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lec10

# lec10 - Announcements Assignment 2 due Tuesday May 3 Edge...

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1 CSE152, Spr 2011 Intro Computer Vision Edge Detection, Corner Detection Lines Introduction to Computer Vision CSE 152 Lecture 10 CSE152, Spr 2011 Intro Computer Vision Announcements Assignment 2 due Tuesday, May 3. Midterm: Thursday, May 5. CSE152, Spr 2011 Intro Computer Vision Last Lecture CSE152, