Spatial filtering using image processing
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(1) Spatial filtering is defined as operations performed on pixels within a neighborhood of an image using a mask or kernel. (2) Filters can be used to blur/smooth an image by reducing noise or sharpen an image by enhancing edges. (3) Common linear filtering methods include averaging, Gaussian, and derivative filters which are implemented using various mask patterns to modify pixels in the filtered image.
![SHARPENING FILTERS
(CONT’D)
• Note that the response of high-pass filtering might be
negative.
• Values must be re-mapped to [0, 255]
sharpened imagesoriginal image](https://image.slidesharecdn.com/spatialfiltering-140329140830-phpapp01/85/Spatial-filtering-using-image-processing-24-320.jpg)
Spatial filtering using image processing
- 1. SPATIAL FILTERING ANUJ ARORA B-TECH 2nd YEAR ELCTRICAL ENGG.
- 2. SPATIAL FILTERING (CONT’D)• Spatial filtering is defined by: (1) An operation that is performed on the pixels inside the Neighborhood (2)First we need to create a N*N matrix called a mask,kernel,filter(neighborhood). (3)The number inside the mask will help us control the kind of operation we are doing. (4)Different number allow us to blur,sharpen,find edges. output image
- 3. SPATIAL FILTERING NEIGHBORHOOD • Typically, the neighborhood is rectangular and its size is much smaller than that of f(x,y) - e.g., 3x3 or 5x5
- 4. SPATIAL FILTERING - OPERATION 1 1 1 1 ( , ) ( , ) ( , ) s t g x y w s t f x s y t Assume the origin of the mask is the center of the mask. / 2 / 2 / 2 / 2 ( , ) ( , ) ( , ) K K s K t K g x y w s t f x s y t for a K x K mask: for a 3 x 3 mask:
- 5. • A filtered image is generated as the center of the mask moves to every pixel in the input image. output image
- 6. STRANGE THINGS HAPPEN AT THE EDGES! Origin x y Image f (x, y) e e e e At the edges of an image we are missing pixels to form a neighbourhood e e e
- 7. HANDLING PIXELS CLOSE TO BOUNDARIES pad with zeroes or 0 0 0 ……………………….0 000……………………….0
- 8. LINEAR VS NON-LINEAR SPATIAL FILTERING METHODS • A filtering method is linear when the output is a weighted sum of the input pixels. • In this slide we only discuss about liner filtering. • Methods that do not satisfy the above property are called non-linear. • e.g.
- 9. LINEAR SPATIAL FILTERING METHODS • Two main linear spatial filtering methods: • Correlation • Convolution
- 10. CORRELATION • TO perform correlation ,we move w(x,y) in all possible locations so that at least one of its pixels overlaps a pixel in the in the original image f(x,y). / 2 / 2 / 2 / 2 ( , ) ( , ) ( , ) ( , ) ( , ) K K s K t K g x y w x y f x y w s t f x s y t
- 11. CONVOLUTION • 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! / 2 / 2 / 2 / 2 ( , ) ( , ) ( , ) ( , ) ( , ) K K s K t K g x y w x y f x y w s t f x s y t
- 13. HOW DO WE CHOOSE THE ELEMENTS OF A MASK? • Typically, by sampling certain functions. Gaussian 1st derivative of Gaussian 2nd derivative of Gaussian
- 14. FILTERS • Smoothing (i.e., low-pass filters) • Reduce noise and eliminate small details. • The elements of the mask must be positive. • Sum of mask elements is 1 (after normalization) Gaussian
- 15. FILTERS • Sharpening (i.e., high-pass filters) • Highlight fine detail or enhance detail that has been blurred. • The elements of the mask contain both positive and negative weights. • Sum of the mask weights is 0 (after normalization) 1st derivative of Gaussian 2nd derivative of Gaussian
- 16. SMOOTHING FILTERS: AVERAGING (LOW-PASS FILTERING)
- 17. SMOOTHING FILTERS: AVERAGING • Mask size determines the degree of smoothing and loss of detail. 3x3 5x5 7x7 15x15 25x25 original
- 18. SMOOTHING FILTERS: AVERAGING (CONT’D) 15 x 15 averaging image thresholding Example: extract, largest, brightest objects
- 19. SMOOTHING FILTERS: GAUSSIAN • The weights are samples of the Gaussian function mask size is a function of σ : σ = 1.4
- 20. SMOOTHING FILTERS: GAUSSIAN (CONT’D) • σ controls the amount of smoothing • As σ increases, more samples must be obtained to represent the Gaussian function accurately. σ = 3
- 23. SHARPENING FILTERS (HIGH PASS FILTERING) • Useful for emphasizing transitions in image intensity (e.g., edges).
- 24. SHARPENING FILTERS (CONT’D) • Note that the response of high-pass filtering might be negative. • Values must be re-mapped to [0, 255] sharpened imagesoriginal image
- 25. SHARPENING FILTERS: UNSHARP MASKING • Obtain a sharp image by subtracting a lowpass filtered (i.e., smoothed) image from the original image: - =
- 26. SHARPENING FILTERS: HIGH BOOST • Image sharpening emphasizes edges . • High boost filter: amplify input image, then subtract a lowpass image. • A is the number of image we taken for boosting. (A-1) + =
- 27. SHARPENING FILTERS: UNSHARP MASKING (CONT’D) • If A=1, we get a high pass filter • If A>1, part of the original image is added back to the high pass filtered image.
- 28. SHARPENING FILTERS: DERIVATIVES • Taking the derivative of an image results in sharpening the image. • The derivative of an image can be computed using the gradient.
- 29. SHARPENING FILTERS: DERIVATIVES (CONT’D) • The gradient is a vector which has magnitude and direction: | | | | f f x y or (approximation)
- 30. SHARPENING FILTERS: DERIVATIVES (CONT’D) • Magnitude: provides information about edge strength. • Direction: perpendicular to the direction of the edge.
- 31. SHARPENING FILTERS: GRADIENT COMPUTATION • Approximate gradient using finite differences: sensitive to horizontal edges sensitive to vertical edges Δx
- 32. SHARPENING FILTERS: GRADIENT COMPUTATION (CONT’D) • We can implement and using masks: • Example: approximate gradient at z5
- 33. SHARPENING FILTERS: GRADIENT COMPUTATION (CONT’D) • A different approximation of the gradient: •We can implement and using the following masks:
- 34. SHARPENING FILTERS: GRADIENT COMPUTATION (CONT’D) • Example: approximate gradient at z5
- 35. EXAMPLE f y f x
- 36. SHARPENING FILTERS: LAPLACIAN The Laplacian (2nd derivative) is defined as: (dot product) Approximate derivatives: