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from PIL import Image
import numpy as np
#import matplotlib.pyplot as plt
class NumpyHDR:
'''Numpy and PIL implementation of a Mertens Fusion alghoritm'''
def __init__(self):
self.input_image: list
self.output_path: str = '/'
self.compress_quality: int = 50
def plot_histogram(image, title="Histogram", bins=256):
"""Plot the histogram of an image.
Args:
image: A numpy array representing an image.
title: The title of the plot.
bins: The number of bins in the histogram.
"""
fig, ax = plt.subplots()
ax.hist(image.ravel(), bins=bins, color='gray', alpha=0.7)
ax.set_title(title)
ax.set_xlabel('Pixel value')
ax.set_ylabel('Frequency')
plt.show()
### Experimental functions above this line. chatGPT sketches
def simple_clip(fused,gamma):
# Apply gamma correction
fused = np.clip(fused, 0, 1)
fused = np.power(fused, 1.0 / gamma)
#hdr_8bit = np.clip(res_mertens * 255, 0, 255).astype('uint8')
fused = (255.0 * fused).astype(np.uint8)
#fused = Image.fromarray(fused)
def convolve2d(image, kernel):
"""Perform a 2D convolution on the given image with the given kernel.
Args:
image: The input image to convolve.
kernel: The kernel to convolve the image with.
Returns:
The convolved image.
"""
# Get the dimensions of the image and kernel.
image_height, image_width = image.shape[:2]
kernel_height, kernel_width = kernel.shape[:2]
# Compute the amount of padding to add to the image.
pad_height = kernel_height // 2
pad_width = kernel_width // 2
# Pad the image with zeros.
padded_image = np.zeros(
(image_height + 2 * pad_height, image_width + 2 * pad_width),
dtype=np.float32,
)
padded_image[pad_height:-pad_height, pad_width:-pad_width] = image
# Flip the kernel horizontally and vertically.
flipped_kernel = np.flipud(np.fliplr(kernel))
# Convolve the padded image with the flipped kernel.
convolved_image = np.zeros_like(image, dtype=np.float32)
for row in range(image_height):
for col in range(image_width):
patch = padded_image[
row : row + kernel_height, col : col + kernel_width
]
product = patch * flipped_kernel
convolved_image[row, col] = product.sum()
return convolved_image
def mask(img, center=50, width=20, threshold=0.2):
mask = 1 / (1 + np.exp((center - img) / width)) # Smooth gradient mask
mask = np.where(img > threshold, mask, 1) # Apply threshold to the mask
mask = img * mask
#plot_histogram(mask, title="mask")
return mask
def shadowlift(img, center=200, width=20, threshold=0.2, amount=1):
mask = 1 / (1 + np.exp((center - img) / width)) # Smooth gradient mask
print(mask)
print(img)
mask = np.where(img < threshold, mask, 1) # Apply threshold to the mask
print(mask)
#plot_histogram(mask, title= "maskin")
img_adjusted = img * mask * amount # Adjust the image with a user-specified amount
return img_adjusted
def highlightdrop(img, center=200, width=20, threshold=0.8, amount: float=1):
mask = 1 / (1 + np.exp((center - img) / width)) # Smooth gradient mask
mask = np.where(img > threshold, mask, 1) # Apply threshold to the mask
img_adjusted = img + mask * (-amount) # Adjust the image with a user-specified amount
return img_adjusted
def mertens_fusion(image_paths, gamma=2.2, contrast_weight=0.2):
"""Fuse multiple exposures into a single HDR image using the Mertens algorithm.
Args:
image_paths: A list of paths to input images.
gamma: The gamma correction value to apply to the input images.
contrast_weight: The weight of the local contrast term in the weight map computation.
Returns:
The fused HDR image.
"""
# Load the input images and convert them to floating-point format.
images = []
for path in image_paths:
img = Image.open(path).convert('RGB')
img = img.resize((1920, 1080))
img = np.array(img).astype(np.float32) / 255.0
img = np.power(img, gamma)
images.append(img)
# Compute the weight maps for each input image based on the local contrast.
weight_maps = []
for img in images:
gray = np.dot(img, [0.2989, 0.5870, 0.1140])
#kernel = np.array([[-1, 1, -1], [1, 7, 1], [-1, 1, -1]])
kernel = np.array([[-1, -1, -1], [-1, 7, -1], [-1, -1, -1]])
laplacian = np.abs(convolve2d(gray, kernel))
weight = np.power(laplacian, contrast_weight)
weight_maps.append(weight)
