We can think of a binary image as a True-False map of the form These are the simplest images one can imagine, and most of the related image-processing algorithms are trivial to code. For example, take the case of feature recognition:
Given the binary image Img below (left) representing a simple text with a few extra features, and any letter of the alphabet, we are able to retrieve all the occurrences of said letter by tracking all the global maxima of a simple correlation (of Img with a suitable image of the required letter as kernel). We have chosen the letter “e” in the following example:
E=Img[8:14,21:26] Correlation = scipy.ndimage.correlate(Img,E) matrix_plot(Correlation == Correlation.max())
A very natural question to ask is, what is a good approximation by binary images to a given gray-scale image Is there any advantage to working with this binary image instead of using the original? Maybe not in general, but for a certain set of simple-enough images, and certain set of image processing procedures, it could turn extremely useful. Let us start by answering first the question of turning grey-scale images into binary:
The half-tone algorithm
The code below shows an algorithm that performs a simulation of continuous tone images through the use of white and black dots varying in spacing (the closer to each other, the darker; the farther apart, the lighter). It is a good exercise to try and interpret what this code does by yourself, and do a write-up. I helped the process by making the variable names self-explanatory, and dropping small hints. Give it a go!
Img = scipy.misc.lena() GlobalError = zeros(Img.shape) ErrorPropagation = zeros(Img.shape) HalftonedImg = zeros(Img.shape) ColorDistributionKernel = array([[0,0,7],[2,5,2]])/16.0 threshold=128 for x in range(Img.shape): for y in range(Img.shape): # We perform some sort of convolution (between what objects?). # and store the result in ErrorPropagation sum_p=0.0 for i in range(ColorDistributionKernel.shape): for j in range(ColorDistributionKernel.shape): xx = minimum(maximum(0,x-i+1),Img.shape-1) yy = minimum(maximum(0,y-j+1),Img.shape-1) sum_p += ColorDistributionKernel[i,j]*GlobalError[xx,yy] ErrorPropagation[x,y]=sum_p # How do ErrorPropagation and GlobalError relate to each other? # How do we use this to populate the halftoned image? # How did we choose the threshold? t=Img[x,y]+ErrorPropagation[x,y] if t>threshold: GlobalError[x,y]=t-2*threshold HalftonedImg[x,y]=1 else: GlobalError[x,y]=t