# How to get a Standard Deviation weighted average in image?

Now I'm trying to implement a SDLWGW algorithm by the MATLAB. currently I'm referencing from Automatic White Balancing Using Luminance Component and Standard Deviation of RGB Components

The problem is I can't understand how to get a $$SDLWA_{R}$$ and $$\overline{L_{red}(k)}$$? Also what if the $$L_{weight}(i,j)$$ is $$0.9$$ then how to calculate the bar of $$L_{red}(k)$$?

I can't understand it.

I want to know that what is the different between $$SD_{red}(k)$$ and $$SD_{red}(l)$$?

$$SDLWA_{R}=\sum_{k=1}^{n}\frac{SD_{red}(k)}{\sum_{l=1}^{n}SD_{red}(l)}\times red_{i,j}(k)$$

What is the $$SD_{red}(l)$$? Especially, what is the $$l$$?

$$\sum_{l=1}^{n}SD_{red}(l)$$

# Update 1

I have got a question one more,

The paper was written like this L_weight(i,j) is a positive single-peak function (e.g Triangular function or Gaussian function) value for the luminance value at i-th row, j-th column of the k-th block. But I can't understand what is the mean? How can I make L_weight(i,j)? Would you please give me any hint please ?

# Update 2

I'm trying to understand a below answer.

Q1. What if I've got a this block then I think that the $$k$$ is to be $$12$$ and $$p$$ is $$5$$, and $$q$$ is $$5$$. am I correct?

Q2. How to get a $$\overline{L\_red(k)}$$ value as below the case?

Q2-1. Especially, I want to know that what does exactly indicate the $$L\_weight(1,1)red_{1,1}(k)$$ and $$L\_weight(1,1)$$, as below the case? I think we know the value of the $$red_{1,1}(k)$$ But I'm confused that how to know the value of $$L\_weight(1,1)$$ ?

# Update 3

Does anyone know the relationship between Gaussian weight and one Block?

• The bar denotes the average over a set of pixels. Please try to rewrite it, and propose a beginning of a Matlab code, so that we can help you where you stop understanding Mar 4, 2016 at 23:20
• @LaurentDuval would you give some hint about what is the different between x,y and i,j in Figure3? I don't have a quite bit understand. I can to assume that that i,j are involved in K then what is the x,y? Mar 4, 2016 at 23:47
• This person has created new accounts to spam questions on this particular topic. It seems like he/she is trying to accomplish a very specific task of image processing, but without the required background and knowledge. Please see: stackoverflow.com/questions/35808504/… Mar 5, 2016 at 1:03
• @jojek Thanks, I have no idea, what do you think? Mar 5, 2016 at 11:01

The $k$ and $l$ indices are to be understood with indexes under the $\sum$ sign. They can be called "free variables". Suppose that the block $k$ has only two pixels, then $p=1$ and $q=2$. So $\overline{L\_red(k)}$ is just a weighted average (a kind of center of mass) of the $2$ red components from the two pixels of the block: $$\frac{L\_weight(1,1)red_{1,1}(k)+L\_weight(1,2)red_{1,2}(k)}{L\_weight(1,1)+L\_weight(1,2)}$$ which gives you a single value for each block. Formula (5) has the same interpretation, you perform the weighted average of those averaged values over blocks, with weights $SD\_red(k)$.
• $L\_weight(i,j)$ is a discrete function with the same size of each block, so you multiply coordinate-wise each pixel of the block by the corresponding pixel in $L\_weight(i,j)$ (Q2-1), sum all $p\times q$ products, and divide by the sum of pixles in $L\_weight(i,j)$ (Q2). On the bottom of page 495, the authors seem to take a constant value. Q1: $p=q=5$, but the block is the first one, $k=1$. Mar 5, 2016 at 15:15