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Spatial filtering using image processing

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spatial filtering in image processing (explanation cocept of …

spatial filtering in image processing (explanation cocept of
mask),lapace filtering

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  • 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
  • 12. CORRELATION AND CONVOLUTION Correlation: Convolution:
  • 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
  • 21. SMOOTHING FILTERS: GAUSSIAN (CONT’D)
  • 22. AVERAGING VS GAUSSIAN SMOOTHING Averaging Gaussian
  • 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: