i. Point processing deals with single pixels, i.e. T is a 1 X 1 operator. It means that the new value f(x,y) depends on the operator T and the present f(x,y)

ii. Following are some of the common examples of point processing

(I) Digital negative

(II) Contrast stretching

(III) Thresholding

(IV) Grey level Slicing

(V) Bit plane slicing

iii. The identity transformation is given in the figure below,(Figure 3), we are going to demonstrate the above mentioned point processing techniques on the Identity transformation

Figure 3

(I) Digital Negative

i. Digital negative, simply means inverting the grey levels, which means black in the original image will be white in digital negative and vice versa.

ii. The figure below (Figure 4) is the digital negative transformation for an 8-bit image

iii. The digital negative can be obtained by a simple transformation given by $s = 255 – r (\text {Where} r_{max} = 255)$

Hence when $r=0, s=255$ and when $r=255, s=0$

In general,

$ s=(L-1)-r$

Where L = Number of grey levels

Figure 4

(II) Contrast stretching

i. Contrast stretching, in general increases the contrast of the images, by making the dark portions darker and the bright portion brighter.

ii. Figure below (Figure 5) shows the transformation used to achieve contrast stretching

Figure 5

iii. The formulation for contrast stretching algorithm is given below,

$s=l.r \space\space\space\space 0\lt=r\lt=a \\ s=m.(r-a) + v \space\space\space\space a\lt=r\lt=b \\ s=n.(r-b) + w \space\space\space\space b\lt=r\lt=(L-1) $

iv. In the above equation, l, m and n are slopes, and it is clear from the figure that l and m are less than 1 whereas m is greater than 1, this increases the dynamic range of the image.

(III) Thresholding

i. Thresholding is a phenomenon which occurs due to extreme contrast stretching. In the contrast stretching diagram if we make the first and the last slope zero (r1=r2=0) and we increase the center slope, we will get a thresholding transformation.

ii. The formula for achieving thresholding is as follows

$s = 0 ;\space\space\space\space if\space r\lt=a \\ s = L - 1 ; \space\space\space\space if\space r\gta$

where L is the number of grey levels.

iii. Thresholding example is shown in the figure 6 below

Figure 6

(IV) Grey Level Slicing

i. In thresholding, the grey level is split into two parts, however in many applications we need a specific range of grey level values. In order to achieve this we use grey level slicing.

ii. The transformation for the same is shown below in figure 7 and figure 8. Figure 7 represents slicing without the background and figure 8 represents slicing with background.

Figure 7

iii. The formula for grey level slicing without background is shown below,

$s = L – 1;\space\space\space\space if\space\space a\lt=r\lt=b \\ s = 0;\space\space \text {otherwise} $

iv. In order to retain the background, we have a different formula which is shown below,

$s = L – 1;\space\space\space\space if\space\space a\lt=r\lt=b \\ s = r; \space\space\space\space \text {otherwise} $

Figure 8

(V) Bit plane slicing

i. In this technique, we find the contribution made by each bit in the final image.

ii. Pixels are digital numbers composed of bits, for example the intensity of each pixel in 256 level grey scale image is composed of 8-bits.

iii. Instead of highlighting intensity level ranges, we could highlight the contribution made to the total image by specific bits. Figure 9, below shows how an 8-bit image may be considered as being composed of eight one bit planes, showing the significance of each bit.

Figure 9. Bit plane representation of an 8 bit image

iv. In bit plane slicing, we will get 8 different images and all 8 images will be binary, showing the significance of each bit in the 8-bit image.

v. Decomposing an image into its bit planes is useful for analyzing the creative importance of each bit in the image, a process that aids in determining the adequacy of the number of bits used to quantize the image.

vi. Also, this type of decomposition is useful for image compression in which, fewer than all planes are used in reconstructing the image.

Application of bit plane slicing:

i. Bit plane slicing can be used for image compression.

ii. Data compression can also be achieved with the help of bit plane slicing.