Image White Balancing with Python

Below is a photo I took in the viewing deck of Taipei 101. Taipei 101 has a glass wall which is green color. Thus, all photos taken inside the building through the wall has a green cast including this one.

To remove the cast of green color, we use the technique of image white balancing. First, we need a reference object with known color. Fortunately this photo has clouds (pointed by the arrow). Clouds are good references since they are white. By averaging the pixels of cloud (mean(img_array[400,500:550,:])), the mean of R/G/B is [201.5, 254.9, 253.9]. Since white color has R/G/B channels roughly equal, to make it white, 52 needs to be added to R channel of the whole image. Like DC cancellation in communication, white balancing removes the bias of the signal.

Code below shows how to do white balancing

filename = 'IMG_9254.JPG'
img = image.load_img(filename)
img_array = np.array(image.img_to_array(img),dtype=np.uint8)
img_shape=img_array.shape
plt.figure()
plt.imshow(img_array)

img_array2 = img_array
img_array2 = np.array(img_array2, dtype=np.uint16)
img_array2[:,:,0] = img_array2[:,:,0] + 52 # white balancing
img_array2 = np.clip(img_array2, 0, 255)

The newly generated image after white balancing, img_array2,  is shown below. The color does look more natural. In case that you want to repeat this, code/image can be found here.

Note on Implementation of “Fast Noise Variance Estimation” by J. Immerkær

Noise variance estimation is a fundamental task of image processing. Among various approaches of noise variance estimate, fast noise variance estimation method proposed by J. Immerkær in [1] stands out because of its good balance between complexity and accuracy.

Based on J. Immerkær's method, to estimate the standard deviation of image noise $\sigma$, we can use equations below:

$F= \begin{bmatrix} 1 & -2 & 1\\ -2 & 4 & -2\\ 1 & -2 & 1\\ \end{bmatrix}$

$\sigma=\frac{\sqrt{\pi/2}}{6(W-2)(H-2)}\sum_{I}|I(x,y)*F|$

$F$ is the high-pass filter. To estimate noise variance, filter $F$ will be applied on the whole image $I(x,y)$ with convolution. The sum of absolute value of convolution results is normalized by width of height of the image, which is $(W-2)(H-2)$. "-2" counts for the boundary effect. The summation is also scaled by $\frac{\sqrt{\pi/2}}{6}$, which is explained next.

Assume a 3x3 block of $I(x,y)$ with each element of $x_{i}$ to be a Gaussian random variable with mean $\mu$ and standard deviation $\sigma$
$I= \begin{bmatrix} x_{1} & x_{2} & x_{3}\\ x_{4} & x_{5} & x_{6}\\ x_{7} & x_{8} & x_{9}\\ \end{bmatrix}$
Then $|I*F|=|x_{1}-2*x_{2}+x_{3}-2*x_{4}+4*x_{5}-2*x_{6}+x_{7}-2*x_{8}+x_{9}|$
Since $E(|I*F|^2)=36\sigma^2$, $|I*F|=6|s|$ where s is Gaussian random variable with mean 0 and standard deviation $\sigma$. We can derive the distribution of $y=|s|$ and it is $\frac{2}{\sqrt{2\pi}\sigma}e^{-\frac{y^2}{2\sigma^2}}$  for $y>=0$ and 0 for $y < 0$. <0 .="" br=""> 

Since $E(|s|)=\sqrt{\frac{2}{\pi}}\sigma$, it explains why the summation is also scaled by $\frac{\sqrt{\pi/2}}{6}$.


[1] J. Immerkær, “Fast Noise Variance Estimation”, Computer Vision and Image Understanding, Vol. 64, No. 2, pp. 300-302, Sep. 1996