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SPATIAL FILTER

Spatial domain filtering involves modifying an image by applying a filter or kernel to pixels within a neighborhood region. There are two main types of spatial filters - smoothing/low-pass filters which blur an image, and sharpening/high-pass filters which enhance edges and details. Smoothing filters replace each pixel value with the average of neighboring pixels, reducing noise. Sharpening filters use derivatives of Gaussian kernels to highlight areas of rapid intensity change, increasing contrast along edges. The effects of filtering depend on the size and shape of the kernel, with larger kernels producing more blurring or sharpening.

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SPATIAL DOMAIN FILTERING 1
2 What are images? •2D image f(x,y). •x and y are spatial co-ordinates. •Amplitude of f at any (x,y) is called intensity or gray level of the image.
3 •Continuous image to discrete image
4 •Result is a matrix of real numbers of size M*N. •Each element in this array is called a pixel.
5 OBJECTIVE The principal objective of enhancement is to process an images so that the result is more suitable than the original image for a SPECIFIC application. Category of image enhancement • Spatial domain • Frequency domain
6 WHAT IS??? Spatial filtering (neighborhood processing) is defined by: A neighborhood An operation that is performed on the pixels inside the neighborhood
7 •Typically, the neighborhood is rectangular and its size is much smaller than that of f(x , y) e.g., 3x3 or 5x5 Neighborhood
8 Neighborhood •Coefficients of neighborhood is also called as filter, mask, filter mask, kernel, template or window. •Image size is M*N and filter mask size m*n. •m=2a+1 and n=2b+1. •a and b are non-negative integers.
9 Assume the origin of the mask is the center of the mask. for a 3 x 3 mask, 1 1 1 1 ( , ) ( , ) ( , ) s t g x y w s t f x s y t      
10 LINEAR V/S NON-LINEAR A filtering method is linear when the output is a weighted sum of the input pixels. Methods that do not satisfy the above property are called non-linear.
11 Linear Spatial Filtering Methods Two main linear spatial filtering methods: Correlation Convolution
12 Correlation: •Process of passing the mask w by the image array f. Convolution •Often used in applications where we need to measure the similarity between images or parts of images (e.g., pattern matching). •Similar to correlation except that the mask is first flipped both horizontally and vertically. Note: if w(x,y) is symmetric, that is w(x,y)=w(-x,-y), then convolution is equivalent to correlation!
13 TOOL BOX IMPLEMENTATION g = imfilter(f, w, filtering_mode, boundary_options, size_options) Common syntax g = imfilter(f, w, ‘replicate’)
14 How do we choose the elements of a mask? Typically, by sampling certain functions. Gaussian 1st derivative of Gaussian 2nd derivative of Gaussian Gaussian 1st derivative of Gaussian 2nd derivative of Gaussian
15 Spatial filters : Smoothing ( low pass) Use: for blurring and noise reduction. How it works? The value of every pixel is replaced by the average of the gray levels in the neighborhood. Type of smoothing filters: 1. Standard average 2. Weighted average. 3. Median filter Gaussian
16 1 1 1 1 1 1 1 1 1  9 1 1 2 1 2 4 2 1 2 1  16 1 Standard average Weighted average 13090120110 200989491 100999190 90859682 Standard averaging filter: (110 +120+90+91+94+98+90+91+99)/9 =883/9 = 98.1 Weighted averaging filter: (110 +2 x 120+90+2 x 91+4 x 94+2 x 98+90+2 x 91+99)/16 =97.81
17 Mask size determines the degree of smoothing and loss of detail. original 3x3 5x5 7x7 15x15 25x25
18 13090120110 200989491 100999590 90859682 95 Steps: 1. Sort the pixels in ascending order: 90,90, 91, 94, 95, 98, 99, 110, 120 2. replace the original pixel value by the median : 95 Median filter(non linear)
19 Very effective for removing “salt and pepper” noise (i.e., random occurrences of black and white pixels). Averaging Median filtering
20 Spatial filters : Sharpening ( high pass) Use: for highlighting fine detail or enhancing detail that has been blurred. 1st derivative of Gaussian 1st derivative of Gaussian 2nd derivative of Gaussian Type of sharpening filters:
21 155153156157153 159156158156159 160156154158155 160160158157154 155156157157157 •154*4 – 158- 156-158-158 = -14 •So the value after filter = -14 •We call the resultant image: sharpened image. •Filtered image=original +sharpened image •The value in the filter image=154-14 =130 SHARPENING – 1ST DERIVATIVE •Apply the following laplace on the highlighted pixel
22 155153156157153 159156158156159 160156154158155 160160158157154 155156157157157 •Apply the following laplace 2nd derivative on the highlighted pixel •154*4 – 158- 156-158-158 = -14 •Apply laplace to all pixels •Then apply it again to our pixel:-14*4 – 10 -10 – (-6) -4 =-74 •So the value after 2nd derivative filter =-74 •The value of pixel in the filter image=154-74 = 80 SHARPENING – 2nd DERIVATIVE
23 Original Image Laplace Sharpened Image Laplace Filtered Image
24 Thank you