pcaspd.py

from colorutil import *

_kdtree = [
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    1,
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    3,
    0.23331728624128514,
    1,
    4,
    5,
    0.38888444995949917,
    1,
    6,
    7,
]
_leaves = [0, 0, 0, 0, 0, 0, 0, 0]
_leaves[0] = [
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]
_leaves[1] = [
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]
_leaves[2] = [
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_leaves[3] = [
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]
_leaves[4] = [
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        [0.065885680935584667, -0.081535103787772789, -0.074894043535235766],
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        [0.1848727553962764, -0.025667008838144274, -0.19572820772501637],
        [0.19939744792365882, 0.030534884159671552, -0.18761520264616918],
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        [0.23412126961610596, 0.1810471186766742, -0.16496277225604214],
        [0.25437439563369924, 0.243540075700411, -0.14315254152093546],
        [0.27238119535487298, 0.27705363403632088, -0.10293015602216077],
        [0.27974802132494492, 0.26652761484042314, -0.039594304208439499],
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        [0.26640018623663941, 0.15852132981474684, 0.13004165932396652],
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        [0.14029003617407457, -0.15340576599607658, 0.24881829303936245],
        [0.12016641532318899, -0.16752456079887612, 0.15873070821246946],
        [0.10164624822148335, -0.17577762395386218, 0.067468504042690197],
        [0.089410770358060859, -0.18045793058552392, -0.0016854256189599761],
        [0.08269718324477647, -0.18413821976709119, -0.046011561597395972],
        [0.078970435952381415, -0.18942539482636803, -0.081310852023504604],
        [0.077236190698826479, -0.19810651758700099, -0.11722195496183985],
        [0.078128214047245154, -0.20781361957367364, -0.14262692290819509],
        [0.081330922754802665, -0.21311647768648992, -0.1429071087037288],
        [0.085934222255144008, -0.21240012121157889, -0.11813863606312774],
        [0.091213426586917917, -0.2076206140544905, -0.076709200601140753],
        [0.095874295058489989, -0.20121939183675031, -0.028556797697128808],
        [0.099534029393298876, -0.19825702909836634, 0.0042295797556599346],
        [0.10473943283766482, -0.2049841860970304, 0.0028641234027122677],
        [0.11417684054175532, -0.2186453078159562, -0.019396343917196059],
    ],
    [
        [0.60865347734153741, 2.2646725849330811, 2.1755099004642635],
        [-9.8383660557126422, 6.2683894228140771, 0.68699163526592699],
        [-0.60969874484391351, 3.3138138494733411, -2.7342910710940136],
    ],
    [
        [0.049383764705882384],
        [0.06474164705882354],
        [0.08724188235294118],
        [0.11563282352941175],
        [0.1417871764705882],
        [0.16211623529411762],
        [0.1830925882352941],
        [0.2058101176470588],
        [0.23096976470588235],
        [0.260266705882353],
        [0.2930696470588236],
        [0.32645152941176464],
        [0.35244670588235305],
        [0.3594874117647059],
        [0.34934082352941187],
        [0.32825705882352935],
        [0.29917282352941177],
        [0.2601567058823529],
        [0.21550011764705884],
        [0.17788152941176472],
        [0.15000129411764704],
        [0.1280862352941176],
        [0.10592399999999995],
        [0.08698305882352939],
        [0.07562905882352944],
        [0.07006647058823529],
        [0.06757694117647059],
        [0.06739905882352942],
        [0.06981635294117652],
        [0.07386341176470589],
        [0.07836988235294118],
        [0.08304258823529415],
        [0.08689329411764704],
        [0.09078635294117647],
        [0.09925670588235296],
        [0.11556564705882352],
    ],
    [[0.14470422044349615], [0.22555260785156037], [0.243266341117927]],
]
_leaves[5] = [
    [
        [0.019868050996831144, -0.027749753424616941, -0.03942012358555199],
        [0.024661572246250985, -0.028873581932186795, -0.055469342807215383],
        [0.032616944544318002, -0.031242567376940839, -0.079565135943359955],
        [0.044365985311729375, -0.033348266548423829, -0.11196318362607999],
        [0.057703623507972361, -0.033252572723346363, -0.14784710983992891],
        [0.07056027120767093, -0.026554041031897162, -0.18098632544861057],
        [0.086329744190157626, -0.010704558899077512, -0.21775522548293674],
        [0.10648189632412142, 0.014573119186707641, -0.25953970937059467],
        [0.13209848796483009, 0.052674812032197885, -0.30769815175822529],
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        [0.28413887998978959, -0.22161353767055048, 0.14490641964425233],
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        [0.17144037684390451, -0.33340655790822438, -0.040205344201102541],
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        [0.039703064424892187, -0.10854798154486134, -0.079187331299548913],
        [0.046732634703127704, -0.12600200359642338, -0.085978853142503892],
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        [0.054971621469177279, -0.14068274633603203, -0.097267369677297183],
    ],
    [
        [-2.8731422712109387, 4.9177684828131047, 1.6869627098096134],
        [-7.7423665572947931, 2.7154691147291157, 2.3269730119732226],
        [-3.4913582437744815, 3.3799910207916737, -2.2366205128983903],
    ],
    [
        [0.01634162790697675],
