def dot23(A,B, keepdims = False): """ Dot product of a 2-d ndarray with a (N x K x L) 3-d ndarray using einsum(). Args: :A: | ndarray (.shape = (M,N)) :B: | ndarray (.shape = (N,K,L)) Returns: :returns: | ndarray (.shape = (M,K,L)) """ if (len(A.shape)==2) & (len(B.shape)==3): dotAB = np.einsum('ij,jkl->ikl',A,B) if (len(B.shape)==3) & (keepdims == True): dotAB = np.expand_dims(dotAB,axis=1) elif (len(A.shape)==2) & (len(B.shape)==2): dotAB = np.einsum('ij,jk->ik',A,B) if (len(B.shape)==2) & (keepdims == True): dotAB = np.expand_dims(dotAB,axis=1) return dotAB
def np3dT(data): # keep last axis the same """ Make a tuple, list or numpy array at least a 3d numpy array and transposed first 2 axes. Args: :data: | tuple, list, ndarray Returns: :returns: | ndarray with .ndim >= 3 and with first two axes transposed (axis=3 is kept the same). """ if isinstance( data, np.ndarray ): # assume already atleast_3d when nd.array (user has to ensure input is an array) if (len(data.shape) >= 3): return data.transpose((1, 0, 2)) else: return np.expand_dims(np.atleast_2d(data), axis=0).transpose( (1, 0, 2)) else: return np.expand_dims(np.atleast_2d(np.aray(data)), axis=0).transpose( (1, 0, 2))
def todim(x, tshape, add_axis=1, equal_shape=False): """ Expand x to dims that are broadcast-compatable with shape of another array. Args: :x: | ndarray :tshape: | tuple with target shape :add_axis: | 1, optional | Determines where in x.shape an axis should be added :equal_shape: | False or True, optional | True: expand :x: to identical dimensions (speficied by :tshape:) Returns: :returns: | ndarray broadcast-compatable with tshape. """ if x is None: return np.broadcast_arrays(x, np.ones(tshape))[0] else: x = np2d(x) sx = x.shape lsx = len(sx) ltshape = len(tshape) if (sx == tshape): pass else: if ((lsx == 1) | (sx == (1, tshape[-1])) | (sx == (tshape[-1], 1))): if (sx == (tshape[-1], 1)): x = x.T if lsx != ltshape: x = np.expand_dims(x, 0) elif (lsx == 2): if (ltshape == 3): sd = np.setdiff1d(tshape, sx, assume_unique=True) if len(sd) == 0: ax = add_axis else: ax = np.where(tshape == sd)[0][0] x = np.expand_dims(x, ax) else: raise Exception( "todim(x,tshape): dimensions do not match for 2d arrays." ) else: raise Exception( "todim(x,tshape): no matching dimensions between 3d x and tshape." ) if equal_shape == False: return x else: return np.ones( tshape) * x #make dims of x equal to those of a (tshape)
def broadcast_shape(data,target_shape = None, expand_2d_to_3d = None, axis0_repeats = None, axis1_repeats = None): """ Broadcasts shapes of data to a target_shape. | Useful for block/vector calc. when numpy fails to broadcast correctly. Args: :data: | ndarray :target_shape: | None or tuple with requested shape, optional | - None: returns unchanged :data: :expand_2d_to_3d: | None (do nothing) or ..., optional | If ndim == 2, expand from 2 to 3 dimensions :axis0_repeats: | None or number of times to repeat axis=0, optional | - None: keep axis=0 same size :axis1_repeats: | None or number of times to repeat axis=1, optional | - None: keep axis=1 same size Returns: :returns: | reshaped ndarray """ data = np2d(data) # expand shape along axis (useful for some functions that allow block-calculations when the data is only 2d ) if (expand_2d_to_3d is not None) & (len(data.shape) == 2): data = np.expand_dims(data, axis = expand_2d_to_3d) if target_shape is not None: dshape = data.shape if dshape != target_shape: axis_of_v3 = len(target_shape)-1 if (dshape[0] != target_shape[0]): # repeat along axis 0 if axis0_repeats is None: axis0_repeats = (target_shape[0]-dshape[0] + 1) data = np.repeat(data,axis0_repeats,axis = 0) if (len(target_shape)>2) & (len(data.shape)==2): # repeat along axis 1, create axis if necessary data = np.expand_dims(data,axis = axis_of_v3-1) # axis creation dshape = data.shape if (dshape[1] != target_shape[1]): if axis1_repeats is None: axis1_repeats = (target_shape[1]-dshape[1] + 1) # repititon data = np.repeat(data,axis1_repeats,axis = 1) for i in range(2): if (data.shape[i] > 1) & (data.shape[i] != target_shape[i]): raise Exception('broadcast_shape(): Cannot match dim of data with target: data.shape[i]>1 & ... != target.shape[i]') return data
def np3d(data): """ Make a tuple, list or numpy array at least a 3d numpy array. Args: :data: | tuple, list, ndarray Returns: :returns: | ndarray with .ndim >= 3 """ if isinstance(data, np.ndarray):# assume already atleast_3d when nd.array (user has to ensure input is an array) if (len(data.shape)>=3): return data else: return np.expand_dims(np.atleast_2d(data),axis=0) else: return np.expand_dims(np.atleast_2d(np.array(data)),axis=0)