# Normalize the weight maps.
total_weight = sum(weight_maps)
weight_maps = [w / total_weight for w in weight_maps]
# Compute the fused HDR image by computing a weighted sum of the input images.
fused = np.zeros(images[0].shape, dtype=np.float32)
for i, img in enumerate(images):
fused += weight_maps[i][:, :, np.newaxis] * img
return fused
def sequence(self):
#list = ['hdr/webcam20_3_2023_ev1.jpg','hdr/webcam20_3_2023_ev-1.jpg']
hdr_image = self.mertens_fusion(self.input_image ,0.7, 0.01)
result = self.simple_clip(hdr_image,1)
image = Image.fromarray(result)
#output_path = f'hdr/webcam_hdr10.jpg'
image.save(self.output_path, quality=self.compress_quality)
class NumpyUtility:
def __init__(self):
'''Utilitys made with chatGPT for experimentation, few are working'''
def compress_dynamic_range(image):
# Find the 1st and 99th percentiles of the image
p1, p99 = np.percentile(image, (1, 99))
# Calculate the range of the image
img_range = p99 - p1
# Calculate the compression factor required to fit the image into 8-bit range
c = 255.0 / img_range
# Subtract the 1st percentile from the image and clip it to the [0, 1] range
new_image = np.clip((image - p1) * c, 0, 255)
# Convert the image to uint8 format
new_image = new_image.astype(np.uint8)
return new_image
def compress_dynamic_range_histo(image, new_min=0, new_max=255):
"""Compress the dynamic range of an image using histogram stretching.
Args:
image: A numpy array representing an image.
new_min: The minimum value of the new range.
new_max: The maximum value of the new range.
Returns:
The compressed image.
"""
# Calculate the histogram of the image.
hist, bins = np.histogram(image.ravel(), bins=256, range=(0, 1))
# Calculate the cumulative distribution function (CDF) of the histogram.
cdf = hist.cumsum()
cdf = (cdf - cdf.min()) / (cdf.max() - cdf.min()) # normalize to [0, 1]
# Interpolate the CDF to get the new pixel values.
new_pixels = np.interp(image.ravel(), bins[:-1], cdf * (new_max - new_min) + new_min)
# Reshape the new pixel values to the shape of the original image.
new_image = new_pixels.reshape((image.shape[0], image.shape[1], image.shape[2]))
return new_image
return fused
def adjust_luminance(image, mask, amount):
# Convert the image to LAB color space
rgb_image = image.astype(np.float32) / 255.0
xyz_image = np.dot(rgb_image, np.array([[0.412453, 0.357580, 0.180423],
[0.212671, 0.715160, 0.072169],
[0.019334, 0.119193, 0.950227]]))
xyz_image = np.clip(xyz_image, 0, 1)
lab_image = np.zeros_like(xyz_image)
lab_image[..., 0] = 116.0 * np.power(xyz_image[..., 1], 1 / 3.0) - 16.0
lab_image[..., 1] = 500.0 * (np.power(xyz_image[..., 0], 1 / 3.0) - np.power(xyz_image[..., 1], 1 / 3.0))
lab_image[..., 2] = 200.0 * (np.power(xyz_image[..., 1], 1 / 3.0) - np.power(xyz_image[..., 2], 1 / 3.0))
# Apply the luminance adjustment to the masked area
lab_image[..., 0][mask == 1] = np.clip(lab_image[..., 0][mask == 1] * (1 + amount), 0, 100)
# Convert the image back to RGB color space
xyz_image[..., 1] = np.power((lab_image[..., 0] + 16.0) / 116.0, 3)
xyz_image[..., 0] = np.power((lab_image[..., 0] + 16.0) / 116.0 + lab_image[..., 1] / 500.0, 3)
xyz_image[..., 2] = np.power((lab_image[..., 0] + 16.0) / 116.0 - lab_image[..., 2] / 200.0, 3)
rgb_image = np.dot(xyz_image, np.array([[3.240479, -1.537150, -0.498535],
[-0.969256, 1.875992, 0.041556],
[0.055648, -0.204043, 1.057311]]))
# Convert the image back to the range [0, 255]
rgb_image = np.clip(rgb_image, 0, 1) * 255.0
rgb_image = rgb_image.astype(np.uint8)
return rgb_image
def gaussian_filter(mask, sigma):
"""
Apply Gaussian filtering to a binary mask.
