Enhancement In Frequency Domain:

The frequency domain methods of image enhancement are based on convolution theorem. This is represented as,

Where.

g(x, y) = h (x, y)*f(x, y)

g(x, y) = Resultant image

h(x, y) = Position invariant operator f(x, y)= Input image

The Fourier transform representation of equation above is,

G (u, v) = H (u, v) F (u, v)

The function H (u, v) in equation is called transfer function. It is used to boost the edges of input image f (x, y) to emphasize the high frequency components.

The different frequency domain methods for image enhancement are as follows.

- Contrast
- Clipping and
- Digital
- Intensity level slicing and
- Bit

### 1. Contrast Stretching:

Due to non-uniform lighting conditions, there may be poor contrast between the background and the feature of interest. Figure 1.1 (a) shows the contrast stretching transformations.

### Fig.1.1 (a) Histogram of input image

**Fig.1.1 (b) Linear Law**

### Fig.1.1 (c) Histogram of the transformed image

** **

These stretching transformations are expressed as

In the area of stretching the slope of transformation is considered to be greater than unity. The parameters of stretching transformations i.e., a and b can be determined by examining the histogram of the image.

### 1. Clipping and Thresholding:

Clipping is considered as the special scenario of contrast stretching. It is the case in which the parameters are α = γ = 0. Clipping is more advantageous for reduction of noise in input signals of range [a, b].

Threshold of an image is selected by means of its histogram. Let us take the image shown in the following figure 1.2.

### Fig. 1.2

The figure 1.2 (b) consists of two peaks i.e., background and object. At the abscissa of histogram minimum (D1) the threshold is selected. This selected threshold (D1) can separate background and object to convert the image into its respective binary form. The thresholding transformations are shown in figure 1.3.

### Fig.1.3

** **

** ****Digital Negative:**

The digital negative of an image is achieved by reverse scaling of its grey levels to the transformation. They are much essential in displaying of medical images.

A digital negative transformation of an image is shown in figure 1.4.

### Fig.1.4

** ****Intensity Level Slicing:**

The images which consist of grey levels in between intensity at background and other objects require to reduce the intensity of the object. This process of changing intensity level is done with the help of intensity level slicing. They are expressed as

The histogram of input image and its respective intensity level slicing is shown in the figure 1.5.

### Fig.1.5

When an image is uniformly quantized then, the n^{th} most significant bit can be extracted and displayed.

Let, u = k_{1} 2^{B-1} + k_{2} 2^{B-2} +… + k_{B-1} 2 + k_{B}

Then, the output is expressed as