Digital Image Processing

DSP is used extensively in image processing. For example as an in class project, lets remove the dithering patterns of dots in this image of Donald Duck.

These dots occur in the printing process used in newspapers in the past as a way to shade the picture without fine pixel or color control. The process was developed in the early nineteenth century by Ben Day, and is called the [Ben Day process].(https://en.wikipedia.org/wiki/Ben_Day_process)

1. Read in the image, find its shape, and display it.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib

im = plt.imread("Donald_Duck.png")
im.shape
print(im.shape)

def plti(im, h=8, **kwargs):
    """
    Helper function to plot an image.
    """
    y = im.shape[0]
    x = im.shape[1]
    w = (y/x) * h
    plt.figure(figsize=(w,h))
    plt.imshow(im, interpolation="none", **kwargs)
    plt.axis('off')
    plt.show()

plti(im)

(371, 417, 3)

1. A little green is visible around the outside of the image, so lets crop the image to remove it.

im1 = im[10:im.shape[0]-10, 10:im.shape[1]-10]

1. Now convert the RGB image to grayscale. The three in the size above are the red, green, and blue components. The formula to convert is $$ L_{gray} = 0.2989R + 0.587G+0.114B$$ where $L_{gray}$ is the grayscale luminosity, $R$ is the red intensity, $G$ is the green intensity, and $B$ is the blue intensity. This formula was specified by the National Television System Committee (NTSC).

def rgb2gray(rgb):
    return np.dot(rgb[...,:3], [0.2989, 0.5870, 0.1140])
gray_im = rgb2gray(im1)
plt.gray()  # Means all further plots will be gray scale.
plti(gray_im)

<Figure size 432x288 with 0 Axes>

1. You figure out how to remove the dithering. A good set of slides on image processing using the methods of our class is here.

Hint: See this web page if you have no ideas, but first please think about it and look at the image closely to see if you can figure it out yourself.