Parameters:
mask (numpy.ndarray): Binary mask to apply filtering on.
sigma (float): Standard deviation of the Gaussian kernel.
Returns:
numpy.ndarray: Binary mask after Gaussian filtering.
"""
# Create a Gaussian kernel with the given sigma
ksize = int(2 * np.ceil(2 * sigma) + 1)
kernel = np.zeros((ksize, ksize))
for i in range(ksize):
for j in range(ksize):
kernel[i, j] = np.exp(-((i - ksize // 2) ** 2 + (j - ksize // 2) ** 2) / (2 * sigma ** 2))
kernel /= np.sum(kernel)
# Apply convolution with the kernel
filtered = np.zeros_like(mask, dtype='float32')
for i in range(mask.shape[0]):
for j in range(mask.shape[1]):
roi = mask[max(i - ksize // 2, 0):min(i + ksize // 2 + 1, mask.shape[0]),
max(j - ksize // 2, 0):min(j + ksize // 2 + 1, mask.shape[1])]
filtered[i, j] = np.sum(roi * kernel[:roi.shape[0], :roi.shape[1]])
return filtered
def binary_opening(mask, kernel):
"""
Perform binary morphological opening on a binary mask using a structuring element.
Parameters:
mask (numpy.ndarray): Binary mask to perform opening on.
kernel (numpy.ndarray): Structuring element used for opening.
Returns:
numpy.ndarray: Binary mask after morphological opening.
"""
# Create padding on all sides of the mask
pad_width = [(kernel.shape[i] // 2, kernel.shape[i] // 2) for i in range(kernel.ndim)]
mask_padded = np.pad(mask, pad_width, mode='constant', constant_values=0)
# Apply morphological erosion using the kernel
eroded = np.zeros_like(mask_padded)
for i in range(mask_padded.ndim):
eroded = np.maximum(eroded, np.apply_along_axis(np.roll, i, mask_padded, shift=-kernel.shape[i] // 2))
eroded = eroded[pad_width[0][0]:-pad_width[0][1], pad_width[1][0]:-pad_width[1][1]]
# Create padding on all sides of the eroded mask
pad_width = [(kernel.shape[i] // 2, kernel.shape[i] // 2) for i in range(kernel.ndim)]
eroded_padded = np.pad(eroded, pad_width, mode='constant', constant_values=0)
# Apply morphological dilation using the kernel
dilated = np.zeros_like(eroded_padded)
for i in range(eroded_padded.ndim):
dilated = np.minimum(dilated, np.apply_along_axis(np.roll, i, eroded_padded, shift=kernel.shape[i] // 2))
dilated = dilated[pad_width[0][0]:-pad_width[0][1], pad_width[1][0]:-pad_width[1][1]]
return dilated
def binary_closing(mask, kernel):
"""
Perform binary morphological closing on a binary mask using a structuring element.
Parameters:
mask (numpy.ndarray): Binary mask to perform closing on.
kernel (numpy.ndarray): Structuring element used for closing.
Returns:
numpy.ndarray: Binary mask after morphological closing.
"""
# Create padding on all sides of the mask
pad_width = [(kernel.shape[i] // 2, kernel.shape[i] // 2) for i in range(kernel.ndim)]
mask_padded = np.pad(mask, pad_width, mode='constant', constant_values=0)
# Apply morphological dilation using the kernel
dilated = np.zeros_like(mask_padded)
for i in range(mask_padded.ndim):
dilated = np.minimum(dilated, np.apply_along_axis(np.roll, i, mask_padded, shift=kernel.shape[i] // 2))
dilated = dilated[pad_width[0][0]:-pad_width[0][1], pad_width[1][0]:-pad_width[1][1]]
# Create padding on all sides of the dilated mask
pad_width = [(kernel.shape[i] // 2, kernel.shape[i] // 2) for i in range(kernel.ndim)]
dilated_padded = np.pad(dilated, pad_width, mode='constant', constant_values=0)
# Apply morphological erosion using the kernel
eroded = np.zeros_like(dilated_padded)
for i in range(dilated_padded.ndim):
eroded = np.maximum(eroded, np.apply_along_axis(np.roll, i, dilated_padded, shift=-kernel.shape[i] // 2))