        [0.01925651162790698],
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        [0.0308424418604651],
        [0.038929418604651184],
        [0.04738895348837209],
        [0.05867534883720931],
        [0.07398430232558138],
        [0.09400197674418607],
        [0.12231],
        [0.16537895348837206],
        [0.23068197674418586],
        [0.3067259302325581],
        [0.34872639534883737],
        [0.3470554651162791],
        [0.32382220930232564],
        [0.28952720930232567],
        [0.24343023255813948],
        [0.19279197674418613],
        [0.15039651162790701],
        [0.11651232558139542],
        [0.08650697674418603],
        [0.05728174418604655],
        [0.0349689534883721],
        [0.022708953488372086],
        [0.01696034883720931],
        [0.013768139534883725],
        [0.011693720930232559],
        [0.011114418604651158],
        [0.012297674418604652],
        [0.015126279069767452],
        [0.019525813953488385],
        [0.024814534883720932],
        [0.029417558139534884],
        [0.03319186046511628],
        [0.03892767441860465],
    ],
    [[0.09158629107524266], [0.19391012739717364], [0.11267655100104398]],
]
_leaves[6] = [
    [
        [0.062980853706992537, -0.034486960453099139, -0.10145784251045439],
        [0.071948098995730042, -0.050710235216232059, -0.12989553216061756],
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        [0.13228621677535937, -0.16174761000739599, -0.27249268792872461],
        [0.13296853857824181, -0.17033843843120122, -0.25885613419808184],
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        [0.19160044932841816, 0.1787739133945988, -0.073332647127686501],
        [0.19233105000846359, 0.17774989945474748, -0.070744658943501015],
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    ],
    [
        [6.1118011666394256, -0.63513140886360919, 0.63054608821267599],
        [7.8648744182941233, -5.5208914966788978, -2.2957204428954197],
        [-2.5397998553619652, 4.0628349508276136, -2.0087487542389759],
    ],
    [
        [0.11082141345549734],
        [0.12562708378708543],
        [0.15212626528795778],
        [0.18540398099476424],
        [0.2098338767888304],
        [0.22079372745200673],
        [0.22691598424083773],
        [0.2311631453926702],
        [0.2352588439790574],
        [0.24043656616055853],
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        [0.26726260120418793],
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        [0.39138952926701537],
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        [0.402476787399651],
        [0.40518048036649174],
        [0.40653693080279224],
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        [0.4121506712390922],
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        [0.4313784830366494],
    ],
    [[0.3215866890260972], [0.3323672084395472], [0.25661207873030195]],
]
_leaves[7] = [
    [
        [0.024217262034941733, 0.022424861331203534, -0.11597058097773272],
        [0.02403058283764492, 0.02700631137955925, -0.13175683714198783],
        [0.02584962642236182, 0.034615278150084458, -0.15944902312481202],
        [0.028674603674140216, 0.044708520266870173, -0.19462684758196688],
        [0.030408322949325203, 0.054460328838252053, -0.223425513225671],
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        [0.22344545686381859, -0.1503206330128766, -0.034895919869831968],
        [0.22550029718410494, -0.1657296472155779, -0.041947308394073415],
        [0.2274376974365879, -0.17433811572116925, -0.046427118880207993],
        [0.22851439734535678, -0.1725841734120255, -0.045204150498454145],
        [0.22895267436941055, -0.16216171901870582, -0.039243233978318227],
        [0.22846257745077686, -0.14569345720152038, -0.029881950824883111],
        [0.22806412172519758, -0.1280730249188762, -0.01977199855440618],
        [0.22740282307110887, -0.11594858475136806, -0.012684279825095651],
        [0.22715823121869261, -0.11326876494437256, -0.012809633265729078],
        [0.22773779852081508, -0.11241775681706437, -0.015429967328365948],
    ],
    [
        [8.0574963533776209, -1.6699022953651796, -0.52760512650374558],
        [-7.36844195862398, 6.6097600002381069, 1.6399525716553454],
        [-1.6228426801747824, 2.223392822149362, -2.9179776383911893],
    ],
    [
        [0.044053163763066186],
        [0.04492414703832752],
        [0.049124770069686456],
        [0.055159989094076614],
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        [0.06289338153310105],
        [0.06597726846689901],
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        [0.07499693501742155],
        [0.08300358592334493],
        [0.1029995324738676],
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        [0.2525250358885018],
        [0.3415762524738676],
        [0.38276632756097567],
        [0.3934586344250871],
        [0.3971811634494772],
        [0.39914832595818833],
        [0.39865097146341455],
        [0.3972447237979091],
        [0.3884461682229966],
        [0.37315658254355394],
        [0.35097260491289156],
        [0.3285678778048779],
        [0.3134223668641114],
        [0.3056770914285714],
        [0.3020083383623695],
        [0.3002939057839717],
        [0.30195210783972143],
        [0.3070093854703835],
        [0.31476829968641135],
        [0.3241799281184667],
        [0.33510864853658495],
        [0.3443250147038329],
        [0.35157725606271795],
        [0.36112905449477356],
    ],
    [[0.287956117643289], [0.3558381900199877], [0.09809903558056805]],
]