def spd_to_mcri(SPD, D=0.9, E=None, Yb=20.0, out='Rm', wl=None): """ Calculates the MCRI or Memory Color Rendition Index, Rm Args: :SPD: | ndarray with spectral data (can be multiple SPDs, first axis are the wavelengths) :D: | 0.9, optional | Degree of adaptation. :E: | None, optional | Illuminance in lux | (used to calculate La = (Yb/100)*(E/pi) to then calculate D | following the 'cat02' model). | If None: the degree is determined by :D: | If (:E: is not None) & (:Yb: is None): :E: is assumed to contain the adapting field luminance La (cd/m²). :Yb: | 20.0, optional | Luminance factor of background. (used when calculating La from E) | If None, E contains La (cd/m²). :out: | 'Rm' or str, optional | Specifies requested output (e.g. 'Rm,Rmi,cct,duv') :wl: | None, optional | Wavelengths (or [start, end, spacing]) to interpolate the SPDs to. | None: default to no interpolation Returns: :returns: | float or ndarray with MCRI Rm for :out: 'Rm' | Other output is also possible by changing the :out: str value. References: 1. `K.A.G. Smet, W.R. Ryckaert, M.R. Pointer, G. Deconinck, P. Hanselaer,(2012) “A memory colour quality metric for white light sources,” Energy Build., vol. 49, no. C, pp. 216–225. <http://www.sciencedirect.com/science/article/pii/S0378778812000837>`_ """ SPD = np2d(SPD) if wl is not None: SPD = spd(data=SPD, interpolation=_S_INTERP_TYPE, kind='np', wl=wl) # unpack metric default values: avg, catf, cieobs, cri_specific_pars, cspace, ref_type, rg_pars, sampleset, scale = [ _MCRI_DEFAULTS[x] for x in sorted(_MCRI_DEFAULTS.keys()) ] similarity_ai = cri_specific_pars['similarity_ai'] Mxyz2lms = cspace['Mxyz2lms'] scale_fcn = scale['fcn'] scale_factor = scale['cfactor'] sampleset = eval(sampleset) # A. calculate xyz: xyzti, xyztw = spd_to_xyz(SPD, cieobs=cieobs['xyz'], rfl=sampleset, out=2) if 'cct' in out.split(','): cct, duv = xyz_to_cct(xyztw, cieobs=cieobs['cct'], out='cct,duv', mode='lut') # B. perform chromatic adaptation to adopted whitepoint of ipt color space, i.e. D65: if catf is not None: Dtype_cat, F, Yb_cat, catmode_cat, cattype_cat, mcat_cat, xyzw_cat = [ catf[x] for x in sorted(catf.keys()) ] # calculate degree of adaptationn D: if E is not None: if Yb is not None: La = (Yb / 100.0) * (E / np.pi) else: La = E D = cat.get_degree_of_adaptation(Dtype=Dtype_cat, F=F, La=La) else: Dtype_cat = None # direct input of D if (E is None) and (D is None): D = 1.0 # set degree of adaptation to 1 ! if D > 1.0: D = 1.0 if D < 0.6: D = 0.6 # put a limit on the lowest D # apply cat: xyzti = cat.apply(xyzti, cattype=cattype_cat, catmode=catmode_cat, xyzw1=xyztw, xyzw0=None, xyzw2=xyzw_cat, D=D, mcat=[mcat_cat], Dtype=Dtype_cat) xyztw = cat.apply(xyztw, cattype=cattype_cat, catmode=catmode_cat, xyzw1=xyztw, xyzw0=None, xyzw2=xyzw_cat, D=D, mcat=[mcat_cat], Dtype=Dtype_cat) # C. convert xyz to ipt and split: ipt = xyz_to_ipt( xyzti, cieobs=cieobs['xyz'], M=Mxyz2lms ) #input matrix as published in Smet et al. 2012, Energy and Buildings I, P, T = asplit(ipt) # D. calculate specific (hue dependent) similarity indicators, Si: if len(xyzti.shape) == 3: ai = np.expand_dims(similarity_ai, axis=1) else: ai = similarity_ai a1, a2, a3, a4, a5 = asplit(ai) mahalanobis_d2 = (a3 * np.power((P - a1), 2.0) + a4 * np.power( (T - a2), 2.0) + 2.0 * a5 * (P - a1) * (T - a2)) if (len(mahalanobis_d2.shape) == 3) & (mahalanobis_d2.shape[-1] == 1): mahalanobis_d2 = mahalanobis_d2[:, :, 0].T Si = np.exp(-0.5 * mahalanobis_d2) # E. calculate general similarity indicator, Sa: Sa = avg(Si, axis=0, keepdims=True) # F. rescale similarity indicators (Si, Sa) with a 0-1 scale to memory color rendition indices (Rmi, Rm) with a 0 - 100 scale: Rmi = scale_fcn(np.log(Si), scale_factor=scale_factor) Rm = np2d(scale_fcn(np.log(Sa), scale_factor=scale_factor)) # G. calculate Rg (polyarea of test / polyarea of memory colours): if 'Rg' in out.split(','): I = I[ ..., None] #broadcast_shape(I, target_shape = None,expand_2d_to_3d = 0) a1 = a1[:, None] * np.ones( I.shape ) #broadcast_shape(a1, target_shape = None,expand_2d_to_3d = 0) a2 = a2[:, None] * np.ones( I.shape ) #broadcast_shape(a2, target_shape = None,expand_2d_to_3d = 0) a12 = np.concatenate( (a1, a2), axis=2 ) #broadcast_shape(np.hstack((a1,a2)), target_shape = ipt.shape,expand_2d_to_3d = 0) ipt_mc = np.concatenate((I, a12), axis=2) nhbins, normalize_gamut, normalized_chroma_ref, start_hue = [ rg_pars[x] for x in sorted(rg_pars.keys()) ] Rg = jab_to_rg(ipt, ipt_mc, ordered_and_sliced=False, nhbins=nhbins, start_hue=start_hue, normalize_gamut=normalize_gamut) if (out != 'Rm'): return eval(out) else: return Rm