eroded = eroded[pad_width[0][0]:-pad_width[0][1], pad_width[1][0]:-pad_width[1][1]]
return eroded
def create_shadow_mask(image, threshold=80, range_width=50):
lab_image = np.apply_along_axis(lambda x: np.dot([0.2126, 0.7152, 0.0722], x), 2, image).astype('float64')
luminance_range = np.max(lab_image) - np.min(lab_image)
if luminance_range < range_width:
range_width = luminance_range
threshold_min = np.min(lab_image) + range_width / 2
threshold_max = np.max(lab_image) - range_width / 2
if threshold < threshold_min:
threshold = threshold_min
elif threshold > threshold_max:
threshold = threshold_max
mask = np.logical_and(lab_image >= threshold - range_width / 2, lab_image <= threshold + range_width / 2)
if np.sum(mask) == 0:
return np.zeros_like(mask).astype(float)
else:
center_line = np.nanmean(np.where(mask, lab_image, np.nan), axis=0)
x = np.arange(center_line.shape[0])
slope = np.zeros(center_line.shape)
slope[1:-1] = (center_line[2:] - center_line[:-2]) / 2
slope[0] = slope[1]
slope[-1] = slope[-2]
intercept = center_line - slope * x
x = np.arange(image.shape[1]) # x-coordinates of pixels
y = np.arange(image.shape[0]) # y-coordinates of pixels
print(y)
x, y = np.meshgrid(x, y) # create 2D arrays of x- and y-coordinates
# compute distances from each pixel to the shadow line
dist = np.abs((y[:, :, np.newaxis] - slope[np.newaxis, np.newaxis, :] * x[:, :, np.newaxis]
- intercept[np.newaxis, np.newaxis, :]) / np.sqrt(1 + slope[np.newaxis, np.newaxis, :] ** 2))
print(dist)
# sigma = np.nanmedian(dist)/0.6745
# mask = np.exp(-0.5*(dist/sigma)**2)
return dist
def highpass_mask(img, cutoff, order=1):
# Calculate the Fourier transform of the image
fft_img = np.fft.fft2(img)
# Shift the zero-frequency component to the center of the spectrum
fft_img = np.fft.fftshift(fft_img)
# Construct a highpass filter in the Fourier domain
x, y = np.meshgrid(np.linspace(-1, 1, img.shape[1]), np.linspace(-1, 1, img.shape[0]))
r = np.sqrt(x ** 2 + y ** 2)
hp_filter = 1 - 1 / (1 + (cutoff / r) ** (2 * order))
# Apply the highpass filter to the Fourier transform of the image
fft_img_hp = fft_img * hp_filter
# Shift the zero-frequency component back to the corners of the spectrum
fft_img_hp = np.fft.ifftshift(fft_img_hp)
# Calculate the inverse Fourier transform of the highpass-filtered image
img_hp = np.fft.ifft2(fft_img_hp)
# Take the absolute value of the real part of the inverse Fourier transform
img_hp = np.abs(np.real(img_hp))
# Normalize the highpass-filtered image to the range [0, 1]
img_hp_norm = img_hp / np.max(img_hp)
# Invert the highpass-filtered image to create a highpass mask
mask = 1 - img_hp_norm
return mask
def cvtColor(hsv_img):
# Assuming you have an HSV image loaded in the variable 'hsv_img'
# Let's convert the image back to RGB color space
h, s, v = np.split(hsv_img, 3, axis=-1)
h = h.reshape(h.shape[:2])
s = s.reshape(s.shape[:2])
v = v.reshape(v.shape[:2])
c = v * s
x = c * (1 - np.abs((h / 60) % 2 - 1))
m = v - c
z = np.zeros_like(h)
# Set up the RGB channels according to the hue value
rgb_img = np.dstack((
np.where((0 <= h) & (h < 60), c,
np.where((120 <= h) & (h < 180), z, np.where((240 <= h) & (h < 300), x, m))),
np.where((300 <= h), c, np.where((60 <= h) & (h < 120), x, np.where((180 <= h) & (h < 240), c, m))),
np.where((0 <= h) & (h < 360), v, m)
))
return rgb_img
def saturate(img, amount):
hsv_img = np.copy(img)
hsv_img = np.asarray(hsv_img, dtype=np.float32) / 255.0 # Normalize pixel values
