saturation.py

# Calculate factor
if beta == 255: alpha = np.infty
else: alpha = (255+beta)/(255-beta)

for x in range(width):
    for y in range(height):
        r, g, b = image.getpixel((x, y))

        μ = (r+g+b)/3

        r_ = truncate(alpha*(r - μ) + μ)
        g_ = truncate(alpha*(g - μ) + μ)
        b_ = truncate(alpha*(b - μ) + μ)

        new_pixel = (int(r_), int(g_), int(b_))
        new_image.putpixel((x, y), new_pixel)