1 / 5

Effective Computation of Linear Filters

Effective Computation of Linear Filters. The following properties are used to shorten the computation time f  g = g  f, f  (g  h) = (f  g)  h, f  (g + h) = f  g + f  h Example: Edge detection - Sobel Example: Edge detection - Laplace. Effective Computation of Linear Filters.

chaeli
Télécharger la présentation

Effective Computation of Linear Filters

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Effective Computation of Linear Filters The following properties are used to shorten the computation time f  g = g  f, f  (g  h) = (f  g)  h, f  (g + h) = f  g + f  h Example: Edge detection - Sobel Example: Edge detection - Laplace

  2. Effective Computation of Linear Filters Example: Sharpening filter Example: Smoothing - Gaussian

  3. Effective Computation of Linear Filters Example: Smoothing combined with edge detection (LoG)

  4. Linear Filters in Frequency Domain • Each linear filter in spatial domain (performed as convolution) has a corresponding filter in frequency domain (performed as multiplication) and vice versa. • Example: Low-pass filters • Ideal low-pass filter 1D: rectangle in frequency, k · sinc ax (sin ax / ax) in spatial domain 2D: rectangular box in frequency, k · sinc ax · sinc by in spatial domain 2D: cylinder in frequency, k · J1(sqrt(x2+y2)) in spatial domain • Non-weighted averaging 1D: rectangle in spatial, k · sinc awx in frequency domain 2D: rectangular box in spatial, k · sinc awx · sinc bwy in frequency domain 2D: cylinder in spatial, k · J1(sqrt(wx2+wy2)) in frequency domain • Weighted Gaussian averaging 1D: a · exp (-b · x2) in spatial, c · exp (-d · wx2) in frequency domain 2D: a · exp (-b · (x2+y2)) in spatial, c · exp (-d · (wx2+wy2)) in frequency

  5. Linear Filters in Frequency Domain • Example: High-pass filters • Sobel 1D: 1st derivative in spatial, multiplication by -(iwx) in frequency domain 2D: 1st derivative in spatial, multiplication by -(iwd) in frequency domain • Laplace 1D: 2nd derivative in spatial, multiplication by -(wx2) in frequency 2D: 2nd derivative in spatial, multiplication by -(wx2+wy2) in frequency

More Related