hsv_img = np.clip(hsv_img, 0, 1) # Clip values to the range [0, 1]
hsv_img = np.squeeze(cv2.cvtColor(hsv_img, cv2.COLOR_RGB2HSV_FULL)) # Convert to HSV
# Let's adjust the saturation of the image
saturation_factor = 1.5 # Adjust this value to your preference
hsv_img[..., 1] *= saturation_factor
# Now let's convert the image back to RGB color space
hsv_img = np.clip(hsv_img, 0, 255) # Clip values to the range [0, 255]
hsv_img = np.asarray(hsv_img, dtype=np.uint8) # Convert back to uint8
rgb_img = cv2.cvtColor(hsv_img, cv2.COLOR_HSV2RGB_FULL) # Convert back to RGB
# The resulting image with increased saturation is stored in the 'rgb_img' variable
def rgb2ycbcr(rgb_img):
# Create the conversion matrix for RGB to YCbCr
conv_mat = np.array([[0.299, 0.587, 0.114],
[-0.168736, -0.331264, 0.5],
[0.5, -0.418688, -0.081312]])
# Reshape the input image to a 2D array of pixels
pixels = rgb_img.reshape(-1, 3)
# Apply the conversion matrix to the pixels
ycbcr_pixels = np.dot(pixels, conv_mat.T)
# Reshape the converted pixels back into the original image shape
ycbcr_img = ycbcr_pixels.reshape(rgb_img.shape)
# Convert the image data type to uint8 and return it
return ycbcr_img.astype(np.uint8)
def ycbcr2rgb(ycbcr_img):
# Create the conversion matrix for YCbCr to RGB
conv_mat = np.array([[1.0, 0.0, 1.402],
[1.0, -0.344136, -0.714136],
[1.0, 1.772, 0.0]])
# Reshape the input image to a 2D array of pixels
pixels = ycbcr_img.reshape(-1, 3)
# Apply the conversion matrix to the pixels
rgb_pixels = np.dot(pixels, conv_mat.T)
# Reshape the converted pixels back into the original image shape
rgb_img = rgb_pixels.reshape(ycbcr_img.shape)
# Convert the image data type to uint8 and return it
return rgb_img.astype(np.uint8)
def adjust_luminance(img, mask, adjustment):
# Convert the input image to the YCbCr color space
img = (255.0 * img).astype(np.uint8)
mask = (255.0 * mask).astype(np.uint8)
ycbcr_img = rgb2ycbcr(img)
ycbcr_mask = rgb2ycbcr(mask)
print(ycbcr_mask)
print(ycbcr_img)
plot_histogram(ycbcr_img, title="ycbcr")
plot_histogram(ycbcr_mask, title="ycmask")
# Separate the luminance channel (Y)
y_channel = ycbcr_img[..., 0]
y_channel_mask = ycbcr_mask[..., 0]
# Apply the adjustment to the luminance channel using the mask
y_adjusted = np.clip(y_channel + (adjustment * y_channel_mask), 0, 255).astype(np.uint8)
# Replace the original luminance channel with the adjusted one
ycbcr_img[..., 0] = y_adjusted
# Convert the image back to the RGB color space and return it
return ycbcr2rgb(ycbcr_img)
def tonemap_reinhard(image, gamma=2.2, intensity=0.18, light_adapt=0.8):
"""
Tonemaps the input HDR image using the Reinhard algorithm.
Args:
image: The input HDR image as a NumPy array.
gamma: The gamma correction value to apply to the output image.
intensity: The target scene brightness.
light_adapt: The adaptation rate for the brightness.
Returns:
The tonemapped output image as a NumPy array.
"""
# Convert the image to floating point RGB.
image = image.astype(np.float32)
# Compute the log average luminance.
lum = np.exp(np.mean(np.log(0.0001 + image)))
# Normalize the image by the log average luminance.
image /= lum
# Apply the Reinhard tonemapping algorithm.
mapped = np.zeros_like(image)
mapped = intensity * (mapped / np.max(mapped))
mapped = light_adapt * (mapped * (1 + mapped / np.max(mapped) ** 2)) / (1 + mapped)
mapped *= lum
# Apply gamma correction to the tonemapped image.
mapped = np.power(np.clip(mapped, 0, 1), 1 / gamma)
