigma is not None:
xyz = np.array(xyz) # make copy of input
for p in range(3):
xyz[:,:,p] = gaussian_filter(xyz[:,:,p], sigma=smooth_sigma)
dx_du, dx_dv = np.gradient(xyz[:,:,0])
dy_du, dy_dv = np.gradient(xyz[:,:,1])
dz_du, dz_dv = np.gradient(xyz[:,:,2])
grad_u = np.stack((dx_du, dy_du, dz_du), axis=2)
grad_v = np.stack((dx_dv, dy_dv, dz_dv), axis=2)
# compute surface normals as cross product of dx/du and dx/dv
xyz_norm = np.cross(grad_u, grad_v, axis=2)
xyz_norm /= np.expand_dims(np.linalg.norm(xyz_norm, axis=2), axis=2)
return xyz_norm
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