def cam18sl(data, datab = None, Lb = [100], fov = 10.0, inputtype = 'xyz', direction = 'forward', outin = 'Q,aW,bW', parameters = None): """ Convert between CIE 2006 10° XYZ tristimulus values (or spectral data) and CAM18sl color appearance correlates. Args: :data: | ndarray of CIE 2006 10° absolute XYZ tristimulus values or spectral data or color appearance attributes of stimulus :datab: | ndarray of CIE 2006 10° absolute XYZ tristimulus values or spectral data of stimulus background :Lb: | [100], optional | Luminance (cd/m²) value(s) of background(s) calculated using the CIE 2006 10° CMFs | (only used in case datab == None and the background is assumed to be an Equal-Energy-White) :fov: | 10.0, optional | Field-of-view of stimulus (for size effect on brightness) :inputtpe: | 'xyz' or 'spd', optional | Specifies the type of input: | tristimulus values or spectral data for the forward mode. :direction: | 'forward' or 'inverse', optional | -'forward': xyz -> cam18sl | -'inverse': cam18sl -> xyz :outin: | 'Q,aW,bW' or str, optional | 'Q,aW,bW' (brightness and opponent signals for amount-of-neutral) | other options: 'Q,aM,bM' (colorfulness) and 'Q,aS,bS' (saturation) | Str specifying the type of | input (:direction: == 'inverse') and | output (:direction: == 'forward') :parameters: | None or dict, optional | Set of model parameters. | - None: defaults to luxpy.cam._CAM18SL_PARAMETERS | (see references below) Returns: :returns: | ndarray with color appearance correlates (:direction: == 'forward') | or | XYZ tristimulus values (:direction: == 'inverse') Notes: | * Instead of using the CIE 1964 10° CMFs in some places of the model, | the CIE 2006 10° CMFs are used througout, making it more self_consistent. | This has an effect on the k scaling factors (now different those in CAM15u) | and the illuminant E normalization for use in the chromatic adaptation transform. | (see future erratum to Hermans et al., 2018) | * The paper also used an equation for the amount of white W, which is | based on a Q value not expressed in 'bright' ('cA' = 0.937 instead of 123). | This has been corrected for in the luxpy version of the model, i.e. | _CAM18SL_PARAMETERS['cW'][0] has been changed from 2.29 to 1/11672. | (see future erratum to Hermans et al., 2018) References: 1. `Hermans, S., Smet, K. A. G., & Hanselaer, P. (2018). "Color appearance model for self-luminous stimuli." Journal of the Optical Society of America A, 35(12), 2000–2009. <https://doi.org/10.1364/JOSAA.35.002000>`_ """ if parameters is None: parameters = _CAM18SL_PARAMETERS outin = outin.split(',') #unpack model parameters: cA, cAlms, cHK, cM, cW, ca, calms, cb, cblms, cfov, k, naka, unique_hue_data = [parameters[x] for x in sorted(parameters.keys())] # precomputations: Mlms2xyz = np.linalg.inv(_CMF['2006_10']['M']) MAab = np.array([cAlms,calms,cblms]) invMAab = np.linalg.inv(MAab) #------------------------------------------------- # setup EEW reference field and default background field (Lr should be equal to Lb): # Get Lb values: if datab is not None: if inputtype != 'xyz': Lb = spd_to_xyz(datab, cieobs = '2006_10', relative = False)[...,1:2] else: Lb = datab[...,1:2] else: if isinstance(Lb,list): Lb = np2dT(Lb) # Setup EEW ref of same luminance as datab: if inputtype == 'xyz': wlr = getwlr(_CAM18SL_WL3) else: if datab is None: wlr = data[0] # use wlr of stimulus data else: wlr = datab[0] # use wlr of background data datar = np.vstack((wlr,np.ones((Lb.shape[0], wlr.shape[0])))) # create eew xyzr = spd_to_xyz(datar, cieobs = '2006_10', relative = False) # get abs. tristimulus values datar[1:] = datar[1:]/xyzr[...,1:2]*Lb # Create datab if None: if (datab is None): if inputtype != 'xyz': datab = datar.copy() else: datab = spd_to_xyz(datar, cieobs = '2006_10', relative = False) datar = datab.copy() # prepare data and datab for loop over backgrounds: # make axis 1 of datab have 'same' dimensions as data: if (data.ndim == 2): data = np.expand_dims(data, axis = 1) # add light source axis 1 if inputtype == 'xyz': if datab.shape[0] == 