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CAP 5415 Computer Vision Fall 2004. Dr. Alper Yilmaz Univ. of Central Florida www.cs.ucf.edu/courses/cap5415/fall2004 Office: CSB 250. Recap (Edge Detection). Prewitt and Sobel edge detectors Compute derivatives In x and y directions Find gradient magnitude

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Top 5415 Computer Vision Fall 2004 Dr. Alper Yilmaz Univ. of Central Florida www.cs.ucf.edu/courses/cap5415/fall2004 Office: CSB 250 Alper Yilmaz, Fall 2004 UCF

Recap (Edge Detection) Prewitt and Sobel edge indicators Compute subsidiaries In x and y bearings Find slope greatness Threshold inclination size Difference amongst Prewitt and Sobel is the subordinate channels Alper Yilmaz, Fall 2004 UCF

Prewitt Edge Detector Prewitt\'s edges in x heading Prewitt\'s edges in y course Alper Yilmaz, Fall 2004 UCF

Sobel Edge Detector Sobel\'s edges in x course Sobel\'s edges in y heading Alper Yilmaz, Fall 2004 UCF

Edge Detection Continued Marr Hildreth Edge Detector Canny Edge Detector Alper Yilmaz, Fall 2004 UCF

Marr Hildreth Edge Detector Smooth picture by Gaussian channel S Apply Laplacian to S Used in mechanics, electromagnetics, wave hypothesis, quantum mechanics and Laplace condition Find zero intersections Scan along every line, record an edge point at the area of zero-intersection. Rehash above stride along every segment Alper Yilmaz, Fall 2004 UCF

Marr Hildreth Edge Detector Gaussian smoothing Find Laplacian is utilized for inclination (subordinate) is utilized for Laplacian Alper Yilmaz, Fall 2004 UCF

Marr Hildreth Edge Detector Deriving the Laplacian of Gaussian (LoG) Homework Alper Yilmaz, Fall 2004 UCF

LoG Filter Y X Alper Yilmaz, Fall 2004 UCF

Finding Zero Crossings Four instances of zero-intersections : {+,- } {+,0,- } {-,+} {-,0,+} Slope of zero-intersection {a, - b} is |a+b|. To check an edge figure incline of zero-intersection Apply an edge to slant Alper Yilmaz, Fall 2004 UCF

On the Separability of LoG Similar to distinguishableness of Gaussian channel Two-dimensional Gaussian can be isolated into 2 one-dimensional Gaussians n 2 augmentations 2 n increases Alper Yilmaz, Fall 2004 UCF

On the Separability of LoG Requires n 2 duplications Requires 4 n duplications Alper Yilmaz, Fall 2004 UCF

Seperability Gaussian Filtering Image + g ( x ) g ( y ) Laplacian of Gaussian Filtering g xx ( x ) g ( x ) Image + g yy ( y ) g ( y ) Alper Yilmaz, Fall 2004 UCF

Example Alper Yilmaz, Fall 2004 UCF

Example Alper Yilmaz, Fall 2004 UCF

Algorithm Compute LoG Use 2D channel Use 4 1D channels Find zero-intersections from every column Find slant of zero-intersections Apply limit to slant and stamp edges Alper Yilmaz, Fall 2004 UCF

Quality of an Edge Robust to clamor Localization Too numerous or too less reactions Alper Yilmaz, Fall 2004 UCF

Quality of an Edge True edge Poor vigor to commotion Poor restriction Too numerous reactions Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Criterion 1: Good Detection: The ideal indicator must minimize the likelihood of false positives and additionally false negatives. Basis 2: Good Localization: The edges identified must be as close as could be allowed to the genuine edges. Single Response Constraint: The finder must return one point just for every edge point. Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Steps Smooth picture with Gaussian channel Compute subordinate of sifted picture Find size and introduction of slope Apply "Non-greatest Suppression" Apply "Hysteresis Threshold" Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector First Two Steps Smoothing Derivative Homework Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Derivative of Gaussian Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector First Two Steps Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Third Step Gradient size and inclination bearing picture angle size Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Fourth Step Non most extreme concealment We wish to stamp focuses along the bend where the extent is greatest . We can do this by searching for a most extreme along a cut typical to the bend (non-greatest concealment). These focuses ought to frame a bend. There are then two algorithmic issues: and soon thereafter is the greatest, and where is the following one? Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Non-Maximum Suppression Suppress the pixels in | S| which are not nearby greatest x " and x "" are the neighbors of x along typical bearing to an edge Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Quantization of Normal Directions 2 3 1 0 Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Non-Maximum Suppression Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Hysteresis Thresholding If the slope at a pixel is above " High ", pronounce it a " edge pixel " underneath " Low ", announce it a " non-edge-pixel " amongst "low" and "high" Consider its neighbors iteratively then proclaim it an "edge pixel" on the off chance that it is associated with an \'edge pixel\' specifically or by means of pixels amongst "low" and "high". Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Hysteresis Thresholding Connectedness x 8 associated 6 associated 4 associated Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Hysteresis Thresholding High Gradient size low Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Hysteresis Thresholding Scan the picture from left to right, beat base. The inclination greatness at a pixel is over a high edge proclaim that as an edge point Then recursively consider the neighbors of this pixel. On the off chance that the slope greatness is over the low edge pronounce that as an edge pixel. Alper Yilmaz, Fall 2004 UCF

Canny Edge Detector Hysteresis Thresholding Alper Yilmaz, Fall 2004 UCF

Homework Derive Laplacian of Gaussian Drive angle of 2D Gaussian Show that slope size is revolution invariant. Due date 27 September 2004 (Monday) Alper Yilmaz, Fall 2004 UCF

Programming Assignment 1 Implement Marr Hildreth Edge Detector Implement Canny Edge Detector Deliverables Short report, issues, comes about, program code, and so on. Regulated yields of pictures Program code Program ought to request a PGM picture from client Ask for the edge esteem, sigma of Gaussian Write out or show the picture Due Date 18 October 2004 Alper Yilmaz, Fall 2004 UCF

Suggested Reading Chapter 4, Emanuele Trucco, Alessandro Verri, "Introductory Techniques for 3-D Computer Vision" Chapter 2, Mubarak Shah, "Essentials of Computer Vision" Alper Yilmaz, Fall 2004 UCF