Find,

i. Negative of the image

ii. Bit plane slicing

iii. Perform contrast modification as per the characteristics given in fig. a

iv. Draw the histogram of new image.

i. Negative of the image.

By definition of Digital negative,

$$S = ( L - 1 ) – r$$

From the fig. b value of L is 16, therefore

$$S = ( 16 - 1 ) – r$$

$S = 15 – r$ … r is pixel value of image

This is the negative of image shown in fig. b

ii. Bit Plane Slicing.

Converting image show in fig. b into binary,

iii. Performing Contrast Stretching.

$$S = l.r \hspace{2cm} 0\lt=r\lt=a \\ S = l.r \hspace{2cm} 0\lt=r\lt=5$$

$$l = \frac25 = 0.4$$

$$S = m.(r-a) + v \hspace{0.5cm} a\lt=r\lt=b \\ S = m.(r-a) + v \hspace{0.5cm} 5\lt=r\lt=10$$

$$m = \frac{12 - 2}{10 - 5} = 2$$

$$S = n.(r-b) + w \hspace{1.5cm} b\lt=r\lt=(L-1) \\ S = n.(r-b) + w \hspace{1.5cm} 10\lt=r\lt=15$$

$$n =\frac{15 - 12}{15 - 10} = 0.6$$

Hence the contrast stretching image is

iv. Drawing New Image Histogram.