Introduction to Digital Image Processing III

Applying filters to an image is an everyday task in not only digital image processing but most of the machine learning applications that deal with images, especially convolution neural networks. But to first use these techniques for machine learning we must first learn to apply even the most basic filters to images. To learn this we will take an example of blurring an image.

Image Blur

Image blurring is nothing new, we use it in most of the image processing applications. It is primarily used to reduce noise from an image before some other algorithm is applied on it. Don’t worry what noise means, we will discuss it later. The most basic tool for image blurring is the averaging filter. It is as simple as it sounds. We basically take a pixel in the original image, calculate the average of the pixel values in the KxK neighborhood of that pixel and put in that value in the pixel of the new image. We call this KxK neighborhood window or filter with size K.

Mean Flter

In this example the concerned pixel is 1 in the middle, we take a 3x3 area around that pixel, calculate the average of these pixel values and put that average in place of 1 in the new image. But you must also think about what happens to the pixel on the edge or at the corners, how can we take a KxK window? To solve this we simply pad the image with zeros, so that average can be calculated for those corner pixels. If the filter size is KxK we will need to pad with K-1 in all directions, and the new image size would be (M+2K-2) x (N+2K-2).

The code it is fairly easy, try it on your own first.

def average_filter(img, k): # filter size = k
    img2 = np.zeros(img.shape).astype("uint8")
    img = np.pad(img, (k-1, k-1), "constant", constant_values=(0,0))
    for i in range(img2.shape[0]):
        for j in range(img2.shape[1]):
            mean = np.mean(img[i:i+2*k-2,j:j+2*k-2])
            img2[i,j] = mean
    return img2
img = cv2.imread("elon.jpg", 0)
img2 = average_filter(img, 3)
cv2.imwrite("mean_blurred.jpg", img2)

Original	Mean Blur

As you can see the image is now blurred, try this with other filter sizes and note your observations. See that the filter is always odd, otherwise you cannot select a central pixel.

Median Filter

Now you will do something even mode interesting, you will remove noise from an image. Noise is something that reduces the “quality” of an image, it is undesirable and can occur due to various reasons, such as defects in the camera, error while transmitting the image, etc. In image processing every image will have some sort of noise in it. We also try to reduce this noise so that the image looks “good” to us.

Salt and pepper

Probably the simplest noise is salt and pepper, and it is exactly what it is named after. Salt is white in color and pepper is black, so it is the presence of black and white spots on the image, the same when you mix some salt and pepper together.

30% Salt and Pepper Noise

The easiest way to remove salt and pepper noise is a median filter. It is similar to the mean filter above but instead of taking the mean we take the median of the pixel values in the KxK neighborhood.

Median Filter

Salt and Pepper Noise	Median Filtered

Try to add salt and pepper noise to the image first, then try to denoise it.

def salt_pepper(img, prob):
    for i in range(img.shape[0]):
        for j in range(img.shape[1]):
            if(np.random.random()<prob):
                if(np.random.random()<0.5):
                    img[i,j] = 0
                else:
                    img[i,j] = 255
    return img

def median_filter(img, k): # filter size = k
    img2 = np.zeros(img.shape).astype("uint8")
    img = np.pad(img, (k-1, k-1), "constant", constant_values=(0,0))
    for i in range(img2.shape[0]):
        for j in range(img2.shape[1]):
            median = np.median(img[i:i+2*k-2,j:j+2*k-2])
            img2[i,j] = median
    return img2
img = cv2.imread("elon.jpg", 0)
noise = salt_pepper(img, 0.3)
cv2.imwrite("noise.jpg", noise)
img2 = median_filter(noise, 3)
cv2.imwrite("median_blurred.jpg", img2)

In this code we first add how much salt and pepper noise we need, and also that both salt and pepper are in equal proportions. Then we denoise the image with a median filter. The result is pretty satisfying, that even such a noisy can be easily cleaned.