1. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.1 Some of Basic Spatial Filtering
2.1.1 Spacial average filter
A spatial average filter in which all coefficients are equal is sometimes called a box filter. If not, it yields a so-called weighted average filter, indicating that pixels are multiplied by different coefficients, thus giving more imporatance (weight) to some pixels at the expense of others.

2. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.1.2 Median filter
Median filters are partically effective in the presence of impulse noise, also called salt-pepper noise because its apperance as white and black dots superimposed on images.
2.1.3 Max filter
Max filters are also called 100th percentile filters that are useful in finding the brightest points in an image. They can reduce pepper noise.

3. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.1.4 Min filter
Min filters are the 0th percentile filters that are useful for finding the lowest point in an image. They can reduce salt noise.
2.1.5 Mid-point filter
Mid-point filters are fit for noise like Gaussian and uniform noise.

4. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.1.6 Adaptive median filter
The adaptive median filtering algorithm works in two levels: Level A and Level B.
Level A:
If A1>0 & A2<0
go to level B
Else
Increase the window size

5. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
If window size >
Output
Else
Repeat Level A
Level B:

6. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
If B1>0 & B2<0
Output
Else
Output
= minimum gray level value in
= maximum gray level value in
= median gray level value in
= gray level coordinates (x,y)
= maximum allowed size of

7. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.2 Some of Basic Frequency Filtering
Filtering in the frequency domain is straightforward. It consists of the following steps:
Multiply the input image by to center the transform;
Compute F(u,v), the DFT of the image from (1);
Multiply F(u,v) by a filter function H(u,v);
Compute the inverse DFT of the result in (3);
Obtain the real part of the result in (4);
Multiply the result in (5) by

8. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.2.1 Ideal filter
Ideal Lowpass Filter:
Ideal Highpass Filter:

9. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.2.2 Butterworth filter
Butterworth Lowpass Filter:
Butterworth Highpass Filter:

10. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.2.3 Gaussian filter
Gaussian Lowpass Filter:
Gaussian Highpass Filter:

11. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.3 Edge detection
Edge detection is a collection of very important image pre-processing methods used to locate changes in the intensity function; edges are pixels where this function (brightness) changes abruptly. An edge is a property attached to an individual pixel and is calculated from the image function behavior in a neighborhood of that pixel. Edges are often used in image analysis for finding region boundaries.

12. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.3.1 Roberts operator
The primary disadvantage of the Roberts operator is its high sensitivity to noise, because very few pixels are used to approximate the gradient.

13. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.3.2 Sobel operator
The Sobel operator approximates the first deritative. The gradient is estimated in eight possible directions, and the convolution result of greatest magnitude indicates the gradient direction. It is often used as a simple detector of horizontality and verticality of edges

14. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.3.3 Laplace operator
The disadvantage of Laplace operator is to respond doubly to some edges in the image.

15. Image Pre-Processing in the Spatial and Frequent Domain
Chapter 2
Image Pre-Processing in the
Spatial and Frequent Domain
2.3.4 LoG operator
LoG is the combination of a Gaussian function and a Laplace operator, the Gaussian function to smooth images and the Laplace operator to provide images with zero crossings used to establish the locations of edges.