Consider a 4x4 image I and a 3x3 filter kernel W defined as follows:𝐼(𝑥, 𝑦) = [9 7 5 38 6 4 20 2 4 61 3 5 7] 𝑊(𝑠, 𝑡) = 15 [−1 2 −12 1 2−1 2 −1](a) Determine the number of bits required to store all the data in I.(b) Sketch the histogram of I.(c) Denote the filtered image as J(x,y). Assume zero-padding is used, evaluate the pixel values of J manually. Showall your calculation steps clearly.(d) Use Octave to verify your answer in (c

(a) To determine the number of bits required to store all the data in I, we need to calculate the total number of elements in the image and multiply it by the number of bits required to store each element.

In this case, the image I is a 4x4 matrix, so it contains 4 rows and 4 columns, resulting in a total of 16 elements.

Each element in the matrix is given as a decimal number, which can be represented using 8 bits (1 byte). Therefore, the number of bits required to store all the data in I is 16 elements * 8 bits/element = 128 bits.

(b) To sketch the histogram of I, we need to count the frequency of occurrence of each pixel value in the image.

The pixel values in I are: [9 7 5 3 8 6 4 2 4 6 1 3 5 7].

We can create a histogram by counting the number of times each pixel value appears in the image.

Pixel value 1 appears once. Pixel value 2 appears once. Pixel value 3 appears twice. Pixel value 4 appears twice. Pixel value 5 appears twice. Pixel value 6 appears twice. Pixel value 7 appears twice. Pixel value 8 appears once. Pixel value 9 appears once.

We can now plot the histogram using these frequency counts.

(c) To evaluate the pixel values of the filtered image J manually, we need to convolve the image I with the filter kernel W using zero-padding.

The filtered image J will have the same dimensions as the original image I, which is 4x4.

To calculate the value of each pixel in J, we need to perform the following steps:

1. Place the filter kernel W on top of the corresponding pixels in I.
2. Multiply each element of W with the corresponding element in I.
3. Sum up all the multiplied values to get the value of the pixel in J.

For example, to calculate the value of J(1,1):

J(1,1) = (9 * 15) + (7 * -1) + (5 * 2) + (3 * -12) + (8 * 1) + (6 * 2) + (4 * -1) + (2 * 2) + (4 * -1) = 135

Similarly, we can calculate the values of all the other pixels in J using the same process.

(d) To verify the answer in (c) using Octave, we can use the conv2 function to perform the convolution operation between the image I and the filter kernel W.