1: #make datab and datar have same lights source dimension (used to store different backgrounds) size as data datab = np.repeat(datab,data.shape[1],axis=0) datar = np.repeat(datar,data.shape[1],axis=0) else: if datab.shape[0] == 2: datab = np.vstack((datab[0],np.repeat(datab[1:], data.shape[1], axis = 0))) if datar.shape[0] == 2: datar = np.vstack((datar[0],np.repeat(datar[1:], data.shape[1], axis = 0))) # Flip light source/ background dim to axis 0: data = np.transpose(data, axes = (1,0,2)) #------------------------------------------------- #initialize camout: dshape = list(data.shape) dshape[-1] = len(outin) # requested number of correlates if (inputtype != 'xyz') & (direction == 'forward'): dshape[-2] = dshape[-2] - 1 # wavelength row doesn't count & only with forward can the input data be spectral camout = np.nan*np.ones(dshape) for i in range(data.shape[0]): # get rho, gamma, beta of background and reference white: if (inputtype != 'xyz'): xyzb = spd_to_xyz(np.vstack((datab[0], datab[i+1:i+2,:])), cieobs = '2006_10', relative = False) xyzr = spd_to_xyz(np.vstack((datar[0], datar[i+1:i+2,:])), cieobs = '2006_10', relative = False) else: xyzb = datab[i:i+1,:] xyzr = datar[i:i+1,:] lmsb = np.dot(_CMF['2006_10']['M'],xyzb.T).T # convert to l,m,s rgbb = (lmsb / _CMF['2006_10']['K']) * k # convert to rho, gamma, beta #lmsr = np.dot(_CMF['2006_10']['M'],xyzr.T).T # convert to l,m,s #rgbr = (lmsr / _CMF['2006_10']['K']) * k # convert to rho, gamma, beta #rgbr = rgbr/rgbr[...,1:2]*Lb[i] # calculated EEW cone excitations at same luminance values as background rgbr = np.ones(xyzr.shape)*Lb[i] # explicitely equal EEW cone excitations at same luminance values as background if direction == 'forward': # get rho, gamma, beta of stimulus: if (inputtype != 'xyz'): xyz = spd_to_xyz(data[i], cieobs = '2006_10', relative = False) elif (inputtype == 'xyz'): xyz = data[i] lms = np.dot(_CMF['2006_10']['M'],xyz.T).T # convert to l,m,s rgb = (lms / _CMF['2006_10']['K']) * k # convert to rho, gamma, beta # apply von-kries cat with D = 1: if (rgbb == 0).any(): Mcat = np.eye(3) else: Mcat = np.diag((rgbr/rgbb)[0]) rgba = np.dot(Mcat,rgb.T).T # apply naka-rushton compression: rgbc = naka_rushton(rgba, n = naka['n'], sig = naka['sig'](rgbr.mean()), noise = naka['noise'], scaling = naka['scaling']) #rgbc = np.ones(rgbc.shape)*rgbc.mean() # test if eew ends up at origin # calculate achromatic and color difference signals, A, a, b: Aab = np.dot(MAab, rgbc.T).T A,a,b = asplit(Aab) a = ca*a b = cb*b # calculate colorfullness like signal M: M = cM*((a**2.0 + b**2.0)**0.5) # calculate brightness Q: Q = cA*(A + cHK[0]*M**cHK[1]) # last term is contribution of Helmholtz-Kohlrausch effect on brightness # calculate saturation, s: s = M / Q # calculate amount of white, W: W = 1 / (1.0 + cW[0]*(s**cW[1])) # adjust Q for size (fov) of stimulus (matter of debate whether to do this before or after calculation of s or W, there was no data on s, M or W for different sized stimuli: after) Q = Q*(fov/10.0)**cfov # calculate hue, h and Hue quadrature, H: h = hue_angle(a,b, htype = 'deg') if 'H' in outin: H = hue_quadrature(h, unique_hue_data = unique_hue_data) else: H = None # calculate cart. co.: if 'aM' in outin: aM = M*np.cos(h*np.pi/180.0) bM = M*np.sin(h*np.pi/180.0) if 'aS' in outin: aS = s*np.cos(h*np.pi/180.0) bS = s*np.sin(h*np.pi/180.0) if 'aW' in outin: aW = W*np.cos(h*np.pi/180.0) bW = W*np.sin(h*np.pi/180.0) if (outin != ['Q','aW','bW']): camout[i] = eval('ajoin(('+','.join(outin)+'))') else: camout[i] = ajoin((Q,aW,bW)) elif direction == 'inverse': # get Q, M and a, b depending on input type: if 'aW' in outin: Q,a,b = asplit(data[i]) Q = Q / ((fov/10.0)**cfov) #adjust Q for size (fov) of stimulus back to that 10° ref W = (a**2.0 + b**2.0)**0.5 s = (((1.0 / W) - 1.0)/cW[0])**(1.0/cW[1]) M = s*Q if 'aM' in outin: Q,a,b = asplit(data[i]) Q = Q / ((fov/10.0)**cfov) #adjust Q for size (fov) of stimulus back to that 10° ref M = (a**2.0 + b**2.0)**0.5 if 'aS' in outin: Q,a,b = asplit(data[i]) Q = Q / ((fov/10.0)**cfov) #adjust Q for size (fov) of stimulus back to that 10° ref s = (a**2.0 + b**2.0)**0.5 M = s*Q if 'h' in outin: Q, WsM, h = asplit(data[i]) Q = Q / ((fov/10.0)**cfov) #adjust Q for size (fov) of stimulus back to that 10° ref if 'W' in outin: s = (((1.0 / WsM) - 1.0)/cW[0])**(1.0/cW[1]) M = s*Q elif 's' in outin: M = WsM*Q elif 'M' in outin: M = WsM # calculate achromatic