def sRGBToSPDOtsu(srgb):
    """Implements Otsu and others, "Reproducing Spectral Reflectances
    from Tristimulus Colors", 2018."""
    global _kdtree, _leaves
    xyz = xyzFromsRGB(srgb)
    xyy = xyzToxyY(xyz)
    node = 0
    node = (
        _kdtree[node + 2]
        if xyy[_kdtree[node + 1]] < _kdtree[node]
        else _kdtree[node + 3]
    )
    node = (
        _kdtree[node + 2]
        if xyy[_kdtree[node + 1]] < _kdtree[node]
        else _kdtree[node + 3]
    )
    node = (
        _kdtree[node + 2]
        if xyy[_kdtree[node + 1]] < _kdtree[node]
        else _kdtree[node + 3]
    )
    leaf = _leaves[node]
    cdiff = matSub(matT(matFromVec(xyz)), leaf[3])
    weights = matMul(leaf[1], cdiff)
    r = matAdd(matMul(leaf[0], weights), leaf[2])
    refl = matT(r)[0]
    # Clamp spectra to interval [0.0001, 1]
    for i in range(len(refl)):
        if refl[i] < 0.0001:
            refl[i] = 0.0001
        if refl[i] > 1:
            refl[i] = 1
    spd = SPD(refl, 10, 380)
    return spd

def _fileread(x):
    f = file(x, "r")
    ret = f.read()
    f.close()
    return ret

def _cmfd65(x):
    c = cie1931cmf(x)
    d = d65Illum(x) / 100.0
    return [cv * d for cv in c]

def _meanarr(arrs):
    arrlen = len(arrs[0])
    numarrs = len(arrs)
    ret = [0 for x in arrs[0]]
    for i in range(numarrs):
        for j in range(arrlen):
            ret[j] += arrs[i][j]
    return [v * 1.0 / numarrs for v in ret]

def _pca(spdxyy, st, en):
    global cmf
    arr = [spdxyy[i][0] for i in range(st, en)]
    pca = PCA(n_components=3)
    pca.fit(np.asarray(arr))
    com = pca.components_
    mat = matT(matNew([com[0], com[1], com[2]]))
    m = matMul(cmf, mat)
    minv = matI(m)
    mean = matT(matFromVec(_meanarr(arr)))
    cmean = matMul(cmf, mean)
    return [mat, minv, mean, cmean]

