Cross Processing Algorithm (Image manipulation)

I was developing an Image processing library in Javascript and was wondering what is the algorithm for achieving the "cross-process" effect

Sort of like this

I based my script on http://photographypla.net/cross-processed-lightroom/

I did the basic channel correction using the a remapping of the colors according to a segmoid (for the red and green channel) and a double exponential for the blue channel. Those function i took from http://www.flong.com/texts/code/shapers_exp/.

The image after the basic correction looks like this:

You can play with this results by the changing the params sFactor1 and sFactor2.

After that i lowered the total contrast and did some local histogram enhancement but i recommend you not to use this part and search for good implementations for highlights shadows and white and black adjustment.

The final result:

The code:

import cv2
import numpy as np
import math

# Define an S shape segmoid that with controlled shape. Based on http://www.flong.com/texts/code/shapers_exp/

# Function for sigmoid creation with s shape facor
def doubleExponentialSigmoid(x, a):

    epsilon = 0.00001
    min_param_a = 0.0 + epsilon
    max_param_a = 1.0 - epsilon
    a = min(max_param_a, max(min_param_a, a))
    a = 1.0 - a # for sensible results
    y = 0
    if x <= 0.5:
        y = (math.pow(2.0 * x, 1.0 / a)) / 2.0
    else:
        y = 1.0 - (pow(2.0 * (1.0-x), 1.0 / a)) / 2.0
    return y

# Function for reverse sigmoid creation with reverse s shape facor
def doubleExponentialSeat(x,a):

    epsilon = 0.00001
    min_param_a = 0.0 + epsilon
    max_param_a = 1.0 - epsilon
    a = min(max_param_a, max(min_param_a, a))
    y = 0
    if x <= 0.5:
        y = (math.pow(2.0*x, 1-a))/2.0;
    else:
        y = 1.0 - (math.pow(2.0*(1.0-x), 1-a))/2.0
    return y

# Function for s shape function creation
def getSigmoidLut(sFactor,reverseShape=False):
    rangeOfValues = np.arange(0, 1+(float(1) / float(255)), float(1) / float(255))
    index = 0
    sigmoidLUT = np.zeros_like(rangeOfValues)
    if reverseShape:
        for v in rangeOfValues:
            sigmoidLUT[index] = doubleExponentialSeat(v, sFactor)
            index = index + 1
    else:
        for v in rangeOfValues:
            sigmoidLUT[index] = doubleExponentialSigmoid(v, sFactor)
            index = index + 1

    return sigmoidLUT

# A function to map one range to another
def RangeMapping(currentMin,currentMax,newMin,newMax):

    newRange = np.zeros((256,1))
    for v in range(256):
        newRange[v] = (((v - currentMin) * (newMax - newMin)) / (currentMax - currentMin)) + newMin

    return newRange

# Function to lower contrast by a factor
def LowerContrast(intensityChannel, factor):

    # Second chane the contrast by the factor
    mappingLUT = RangeMapping(np.min(intensityChannel),np.max(intensityChannel),np.round(np.min(intensityChannel)*factor),np.round(np.max(intensityChannel)/factor))
    newIntensity = cv2.LUT(intensityChannel,mappingLUT)

    return newIntensity

# This cross processing is based on the tutorial in http://photographypla.net/cross-processed-lightroom/

# Params
sFactor1 = 0.7
sFactor2 = 0.3
lowContrastFactor = 1.05

# Read image
I = cv2.imread('im.jpg')

# Step 1: Separate to the three channels
R,G,B = cv2.split(I)

# Step 2: Map to a S curve each channel

# Get a S shaped segmoid
redChannelLUT = np.round(getSigmoidLut(sFactor1,False)*255).astype(np.uint8)
greenChannelLUT = redChannelLUT
blueChannelLUT =np.round(getSigmoidLut(sFactor2,True)*255).astype(np.uint8)

# Apply correction
redChannelCorrection = cv2.LUT(R, redChannelLUT)
greenChannelCorrection = cv2.LUT(G, greenChannelLUT)
blueChannelCorrection = cv2.LUT(B, blueChannelLUT)

# Step 3: Merge corrected channels
ICorrection = cv2.merge((redChannelCorrection,greenChannelCorrection,blueChannelCorrection))

# From here you can do whatever you want to the colors shadows highlights etc...
# Separate color and intensity
Iycr = cv2.cvtColor(ICorrection,cv2.COLOR_RGB2YCR_CB)
intensityCh,C,R = cv2.split(Iycr)

# Step 4: lower contrast
newLowerIntensityContrast = LowerContrast(intensityCh,lowContrastFactor)

# Step 5: Local contrast enhacment
clahe = cv2.createCLAHE(clipLimit=1.0, tileGridSize=(8,8))
ICorrectedShadows = clahe.apply(newLowerIntensityContrast.astype(np.uint8))

# Final step re construct image
IycrLowContrast = cv2.merge((ICorrectedShadows,C,R))
finalImage = cv2.cvtColor(IycrLowContrast,cv2.COLOR_YCrCb2RGB)

cv2.imshow('Original',I)
cv2.imshow('ColorCorrection',ICorrection)
cv2.imshow('LowContrast',newLowerIntensityContrast.astype(np.uint8))
cv2.imshow('Final',finalImage)