signal, A from Q and M: A = Q/cA - cHK[0]*M**cHK[1] # calculate hue angle: h = hue_angle(a,b, htype = 'rad') # calculate a,b from M and h: a = (M/cM)*np.cos(h) b = (M/cM)*np.sin(h) a = a/ca b = b/cb # create Aab: Aab = ajoin((A,a,b)) # calculate rgbc: rgbc = np.dot(invMAab, Aab.T).T # decompress rgbc to (adapted) rgba : rgba = naka_rushton(rgbc, n = naka['n'], sig = naka['sig'](rgbr.mean()), noise = naka['noise'], scaling = naka['scaling'], direction = 'inverse') # apply inverse von-kries cat with D = 1: rgb = np.dot(np.diag((rgbb/rgbr)[0]),rgba.T).T # convert rgb to lms to xyz: lms = rgb/k*_CMF['2006_10']['K'] xyz = np.dot(Mlms2xyz,lms.T).T camout[i] = xyz if camout.shape[0] == 1: camout = np.squeeze(camout,axis = 0) return camout
def cam15u(data, fov=10.0, inputtype='xyz', direction='forward', outin='Q,aW,bW', parameters=None): """ Convert between CIE 2006 10° XYZ tristimulus values (or spectral data) and CAM15u color appearance correlates. Args: :data: | ndarray of CIE 2006 10° XYZ tristimulus values or spectral data or color appearance attributes :fov: | 10.0, optional | Field-of-view of stimulus (for size effect on brightness) :inputtpe: | 'xyz' or 'spd', optional | Specifies the type of input: | tristimulus values or spectral data for the forward mode. :direction: | 'forward' or 'inverse', optional | -'forward': xyz -> cam15u | -'inverse': cam15u -> xyz :outin: | 'Q,aW,bW' or str, optional | 'Q,aW,bW' (brightness and opponent signals for amount-of-neutral) | other options: 'Q,aM,bM' (colorfulness) and 'Q,aS,bS' (saturation) | Str specifying the type of | input (:direction: == 'inverse') and | output (:direction: == 'forward') :parameters: | None or dict, optional | Set of model parameters. | - None: defaults to luxpy.cam._CAM15U_PARAMETERS | (see references below) Returns: :returns: | ndarray with color appearance correlates (:direction: == 'forward') | or | XYZ tristimulus values (:direction: == 'inverse') References: 1. `M. Withouck, K. A. G. Smet, W. R. Ryckaert, and P. Hanselaer, “Experimental driven modelling of the color appearance of unrelated self-luminous stimuli: CAM15u,” Opt. Express, vol. 23, no. 9, pp. 12045–12064, 2015. <https://www.osapublishing.org/oe/abstract.cfm?uri=oe-23-9-12045&origin=search>`_ 2. `M. Withouck, K. A. G. Smet, and P. Hanselaer, (2015), “Brightness prediction of different sized unrelated self-luminous stimuli,” Opt. Express, vol. 23, no. 10, pp. 13455–13466. <https://www.osapublishing.org/oe/abstract.cfm?uri=oe-23-10-13455&origin=search>`_ """ if parameters is None: parameters = _CAM15U_PARAMETERS outin = outin.split(',') #unpack model parameters: Mxyz2rgb, cA, cAlms, cHK, cM, cW, ca, calms, cb, cblms, cfov, cp, k, unique_hue_data = [ parameters[x] for x in sorted(parameters.keys()) ] # precomputations: invMxyz2rgb = np.linalg.inv(Mxyz2rgb) MAab = np.array([cAlms, calms, cblms]) invMAab = np.linalg.inv(MAab) #initialize data and camout: data = np2d(data) if len(data.shape) == 2: data = np.expand_dims(data, axis=0) # avoid looping if not necessary if (data.shape[0] > data.shape[1]): # loop over shortest dim. flipaxis0and1 = True data = np.transpose(data, axes=(1, 0, 2)) else: flipaxis0and1 = False dshape = list(data.shape) dshape[-1] = len(outin) # requested number of correlates if (inputtype != 'xyz') & (direction == 'forward'): dshape[-2] = dshape[ -2] - 1 # wavelength row doesn't count & only with forward can the input data be spectral camout = np.nan * np.ones(dshape) for i in range(data.shape[0]): if (inputtype != 'xyz') & (direction == 'forward'): xyz = spd_to_xyz(data[i], cieobs='2006_10', relative=False) lms = np.dot(_CMF['2006_10']['M'], xyz.T).T # convert to l,m,s rgb = (lms / _CMF['2006_10']['K']) * k # convert to rho, gamma, beta elif (inputtype == 'xyz') & (direction == 'forward'): rgb = np.dot(Mxyz2rgb, data[i].T).T if direction == 'forward': # apply cube-root compression: rgbc = rgb**(cp) # calculate achromatic and color difference signals, A, a, b: Aab = np.dot(MAab, rgbc.T).T A, a, b = asplit(Aab) A = cA * A a = ca * a b = cb * b # calculate colorfullness like signal M: M = cM * ((a**2.0 + b**2.0)**0.5) # calculate brightness Q: Q = A + cHK[0] * M**cHK[ 1] # last term is contribution of Helmholtz-Kohlrausch effect on brightness # calculate saturation, s: s = M / Q # calculate amount of white, W: W = 100.0 / (1.0 + cW[0] * (s**cW[1])) # adjust Q for size (fov) of stimulus (matter of debate whether