def _deltae(spdxyy, st, en):
    pcas = None
    try:
        pcas = _pca(spdxyy, st, en)
    except:
        return 99999  # Unexpected error
    ret = 0.0
    for i in range(st, en):
        s = matT(matFromVec(spdxyy[i][0]))
        cdiff = matSub(matT(matFromVec(spdxyy[i][2])), pcas[3])
        weights = matMul(pcas[1], cdiff)
        r = matAdd(matMul(pcas[0], weights), pcas[2])
        sdiff = matT(matSub(s, r))[0]
        normsq = vecDot(sdiff, sdiff)
        ret += normsq
    return ret

def _splitAxis(spdxyy):
    spx = [x for x in spdxyy]
    spy = [x for x in spdxyy]
    spx.sort(lambda a, b: cmp(a[1][0], b[1][0]))
    spy.sort(lambda a, b: cmp(a[1][1], b[1][1]))
    de = -1
    best = 0
    axis = 0
    parts = 25  # Use only several split possibilities to save time
    for i in range(1, min(parts - 1, len(spx) - 1)):
        point = len(spx) * i / parts
        if point < 3 or point == len(spx) - 3:
            continue
        cde = _deltae(spx, 0, point) + _deltae(spx, point, len(spx))
        if de < 0 or cde < de:
            de = cde
            best = point
            axis = 0
        cde = _deltae(spy, 0, point) + _deltae(spy, point, len(spy))
        if de < 0 or cde < de:
            de = cde
            best = point
            axis = 1
    if axis == 0:
        return [spx[:best], spx[best:], spx[best][1][0], axis]
    return [spy[:best], spy[best:], spx[best][1][0], axis]

# Generates algorithm data from JSON array of reflectance curves
# (stored in a file named "specs.json").
# Each curve is an array of 36 reflectance factors (from 0 through 1)
# starting at 380 nm and continuing to 730 nm, with a wavelength
# interval of 10 nm.
if __name__ == "__main__":
    # Uses PCA from scikit-learn package
    from sklearn.decomposition import PCA
    import numpy as np
    import json

    specs = json.loads(_fileread("specs.json"))
    for sp in specs:
        if len(sp) != 36:
            raise ValueError
    xyz = [spectrumToTristim(SPD(specs[i], 10, 380).calc) for i in range(len(specs))]
    spdxyy = [[specs[i], xyzToxyY(xyz[i]), xyz[i]] for i in range(len(specs))]
    cmf = matNew([_cmfd65(x) for x in brange(10, 380, 730)])
    cmf = matT(cmf)
    weight = sum(cmf[1]) * 1.0
    cmf = matScale(cmf, 1.0 / weight)

    sp1 = _splitAxis(spdxyy)
    sp2 = _splitAxis(sp1[0])
    sp3 = _splitAxis(sp1[1])
    sp4 = _splitAxis(sp2[0])
    sp5 = _splitAxis(sp2[1])
    sp6 = _splitAxis(sp3[0])
    sp7 = _splitAxis(sp3[1])
    splits = []
    kd = [4, 8, 12, 16, 20, 24, 0, 1, 2, 3, 4, 5, 6, 7]
    kdi = 0
    for sp in [sp1, sp2, sp3, sp4, sp5, sp6, sp7]:
        splits += [sp[2], sp[3]]
        splits += kd[kdi : kdi + 2]
        kdi += 2
    print("_kdtree=%s" % (splits))
    print("_leaves=[0,0,0,0,0,0,0,0]")
    leavei = 0
    for sp in [sp4, sp5, sp6, sp7]:
        pca1 = _pca(sp[0], 0, len(sp[0]))
        print("_leaves[%d]=[%s," % (leavei, pca1[0]))
        print("  %s," % (pca1[1]))
        print("  %s," % (pca1[2]))
        print("  %s]" % (pca1[3]))
        leavei += 1
        pca2 = _pca(sp[1], 0, len(sp[1]))
        print("_leaves[%d]=[%s," % (leavei, pca2[0]))
        print("  %s," % (pca2[1]))
        print("  %s," % (pca2[2]))
        print("  %s]" % (pca2[3]))
        leavei += 1