You're looking for 1D Convolution which takes a filter with which you "convolve" the image. For example, you can use a Median filter (borrowing example from Wikipedia)
x = [2 80 6 3]
y[1] = Median[2 2 80] = 2
y[2] = Median[2 80 6] = Median[2 6 80] = 6
y[3] = Median[80 6 3] = Median[3 6 80] = 6
y[4] = Median[6 3 3] = Median[3 3 6] = 3
so
y = [2 6 6 3]
So here, the window size is 3 since you're looking at 3 pixels at a time and replacing the pixel around this window with the median. A window of 3 means, we look at the first pixel before and first pixel after the pixel we're currently evaluating, 5 would mean 2 pixels before and after, etc.
For a mean filter, you do the same thing except replace the pixel around the window with the average of all the values, i.e.
x = [2 80 6 3]
y[1] = Mean[2 2 80] = 28
y[2] = Mean[2 80 6] = 29.33
y[3] = Mean[80 6 3] = 29.667
y[4] = Mean[6 3 3] = 4
so
y = [28 29.33 29.667 4]
So for your problem, y[3] is the "mean brightest point".
Note how the borders are handled for y[1] (no pixels before it) and y[4] (no pixels after it)- this example "replicates" the pixel near the border. Therefore, we generally "pad" an image with replicated or constant borders, convolve the image and then remove those borders.
This is a standard operation which you'll find in many computational packages.