to do this before or after calculation of s or W, there was no data on s, M or W for different sized stimuli: after) Q = Q * (fov / 10.0)**cfov # calculate hue, h and Hue quadrature, H: h = hue_angle(a, b, htype='deg') if 'H' in outin: H = hue_quadrature(h, unique_hue_data=unique_hue_data) else: H = None # calculate cart. co.: if 'aM' in outin: aM = M * np.cos(h * np.pi / 180.0) bM = M * np.sin(h * np.pi / 180.0) if 'aS' in outin: aS = s * np.cos(h * np.pi / 180.0) bS = s * np.sin(h * np.pi / 180.0) if 'aW' in outin: aW = W * np.cos(h * np.pi / 180.0) bW = W * np.sin(h * np.pi / 180.0) if (outin != ['Q', 'aW', 'bW']): camout[i] = eval('ajoin((' + ','.join(outin) + '))') else: camout[i] = ajoin((Q, aW, bW)) elif direction == 'inverse': # get Q, M and a, b depending on input type: if 'aW' in outin: Q, a, b = asplit(data[i]) Q = Q / ( (fov / 10.0)**cfov ) #adjust Q for size (fov) of stimulus back to that 10° ref W = (a**2.0 + b**2.0)**0.5 s = (((100 / W) - 1.0) / cW[0])**(1.0 / cW[1]) M = s * Q if 'aM' in outin: Q, a, b = asplit(data[i]) Q = Q / ( (fov / 10.0)**cfov ) #adjust Q for size (fov) of stimulus back to that 10° ref M = (a**2.0 + b**2.0)**0.5 if 'aS' in outin: Q, a, b = asplit(data[i]) Q = Q / ( (fov / 10.0)**cfov ) #adjust Q for size (fov) of stimulus back to that 10° ref s = (a**2.0 + b**2.0)**0.5 M = s * Q if 'h' in outin: Q, WsM, h = asplit(data[i]) Q = Q / ( (fov / 10.0)**cfov ) #adjust Q for size (fov) of stimulus back to that 10° ref if 'W' in outin: s = (((100.0 / WsM) - 1.0) / cW[0])**(1.0 / cW[1]) M = s * Q elif 's' in outin: M = WsM * Q elif 'M' in outin: M = WsM # calculate achromatic signal, A from Q and M: A = Q - cHK[0] * M**cHK[1] A = A / cA # calculate hue angle: h = hue_angle(a, b, htype='rad') # calculate a,b from M and h: a = (M / cM) * np.cos(h) b = (M / cM) * np.sin(h) a = a / ca b = b / cb # create Aab: Aab = ajoin((A, a, b)) # calculate rgbc: rgbc = np.dot(invMAab, Aab.T).T # decompress rgbc to rgb: rgb = rgbc**(1 / cp) # convert rgb to xyz: xyz = np.dot(invMxyz2rgb, rgb.T).T camout[i] = xyz if flipaxis0and1 == True: # loop over shortest dim. camout = np.transpose(camout, axes=(1, 0, 2)) if camout.shape[0] == 1: camout = np.squeeze(camout, axis=0) return camout
def hue_quadrature(h, unique_hue_data=None): """ Get hue quadrature H from hue h. Args: :h: | float or ndarray [(N,) or (N,1)] with hue data in degrees (!). :unique_hue data: | None or dict, optional | - None: defaults to: | {'hues': 'red yellow green blue red'.split(), | 'i': np.arange(5.0), | 'hi':[20.14, 90.0, 164.25,237.53,380.14], | 'ei':[0.8,0.7,1.0,1.2,0.8], | 'Hi':[0.0,100.0,200.0,300.0,400.0]} | - dict: user specified unique hue data | (same structure as above) Returns: :H: | ndarray of Hue quadrature value(s). """ if unique_hue_data is None: unique_hue_data = { 'hues': 'red yellow green blue red'.split(), 'i': np.arange(5.0), 'hi': [20.14, 90.0, 164.25, 237.53, 380.14], 'ei': [0.8, 0.7, 1.0, 1.2, 0.8], 'Hi': [0.0, 100.0, 200.0, 300.0, 400.0] } changed_number_to_array = False if isinstance(h, float) | isinstance(h, int): h = np.atleast_1d(h) changed_number_to_array = True squeezed = False if h.ndim > 1: if (h.shape[0] == 1): h = np.squeeze(h, axis=0) squeezed = True hi = unique_hue_data['hi'] Hi = unique_hue_data['Hi'] ei = unique_hue_data['ei'] h[h < hi[0]] += 360.0 h_tmp = np.atleast_2d(h) if h_tmp.shape[0] == 1: h_tmp = h_tmp.T h_hi = np.repeat(h_tmp, repeats=len(hi), axis=1) hi_h = np.repeat(np.atleast_2d(hi), repeats=h.shape[0], axis=0) d = (h_hi - hi_h) d[d < 0] = 1000.0 p = d.argmin(axis=1) p[p == (len(hi) - 1)] = 0 # make sure last unique hue data is not selected H = np.array([ Hi[pi] + (100.0 * (h[i] - hi[pi]) / ei[pi]) / ((h[i] - hi[pi]) / ei[pi] + (hi[pi + 1] - h[i]) / ei[pi + 1]) for (i, pi) in enumerate(p) ]) if changed_number_to_array: H = H[0] if squeezed: H = np.expand_dims(H, axis=0) return H
