Spatial Domain Filtering.pdf
- 1. By Mr. S. M. Karve
- 3. Introduction To Filters FILTER: Filter is a process that removes some unwanted components or small details in a image. TYPES OF FILTERS : O SPATIAL DOMAIN FILTERS O FREQUENCY DOMAIN FILTERS
- 4. SPATIAL FILTER The spatial filter is just moving the filter mask from point to point in an image. The filter mask may be 3x3 mask or 5x5 mask or to be 7x7 mask. Example 3x3 mask in a 5x5 image
- 5. Generating Spatial Filter mask O Generate mxn linear Spatial filter requires mn mask coefficients.These are selected based on the type of filter. so it computes the sum of products Example ,the average of 3x3 neighborhood on (x,y) is calculated by using the formula O If we take Gaussian function of 2 values the basic formula as follows O ‘σ’ is standard deviation , x and y are integers.
- 6. The Approaches of Spatial Filtering Spatial filter consist of two steps O A neighborhood (small rectangle) O A predefined operation performed on image pixels. Filtering creates a new pixel value replaced by old pixel value.
- 7. 3*3 mask and the image section
- 8. Types Of Spatial Filters There are two types of filter, 1.Linear Spatial Filter 2.Non Linear Spatial Filter O Each pixel in an image can be replaced with constant value then it is called as linear spatial filter otherwise it is called as non-linear.
- 9. Spatial Filter Expression O For m x n size of image, we assume m=2a+1 & n=2b+1 where a,b are positive integers. so the linear spatial filter of image MxN with filter size mxn is by following expression.
- 10. Spatial Correlation & Convolution O Correlation is moving the filter over the image find the sum of products in each location. O Convolution process is same as correlation but the filter is first rotate by 180 degree.
- 11. Smoothing Spatial Filters OSmoothing filters are used for blurring and for noise reduction. OBlurring is used as preprocessing such as removal of small details from image. ONoise reduction is blurring with linear or non linear filter.
- 12. IMAGE SMOOTHING
- 13. TYPES OF SMOOTHING SPATIAL FILTER SMOOTHING FILTERS NON-LINEAR FILTERS LINEAR FILTERS MINMAX FILTERS MEDIAN FILTERS AVERAGING FILTERS
- 14. Smoothing With Linear Filter AVERAGING FILTER: O The output of linear spatial filter computes the average of pixels is called averaging filter or low pass filter. O The major usage of average filter is reduction of irrelevant detail in an image. 1 1 1 1 1 1 1 1 2 1 2 4 2 1 2 1 1/9 x 1/16 x 1 1
- 15. Cont,. O Standard average of pixels calculated as follows O At the end of filtering the entire image is divided by 9. O So mxn is equal to 1/mn. Thus the coefficients pixels are equal, so the filter is called box filter.
- 16. Non- Linear Spatial Filter(order Statistic Filter) MEDIAN FILTER: O This filter ordering the pixels by replacing the value of the center pixel with the value of rank list. The best know filter in this category is median filter. This is best for noise reduction. O This median filter is effective for impulse noise called as salt & pepper noise.
- 17. MAX FILTER: OThe max filter also used for spatial filtering.This is used for finding the brightest points of an image. OExpression of max filter is R=max {Zk| k= 1,2,3,…….9}
- 18. MIN FILTER: The min filter also used it is opposite of max that is find the dull points of an image. Expression of max filter is R=min{Zk| k= 1,2,3,…….9}
- 19. Sharpening Spatial Filters O The sharpening spatial is to highlight the transactions in intensity . O There are many applications, such as electronic priming, medical images, military systems are used this sharpening technique.
- 21. Foundation Sharpening filters that are based on two derivatives. 1.First derivatives. 2.Second derivatives. First derivative : O Must be zero for area of constant intensity. O Must be nonzero of intensity step or map. O Must be nonzero along ramp. (σ f/σ x) = f (x +1) – f (x).
- 22. Second derivative O Must be zero in constant areas. O Must be nonzero at one end and other end of intensity ramp. O Must be zero along ramps.
- 23. Image Sharpening(the Laplacian) O This approach uses the second order derivative for construct the filter mask. O The laplacian for the image function f(x,y) of two variable is, O The X direction, O For Y direction,
- 24. By concluding the above three equations, Taking the derivative of an image results in sharpening of an image. The derivative of an image cam be computing by using gradient