#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
tensor: Compute colour metric tensors. Part of the colourlab package.
Copyright (C) 2013-2021 Ivar Farup
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or (at
your option) any later version.
This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
"""
import numpy as np
from . import data, space
# =============================================================================
# Colour metric tensors
# =============================================================================
[docs]def construct_tensor(sp, tensor_ndata, dat):
"""
Construct the Tensors object with correct dimensions
The tensors_ndata has shape N x 3 x 3. Construct Tensors object
with shape corresponding to the data points in dat.
Parameters
----------
sp: space.Space
The colour space of the tensor_ndata
tensor_ndata: ndarray
N x 3 x 3 ndarray of tensor data.
dat: data.Points
Colour data points
"""
sh = np.hstack((np.array(dat.sh), 3))
return data.Tensors(sp, np.reshape(tensor_ndata, sh), dat)
[docs]def euclidean(sp, dat):
"""
Compute the general Euclidean metric in the given colour space.
Returns Tensors.
Parameters
----------
sp : space.Space
The colour space in which the metric tensor is Euclidean.
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
Euclidean : Tensors
The metric tensors.
"""
g = sp.empty_matrix(dat.flattened_XYZ)
for i in range(np.shape(g)[0]):
g[i] = np.eye(3)
return construct_tensor(sp, g, dat)
[docs]def polar(sp, dat):
"""
Compute the general Euclidean metric in cylindrical coordinates.
Assumes z, r, theta (LCh) order. Returns Tensors.
Parameters
----------
sp : space.Space
The colour space in which the metric tensor is Euclidean, with
cylindrical coordinates
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
Tensors
The metric tensors.
"""
g = sp.empty_matrix(dat.flattened_XYZ)
points = dat.get_flattened(sp)
for i in range(np.shape(g)[0]):
g[i] = np.eye(3)
g[i, 2, 2] = points[i, 1]**2
return construct_tensor(sp, g, dat)
[docs]def dE_ab(dat):
"""
Compute the DEab metric as Tensors for the given data points.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
DEab : Tensors
The metric tensors.
"""
return euclidean(space.cielab, dat)
[docs]def dE_uv(dat):
"""
Compute the DEuv metric as Tensors for the given data points.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
DEuv : Tensors
The metric tensors.
"""
return euclidean(space.cieluv, dat)
[docs]def dE_E(dat):
"""
Compute the DEE metric as Tensors for the given data points.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
DEE : Tensors
The metric tensors.
"""
return euclidean(space.lgj_e, dat)
[docs]def dE_DIN99(dat):
"""
Compute the DIN99 metric as Tensors for the given data points.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
DIN99 : Tensors
The metric tensors.
"""
return euclidean(space.din99, dat)
[docs]def dE_DIN99b(dat):
"""
Compute the DIN99b metric as Tensors for the given data points.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
DIN99b : Tensors
The metric tensors.
"""
return euclidean(space.din99b, dat)
[docs]def dE_DIN99c(dat):
"""
Compute the DIN99c metric as Tensors for the given data points.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
DIN99c : Tensors
The metric tensors.
"""
return euclidean(space.din99c, dat)
[docs]def dE_DIN99d(dat):
"""
Compute the DIN99d metric as Tensors for the given data points.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
DIN99d : Tensors
The metric tensors.
"""
return euclidean(space.din99d, dat)
[docs]def dE_00(dat, k_L=1, k_C=1, k_h=1):
"""
Compute the Riemannised CIEDE00 metric for the given data points.
Returns Tensors. Be aware that the tensor is singluar at C = 0.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
k_L : float
Parameter of the CIEDE00 metric
k_C : float
Parameter of the CIEDE00 metric
k_h : float
Parameter of the CIEDE00 metric
Returns
-------
DE00 : Tensors
The metric tensors.
