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Overview of Image Filtering Techniques: Spatial and Frequency Domains

This document provides an overview of various image filtering techniques, focusing on spatial and frequency domains. It covers the application of convolution filters, including mean filters, and explores edge detection methods. The significance of preserving important image properties while filtering is emphasized, particularly in object recognition and image segmentation. Techniques such as the Canny algorithm and non-maximum suppression are discussed for effective edge identification. Understanding these methods is crucial for advancing in areas such as computer vision and image processing.

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Overview of Image Filtering Techniques: Spatial and Frequency Domains

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  1. Multimedia Systems &Interfaces Karrie G. KarahaliosSpring 2007

  2. Overview • Filters • Edge Detection • Non Photo-realistic Rendering

  3. Image Filtering Overview http://www.courses.fas.harvard.edu/~ext12559/lectures/2005-11-29-Filtering.pdfby Chris Wren

  4. Spatial domain refers to planar region of intensity values Frequency domain think of each color plane as a sinusoidal function of changing intensity values apply DFT to subsets of pixels for compression Spatial and Frequency Domains

  5. Convolution Filters • Filter an image by replacing each pixel in the source with a weighted sum of its neighbors • Define the filter using a convolution mask, also referred to as a kernel • non-zero values in small neighborhood, typically centered around a central pixel • generally have odd number of rows/columns

  6. 20 12 14 23 45 15 19 33 55 34 81 22 8 64 49 95 Mean Filter Subset of image Convolution filter

  7. Mean Filter 20 12 14 23 45 15 19 33 55 34 81 22 8 64 49 95 Subset of image Convolution filter

  8. Common 3x3 Filters • Low/High pass filter • Blur operator • H/V Edge detector

  9. Edge Detection • Identify areas of strong intensity contrast • filter unecessary data; preserve important properties • Fundamental technique • object recognition, orientation • image segmentation • e.g., use gestures as input • identify shapes, match to templates, invoke commands

  10. Identify high slope in first derivative Pixel is on an edge if value of the gradient exceeds a threshold Characteristics of Edges http://www.pages.drexel.edu/~weg22/edge.html

  11. Basic Method • Step 1: filter noise using mean filter • Step 2: compute spatial gradient • Step 3: mark points > threshold as edges

  12. Compute partials Compute gradient Compute length Divide by length Compute Spatial Gradient

  13. Compute Partials P3 – P1 + 2*P6 – 2*P4+ P9 – P7 P7 – P1 + 2*P8 – 2*P2+ P9 – P3

  14. Given gradient at each pixel and threshold mark pixels where gradient > threshold as edges Canny algorithm extends basic method Mark Edge Points http://www.cee.hw.ac.uk/hipr/html/sobel.html

  15. Compute direction of maximum change Compute Edge Direction

  16. For each pixel If G(x,y) < either neighbor along Normal direction, then set G(x,y) = 0 Suppress local change when larger change nearby helps reduce false positives Apply Non-Max Suppression

  17. Hysteresis • Oscillation of gradient at threshold • Use two thresholds • T1 and T2 with T2 > T1 • Mark pixel as edge pixel if G(x,y) > T2 • keep pixels along normal direction withG(x,y) > T1

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