Image getting dark

Question

I did a program in python to apply Gaussian noise on an image as follows. Input image is :

from PIL import Image
from math import *

import numpy

list1 = []
list2 = []

im = Image.open("313.JPG")
im.show()
list1 = list(im.getdata())

length = len(list1)
total = 0
for i in list1:
    total = total + i
mean = total /length  #mean
sd = numpy.std(list1) #standard deviation
print "mean is %d" %(mean)
print "sd is %d" %(sd)
for i in list1:
    g = (1/(sd * sqrt(2*pi)))*(exp(-((i - mean)**2)/(2*(sd**2)))) #gaussian 
    list2.append(g)
im.putdata(list2)
im.save('q4.jpg')             
im.show()

But I am getting a complete dark image instead of getting noise on image.Please help.I'm expecting the below image as output.

Answer 1

from PIL import Image
from math import *
import numpy

list1 = []
im = Image.open("313.JPG")
im.show()
list1 = list(im.getdata())
length = len(list1)

# generate random noise data with mean 0 and sd 10
list2 = numpy.random.normal(0, 10, length)
# Add this to the image data
list3 = list1+list2

im.putdata(list3)
im.show()

Answer 2

Since gaussian is normalized, and its peak is in 1/sqrt(2pi), you should multiply g for 255*sqrt(2*math.pi).

Since yout g is not a normal gaussian, but it is also normalized by 1/sd, to let g span fro m0 to 255 you shoud moltiply g by N as follows:

N = 255.*sqrt(2.*pi)*sd
g = N*(1/(sd * sqrt(2*pi)))*(exp(-((i - mean)**2)/(2*(sd**2))))

This is what I get with your image as input:

It is correct: your algorithm just compute for every pixel, its gaussian value (where the gaussian is centered in the mean value): this means that pixel with a value near the average value will get brigher and pixel distant from the average get darker. No way to get a noise from that. You should re think your algorithm.