"""
lch = dat.get_flattened(space.ciede00lch)
L = lch[:, 0]
C = lch[:, 1]
h = lch[:, 2]
h_deg = np.rad2deg(h)
h_deg[h_deg < 0] = h_deg[h_deg < 0] + 360
S_L = 1 + (0.015 * (L - 50)**2) / np.sqrt(20 + (L - 50)**2)
S_C = 1 + 0.045 * C
T = 1 - 0.17 * np.cos(np.deg2rad(h_deg - 30)) + \
.24 * np.cos(2*h) + \
.32 * np.cos(np.deg2rad(3 * h_deg + 6)) - \
.2 * np.cos(np.deg2rad(4 * h_deg - 63))
S_h = 1 + 0.015 * C * T
R_C = 2 * np.sqrt(C**7 / (C**7 + 25**7))
d_theta = 30 * np.exp(-((h_deg - 275) / 25)**2)
R_T = - R_C * np.sin(np.deg2rad(2 * d_theta))
g = space.ciede00lch.empty_matrix(lch)
g[:, 0, 0] = (k_L * S_L)**(-2)
g[:, 1, 1] = (k_C * S_C)**(-2)
g[:, 2, 2] = C**2 * (k_h * S_h)**(-2)
g[:, 1, 2] = .5 * C * R_T / (k_C * S_C * k_h * S_h)
g[:, 2, 1] = .5 * C * R_T / (k_C * S_C * k_h * S_h)
return construct_tensor(space.ciede00lch, g, dat)
[docs]def poincare_disk(sp, dat):
"""
Compute the general Poincare Disk metric in the given colour space.
Returns Tensors. Assumes that sp is a Poincare Disk of some
kind, and thus has a radius of curvature as sp.R.
Parameters
----------
dat : data.Points
The colour points for which to compute the metric.
Returns
-------
Poincare : Tensors
The metric tensors.
"""
d = dat.get_flattened(sp)
g = sp.empty_matrix(d)
for i in range(np.shape(g)[0]):
g[i, 0, 0] = 1
g[i, 1, 1] = sp.R**2 * 4. / (1 - d[i, 1]**2 - d[i, 2]**2)**2
g[i, 2, 2] = sp.R**2 * 4. / (1 - d[i, 1]**2 - d[i, 2]**2)**2
return construct_tensor(sp, g, dat)
# TODO:
#
# Functions (returning Tensors):
# stiles
# helmholz
# schrodinger
# vos
# SVF
# CIECAM02
# CAM16
# +++
# =============================================================================
# Christoffel symbols
# =============================================================================
[docs]def christoffel(sp, tensor, dat, du=1e-8):
"""
Compute the Christoffel symbols numerically.
Compute the Christoffel symbols of the second kind for the given metric
tensor function in the given colour space at the given data points.
Parameters
----------
sp : space.Space
The colour space.
tensor : func
Function returning the metric tensor of the data
dat : data.Points
The colour data points (or image)
du : float
Delta u for the computation of the numerical derivatives
Returns
-------
ndata :
The Christoffel symbols of the second kind as M x ... x N x 3 x 3 x 3
ndarray (for M x ... x N x 3 data points)
"""
x = dat.get(sp)
dxi = np.zeros(x.shape)
dxj = np.zeros(x.shape)
dxk = np.zeros(x.shape)
dxi[..., 0] = du
dxj[..., 1] = du
dxk[..., 2] = du
datpdxi = data.Points(sp, x + dxi)
datpdxj = data.Points(sp, x + dxj)
datpdxk = data.Points(sp, x + dxk)
g = tensor(dat).get(sp)
gpdxi = tensor(datpdxi).get(sp)
gpdxj = tensor(datpdxj).get(sp)
gpdxk = tensor(datpdxk).get(sp)
dgdx = np.zeros(np.hstack((np.array(g.shape), 3)))
dgdx[..., 0] = (gpdxi - g) / du
dgdx[..., 1] = (gpdxj - g) / du
dgdx[..., 2] = (gpdxk - g) / du
Gamma = np.zeros(dgdx.shape) # first kind
for c in range(3):
for a in range(3):
for b in range(3):
Gamma[..., c, a, b] = .5 * (dgdx[..., c, a, b] +
dgdx[..., c, b, a] -
dgdx[..., a, b, c])
ginv = np.linalg.inv(g)
return np.einsum('...ij,...jkl', ginv, Gamma) # convert to second kind