Spatial filtering
- 1. T.Deepika Msc(IT) Department of CS and IT Nadar saraswathi college of arts and science Theni
- 2. Spatial Filtering (cont’d) The word “filtering” comes from the frequency domain where “filters” are classified as: Low-pass (i.e., preserve low frequencies) High-pass (i.e., preserve high frequencies) Band-pass (i.e., preserve frequencies within a band) Band-reject (i.e., reject frequencies within a band)
- 3. Spatial Filtering (cont’d) Need to define: (1) a neighborhood (or mask) (2) an operation output image
- 4. Spatial Filtering – Neighborhood (or Mask) • Typically, the neighborhood is rectangular and its size is much smaller than that of f(x,y) - e.g., 3x3 or 5x5
- 5. Filter Categories We will focus on two types of filters: Smoothing (low-pass) filters Sharpening (high-pass) filters
- 6. Smoothing Filters (low-pass) Useful for reducing noise and eliminating small details. The elements of the mask must be positive. Mask elements sum to 1 (assuming normalization).
- 7. Smoothing filters – Example smoothed imageinput image
- 8. Sharpening Filters (high-pass) Useful for highlighting fine details. The elements of the mask contain both positive and negative weights. Mask elements sum to 0.
- 9. Sharpening Filters - Example Useful for highlighting fine details. e.g., emphasize edges
- 10. Sharpening Filters - Example sharpened imageinput image (for better visualization, the original image has been added to the sharpened image)
- 11. Common Smoothing Filters Averaging Gaussian Median filtering (non-linear)
- 13. Smoothing Filters: Averaging (cont’d) Mask size determines degree of smoothing (i.e., loss of detail). 3x3 5x5 7x7 15x15 25x25 original
- 14. Smoothing Filters: Averaging (cont’d) 15 x 15 averaging image thresholding Example: extract largest, brightest objects
- 15. Smoothing filters: Gaussian The weights are samples of a 2D Gaussian function:
- 16. Smoothing filters: Gaussian (cont’d) Mask size depends on σ
- 17. Smoothing filters: Gaussian (cont’d) • σ controls the amount of smoothing σ = 3 σ = 1.4
- 19. Averaging vs Gaussian Smoothing Averaging Gaussian
- 20. Smoothing Filters: Median Filtering (non-linear) Very effective for removing “salt and pepper” noise (i.e., random occurrences of black and white pixels). averaging median filtering
- 21. Smoothing Filters: Median Filtering (cont’d) Replace each pixel by the median in a neighborhood around the pixel. The size of the neighborhood controls the amount of smoothing.
- 22. Common Sharpening Filters Unsharp masking High Boost filter Gradient (1st derivative) Laplacian (2nd derivative)
- 23. Sharpening Filters: Unsharp Masking Obtain a sharp image by subtracting a lowpass filtered (i.e., smoothed) image from the original image: - = (with contrast enhancement)
- 24. Sharpening Filters: High Boost Image sharpening emphasizes edges but details are lost. Idea: amplify input image, then subtract a lowpass image. (A-1) + =
- 25. Sharpening Filters: High Boost (cont’d) If A=1, the result is unsharp masking. If A>1, part of the original image is added back to the high pass filtered image. One way to implement high boost filtering is using the masks below High boost
- 26. Sharpening Filters: High Boost (cont’d) A=1.4 A=1.9
- 27. Sharpening Filters: Derivatives The derivative of an image results in a sharpened image. Image derivatives can be computed using the gradient:
- 28. Gradient The gradient is a vector which has magnitude and direction: | | | | f f x y or (approximation)
- 29. Gradient (cont’d) Gradient magnitude: provides information about edge strength. Gradient direction: perpendicular to the direction of the edge.
- 30. Gradient Computation Approximate partial derivatives using finite differences: Δx
- 31. Gradient Computation (cont’d) sensitive to vertical edges sensitive to horizontal edges f(x3,y3)-f(x3,y2) y3-y2 y2=y3+Dy, y3=y, x3=x, Dy=1
- 33. Implement Gradient Using Masks We can implement and using masks: (x+1/2,y) (x,y+1/2) * * good approximation at (x+1/2,y) good approximation at (x,y+1/2)
- 34. Implement Gradient Using Masks (cont’d) A different approximation of the gradient: • We can implement and using the following masks: * (x+1/2,y+1/2) good approximation
- 35. Implement Gradient Using Masks (cont’d) • Other approximations Sobel Prewitt
- 36. Example: Gradient Magnitude Image f y f x Gradient Magnitude (isotropic)
- 37. Laplacian The Laplacian (2nd derivative) is defined as: (dot product) Approximate 2nd derivatives:
- 38. Laplacian (cont’d) Laplacian Mask Edges can be found by detecting the zero- crossings input image output image 5 5 5 5 5 -5 -5-10 -10 -1010
- 39. Example: Laplacian vs Gradient Laplacian Sobel • Laplacian localizes edges better (zero-crossings). • Higher order derivatives more sensitive to noise. • Laplacian is less computational expensive. • Laplacian can provide edge magnitude information but no information about edge direction.
- 40. Thankyou