3) Consider the two grayscale images below: They are both 256x256 pixels in size

Question

3) Consider the two grayscale images below: They are both 256x256 pixels in size. Image (a) has intensity value 150 in its left half and intensity value 50 in its right half. Image (b) is a checkerboard with squares measuring 32x32 pixels, half of intensity value 150 and the other half of intensity value 50 (a) Do these two images have the same histogram? Briefly state why or why not. (b) Now, suppose you perform histogram equalization on the two images. Do the resulting images have the same histogram? Briefly state why or why not. (c) Suppose you blur each of the original images with a 3x3 averaging mask. Do the resulting images have the same histogram? Briefly state why or why not.

Explanation / Answer

a. Yes, these two images will have the same histogram.

Reason: Histogram depends on the intensity value and the number of pixels having a particular intensity value.

In Image (a), half of the pixels have intensity value of 150 and the other half pixels have intensity value of 50. Also, in Image (b), half of the pixels have an intensity value of 150 and the other half have intensity value of 50. Since there are two intensity values in both of them which are same and the count of the number of pixels having that particular intensity value is also same, the histogram of both the images will be same.

b. Yes, the histogram equalization will also lead to the same histogram.

Reason: Histogram equalization depends on histogram for uniform distribution of intensity values throughout the range (0-255). As the histogram is same for both the images, the histogram equalization will also be same.

c. No, the histogram of the resulting images after applying averaging mask to blur the image won’t be same for these two images.

Reason: Blurring through 3*3 averaging mask is a neighborhood operation and thus, the resulting intensity values after applying the averaging mask will be different for both the images. In Image(a), the intensity values are uniform whereas in Image(b), there contain different intensity value in every alternate 32*32 square. So, as the resulting intensity values will be different for both of them, the histogram will also be different.

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