# Convert the tonemapped image to 8-bit RGB.
mapped = (255 * mapped).astype(np.uint8)
return mapped
def f(t):
# Helper function to compute the nonlinear transformation function for the LAB color space
delta = 6.0 / 29.0
t_thresh = delta ** 3
return np.where(t > t_thresh, t ** (1 / 3), (1 / 3) * (29 / 6) ** 2 * t + 4 / 29)
def numpy_lab2rgb(lab_img):
XYZ = np.zeros_like(lab_img, dtype=np.float32)
XYZ[..., 0] = (lab_img[..., 0] + 16.0) / 116.0
XYZ[..., 1] = (lab_img[..., 1] / 500.0) + XYZ[..., 0]
XYZ[..., 2] = XYZ[..., 0] - (lab_img[..., 2] / 200.0)
mask = XYZ > 0.2068966
XYZ[mask] = XYZ[mask] ** 3
XYZ[~mask] = (XYZ[~mask] - 16.0 / 116.0) / 7.787
D50 = np.array([0.9642, 1.0, 0.8249], dtype=np.float32)
RGB_linear = np.dot(XYZ,
np.array([[3.2406, -1.5372, -0.4986], [-0.9689, 1.8758, 0.0415], [0.0557, -0.2040, 1.0570]],
dtype=np.float32).T)
RGB_linear = np.clip(RGB_linear, 0.0, 1.0)
RGB_linear_D50 = RGB_linear / D50
sRGB = np.where(RGB_linear_D50 <= 0.0031308, 12.92 * RGB_linear_D50,
1.055 * (RGB_linear_D50 ** (1.0 / 2.4)) - 0.055)
sRGB = np.clip(sRGB, 0.0, 1.0)
return (RGB_linear_D50 * 255).astype(np.uint8)
def numpy_split_lab(lab_img):
L, a, b = np.rollaxis(lab_img, axis=-1)
return L, a, b
def numpy_merge_lab(l_channel_adjusted, a_channel, b_channel):
merged_lab = np.dstack((l_channel_adjusted, a_channel, b_channel))
return merged_lab
def rgb2lab(img):
# Convert the RGB image to a float array with values between 0 and 1
img = img.astype(np.float32) / 255.0
# Convert the RGB image to the XYZ color space
# using the transformation matrix specified by the CIE
# (https://en.wikipedia.org/wiki/CIE_1931_color_space)
r, g, b = np.split(img, 3, axis=2)
x = 0.412453 * r + 0.357580 * g + 0.180423 * b
y = 0.212671 * r + 0.715160 * g + 0.072169 * b
z = 0.019334 * r + 0.119193 * g + 0.950227 * b
# Convert the XYZ image to the LAB color space using the D50 white point
# (https://en.wikipedia.org/wiki/Lab_color_space#Conversion_from_XYZ_to_Lab)
x /= 0.950456
z /= 1.088754
l = 116.0 * f(y) - 16.0
a = 500.0 * (f(x) - f(y))
b = 200.0 * (f(y) - f(z))
# Stack the LAB channels back into a single image and return it
return np.concatenate((l, a, b), axis=2)
def apply_luminance_mask_lab(img, mask):
# Convert the image to the LAB color space
lab_img = rgb2lab(img)
print(lab_img)
lab_mask = rgb2lab(mask)
print(lab_mask)
# Split the LAB image into its channels
l_channel, a_channel, b_channel = numpy_split_lab(lab_img)
l_channel_mask, a_channel, b_channel = numpy_split_lab(lab_mask)
# Apply the mask to the luminance channel
l_channel_adjusted = l_channel + l_channel_mask # np.where(l_channel_mask > 0, l_channel - 50, l_channel)
# Merge the adjusted channels back into a LAB image
lab_img_adjusted = numpy_merge_lab(l_channel_adjusted, a_channel, b_channel)
# Convert the adjusted image back to the RGB color space and return it
return numpy_lab2rgb(lab_img_adjusted)
def rgb2lab(img):
# Convert the RGB image to a float array with values between 0 and 1
img = img.astype(np.float32) / 255.0
# Convert the RGB image to the XYZ color space
# using the transformation matrix specified by the CIE
# (https://en.wikipedia.org/wiki/CIE_1931_color_space)
r, g, b = np.split(img, 3, axis=2)
x = 0.412453 * r + 0.357580 * g + 0.180423 * b
y = 0.212671 * r + 0.715160 * g + 0.072169 * b
z = 0.019334 * r + 0.119193 * g + 0.950227 * b
# Convert the XYZ image to the LAB color space using the D50 white point
# (https://en.wikipedia.org/wiki/Lab_color_space#Conversion_from_XYZ_to_Lab)
x /= 0.950456
z /= 1.088754
l = 116.0 * f(y) - 16.0
a = 500.0 * (f(x) - f(y))
b = 200.0 * (f(y) - f(z))
# Stack the LAB channels back into a single image and return it
return np.concatenate((l, a, b), axis=2)