How to generate noise in an image using python?

Question

How to generate a periodic noise of the type Moiré in an image at gray levels using Python?

Answer 1

Based on the concept of Moiré from Wikipedia and a little bit of Geometria Analítica, I created a little routine to apply the effect on an image superimposing it on itself.

Routine:

from PIL import Image
import math

def moire(source, target, angle, distance, offsetx = 2, offsety = 2):

    #imagem de entrada
    img = Image.open(source)
    pm = img.load()
    # imagem de saída (usando a mesma para gerar sobreposição)
    imgout = Image.open(source)
    pmout = imgout.load()

    # valores para as transformações    
    cosseno = math.cos(angle)
    seno = math.sin(angle)
    # distância em cada eixo
    dx = distance * cosseno 
    dy = distance * seno

    for x in range(0, img.size[0], offsetx):
        for y in range(0, img.size[1], offsety):
            # calcula coordenada transformada (rotação + deslocamento)
            x2, y2 = dx + math.floor(x * cosseno - y * seno), dy + math.floor(x * seno + y * cosseno)
            # ajusta valores fora da imagem (como se a mesma repetisse infinitamente)
            if x2 < 0:
                x2 = img.size[0] + x2
            elif x2 >= img.size[0]:
                x2 = x2 - img.size[0]
            if y2 < 0:
                y2 = img.size[1] + y2
            elif y2 >= img.size[1]:
                y2 = y2 - img.size[1]
            # desenha ponto transformado 
            pmout[x, y] = pm[x2, y2] 

    # salva a imagem
    imgout.save(target)

Note that in the first line I do the import of the image library Pillow (successor to the PIL).

Next is the function that receives the following parameters:

1. source: input image
2. target: location where to save the result
3. angle: angle of the moiré, that is, how much the image will be rotated
4. distance: distance of the moiré, that is, how much the image will be shifted from its origin in relation to the informed angle
5. offsetx: the frequency with which the moiré points will be applied in the coordinate x, that is, the value 1 indicates that all pixels will be processed, the value 2 indicates that one pixel yes and another no and so on.
6. offsety: the same as before in the co-ordinate y

Examples

Date the image:

Example 1

# gira a imagem em 45º e aplica o efeito em todos os pontos
moire(r'linhas.png', r'linhas-output-1.png', math.pi / 4, 0, 1, 1)

Example 2

# gira 30º, ponto sim, ponto não, e desloca 50 pixels nesse ângulo
moire(r'linhas.png', r'linhas-output-2.png', math.pi / 3, 50, 2, 2)

Example 3

# gira 18º e desenha apenas a cada 5 pontos
moire(r'linhas.png', r'linhas-output-3.png', math.pi / 5, 0, 5, 5)

Answer 2

That was the solution I came to - it may not be the most elegant, it may not be the most efficient - but it served the purpose:

    from scipy import misc
    import numpy as np
    
    orig = misc.imread('bear_original.jpg')
    sh = orig.shape[0], orig.shape[1]
    noise = np.zeros(sh, dtype='float64')
    
    X, Y = np.meshgrid(range(0, sh[0]), range(0, sh[1]))
    
    A = 40
    u0 = 45
    v0 = 50
    
    noise += A*np.sin(X*u0 + Y*v0)
    
    A = -18
    u0 = -45
    v0 = 50
    
    noise += A*np.sin(X*u0 + Y*v0)
    
    noiseada = orig+noise
    misc.imsave('bearnoise.jpg', noiseada)

Noise

Noise applied to the image