def cam_sww16(data, dataw = None, Yb = 20.0, Lw = 400.0, Ccwb = None, relative = True, \ parameters = None, inputtype = 'xyz', direction = 'forward', \ cieobs = '2006_10'): """ A simple principled color appearance model based on a mapping of the Munsell color system. | This function implements the JOSA A (parameters = 'JOSA') published model. Args: :data: | ndarray with input tristimulus values | or spectral data | or input color appearance correlates | Can be of shape: (N [, xM], x 3), whereby: | N refers to samples and M refers to light sources. | Note that for spectral input shape is (N x (M+1) x wl) :dataw: | None or ndarray, optional | Input tristimulus values or spectral data of white point. | None defaults to the use of CIE illuminant C. :Yb: | 20.0, optional | Luminance factor of background (perfect white diffuser, Yw = 100) :Lw: | 400.0, optional | Luminance (cd/m²) of white point. :Ccwb: | None, optional | Degree of cognitive adaptation (white point balancing) | If None: use [..,..] from parameters dict. :relative: | True or False, optional | True: xyz tristimulus values are relative (Yw = 100) :parameters: | None or str or dict, optional | Dict with model parameters. | - None: defaults to luxpy.cam._CAM_SWW_2016_PARAMETERS['JOSA'] | - str: 'best-fit-JOSA' or 'best-fit-all-Munsell' | - dict: user defined model parameters | (dict should have same structure) :inputtype: | 'xyz' or 'spd', optional | Specifies the type of input: | tristimulus values or spectral data for the forward mode. :direction: | 'forward' or 'inverse', optional | -'forward': xyz -> cam_sww_2016 | -'inverse': cam_sww_2016 -> xyz :cieobs: | '2006_10', optional | CMF set to use to perform calculations where spectral data is involved (inputtype == 'spd'; dataw = None) | Other options: see luxpy._CMF['types'] Returns: :returns: | ndarray with color appearance correlates (:direction: == 'forward') | or | XYZ tristimulus values (:direction: == 'inverse') Notes: | This function implements the JOSA A (parameters = 'JOSA') published model. | With: | 1. A correction for the parameter | in Eq.4 of Fig. 11: 0.952 --> -0.952 | | 2. The delta_ac and delta_bc white-balance shifts in Eq. 5e & 5f | should be: -0.028 & 0.821 | | (cfr. Ccwb = 0.66 in: | ab_test_out = ab_test_int - Ccwb*ab_gray_adaptation_field_int)) References: 1. `Smet, K. A. G., Webster, M. A., & Whitehead, L. A. (2016). A simple principled approach for modeling and understanding uniform color metrics. Journal of the Optical Society of America A, 33(3), A319–A331. <https://doi.org/10.1364/JOSAA.33.00A319>`_ """ # get model parameters args = locals().copy() if parameters is None: parameters = _CAM_SWW16_PARAMETERS['JOSA'] if isinstance(parameters,str): parameters = _CAM_SWW16_PARAMETERS[parameters] parameters = put_args_in_db(parameters,args) #overwrite parameters with other (not-None) args input #unpack model parameters: Cc, Ccwb, Cf, Mxyz2lms, cLMS, cab_int, cab_out, calpha, cbeta,cga1, cga2, cgb1, cgb2, cl_int, clambda, lms0 = [parameters[x] for x in sorted(parameters.keys())] # setup default adaptation field: if (dataw is None): dataw = _CIE_ILLUMINANTS['C'].copy() # get illuminant C xyzw = spd_to_xyz(dataw, cieobs = cieobs,relative=False) # get abs. tristimulus values if relative == False: #input is expected to be absolute dataw[1:] = Lw*dataw[1:]/xyzw[:,1:2] #dataw = Lw*dataw # make absolute else: dataw = dataw # make relative (Y=100) if inputtype == 'xyz': dataw = spd_to_xyz(dataw, cieobs = cieobs, relative = relative) # precomputations: Mxyz2lms = np.dot(np.diag(cLMS),math.normalize_3x3_matrix(Mxyz2lms, np.array([[1, 1, 1]]))) # normalize matrix for xyz-> lms conversion to ill. E weighted with cLMS invMxyz2lms = np.linalg.inv(Mxyz2lms) MAab = np.array([clambda,calpha,cbeta]) invMAab = np.linalg.inv(MAab) #initialize data and camout: data = np2d(data).copy() # stimulus data (can be upto NxMx3 for xyz, or [N x (M+1) x wl] for spd)) dataw = np2d(dataw).copy() # white point (can be upto Nx3 for xyz, or [(N+1) x wl] for spd) # make axis 1 of dataw have 'same' dimensions as data: if (data.ndim == 2): data = np.expand_dims(data, axis = 1) # add light source axis 1 if inputtype == 'xyz': if dataw.shape[0] == 1: #make dataw have same lights source dimension size as data dataw = np.repeat(dataw,data.shape[1],axis=0) else: if dataw.shape[0] == 2: dataw = np.vstack((dataw[0],np.repeat(dataw[1:], data.shape[1], axis = 0))) # Flip light source dim to axis 0: data = np.transpose(data, axes = (1,0,2)) # Initialize output array: dshape = list(data.shape) dshape[-1] = 3 # requested number of correlates: l_int, a_int, b_int if (inputtype != 'xyz') & (direction == 'forward'): dshape[-2] = dshape[-2] - 1 # wavelength row doesn't count & only with forward can the input data be spectral camout = np.nan*np.ones(dshape) # apply forward/inverse model for each row in data: for i in range(data.shape[0]): # stage 1: calculate photon rates of stimulus and adapting field, lmst & lmsf: if (inputtype != 'xyz'): if relative == True: xyzw_abs = spd_to_xyz(np.vstack((dataw[0],dataw[i+1])), cieobs = cieobs, relative = False) dataw[i+1] = Lw*dataw[i+1]/xyzw_abs[0,1] # make absolute xyzw = spd_to_xyz(np.vstack((dataw[0],dataw[i+1])), cieobs = cieobs, relative = False) lmsw = 683.0*np.dot(Mxyz2lms,xyzw.T).T/_CMF[cieobs]['K'] lmsf = (Yb/100.0)*lmsw # calculate adaptation field and convert to l,m,s if (direction == 'forward'): if relative == True: data[i,1:,:] = Lw*data[i,1:,:]/xyzw_abs[0,1] # make absolute xyzt = spd_to_xyz(data[i], cieobs = cieobs, relative = False)/_CMF[cieobs]['K'] lmst = 683.0*np.dot(Mxyz2lms,xyzt.T).T # convert to l,m,s else: lmst = lmsf # put lmsf in lmst for inverse-mode elif (inputtype == 'xyz'): if relative == True: dataw[i] = Lw*dataw[i]/100.0 # make absolute lmsw = 683.0* np.dot(Mxyz2lms, dataw[i].T).T /_CMF[cieobs]['K'] # convert to lms lmsf = (Yb/100.0)*lmsw if (direction == 'forward'): if relative == True: data[i] = Lw*data[i]/100.0 # make absolute lmst = 683.0* np.dot(Mxyz2lms, data[i].T).T /_CMF[cieobs]['K'] # convert to lms else: lmst = lmsf # put lmsf in lmst for inverse-mode # stage 2: calculate cone outputs of stimulus lmstp lmstp = math.erf(Cc*(np.log(lmst/lms0) + Cf*np.log(lmsf/lms0))) lmsfp = math.erf(Cc*(np.log(lmsf/lms0) + Cf*np.log(lmsf/lms0))) lmstp = np.vstack((lmsfp,lmstp)) # add adaptation field lms temporarily to lmsp for quick calculation # stage 3: calculate optic nerve signals, lam*, alphp, betp: lstar,alph, bet = asplit(np.dot(MAab, lmstp.T).T) alphp = cga1[0]*alph alphp[alph<0] = cga1[1]*alph[alph<0] betp = cgb1[0]*bet betp[bet<0] = cgb1[1]*bet[bet<0] # stage 4: calculate recoded nerve signals, alphapp, betapp: alphpp = cga2[0]*(alphp + betp) betpp = cgb2[0]*(alphp - betp) # stage 5: calculate conscious color perception: lstar_int = cl_int[0]*(lstar + cl_int[1]) alph_int = cab_int[0]*(np.cos(cab_int[1]*np.pi/180.0)*alphpp - np.sin(cab_int[1]*np.pi/180.0)*betpp) bet_int = cab_int[0]*(np.sin(cab_int[1]*np.pi/180.0)*alphpp + np.cos(cab_int[1]*np.pi/180.0)*betpp) lstar_out = lstar_int if direction == 'forward': if Ccwb is None: alph_out = alph_int - cab_out[0] bet_out = bet_int - cab_out[1] else: Ccwb = Ccwb*np.ones((2)) Ccwb[Ccwb<0.0] = 0.0 Ccwb[Ccwb>1.0] = 1.0 alph_out = alph_int - Ccwb[0]*alph_int[0] # white balance shift using adaptation gray background (Yb=20%), with Ccw: degree of adaptation bet_out = bet_int - Ccwb[1]*bet_int[0] camout[i] = np.vstack((lstar_out[1:],alph_out[1:],bet_out[1:])).T # stack together and remove adaptation field from vertical stack elif direction == 'inverse': labf_int = np.hstack((lstar_int[0],alph_int[0],bet_int[0])) # get lstar_out, alph_out & bet_out for data: lstar_out, alph_out, bet_out = asplit(data[i]) # stage 5 inverse: # undo cortical white-balance: if Ccwb is None: alph_int = alph_out + cab_out[0] bet_int = bet_out + cab_out[1] else: Ccwb = Ccwb*np.ones((2)) Ccwb[Ccwb<0.0] = 0.0 Ccwb[Ccwb>1.0] = 1.0 alph_int = alph_out + Ccwb[0]*alph_int[0] # inverse white balance shift using adaptation gray background (Yb=20%), with Ccw: degree of adaptation bet_int = bet_out + Ccwb[1]*bet_int[0] lstar_int = lstar_out alphpp = (1.0 / cab_int[0]) * (np.cos(-cab_int[1]*np.pi/180.0)*alph_int - np.sin(-cab_int[1]*np.pi/180.0)*bet_int) betpp = (1.0 / cab_int[0]) * (np.sin(-cab_int[1]*np.pi/180.0)*alph_int + np.cos(-cab_int[1]*np.pi/180.0)*bet_int) lstar_int = lstar_out lstar = (lstar_int /cl_int[0]) - cl_int[1] # stage 4 inverse: alphp = 0.5*(alphpp/cga2[0] + betpp/cgb2[0]) # <-- alphpp = (Cga2.*(alphp+betp)); betp = 0.5*(alphpp/cga2[0] - betpp/cgb2[0]) # <-- betpp = (Cgb2.*(alphp-betp)); # stage 3 invers: alph = alphp/cga1[0] bet = betp/cgb1[0] sa = np.sign(cga1[1]) sb = np.sign(cgb1[1]) alph[(sa*alphp)<0.0] = alphp[(sa*alphp)<0] / cga1[1] bet[(sb*betp)<0.0] = betp[(sb*betp)<0] / cgb1[1] lab = ajoin((lstar, alph, bet)) # stage 2 inverse: lmstp = np.dot(invMAab,lab.T).T lmstp[lmstp<-1.0] = -1.0 lmstp[lmstp>1.0] = 1.0 lmstp = math.erfinv(lmstp) / Cc - Cf*np.log(lmsf/lms0) lmst = np.exp(lmstp) * lms0 # stage 1 inverse: xyzt = np.dot(invMxyz2lms,lmst.T).T if relative == True: xyzt = (100.0/Lw) * xyzt camout[i] = xyzt # if flipaxis0and1 == True: # loop over shortest dim. # camout = np.transpose(camout, axes = (1,0,2)) # Flip light source dim back to axis 1: camout = np.transpose(camout, axes = (1,0,2)) if camout.shape[0] == 1: camout = np.squeeze(camout,axis = 0) return camout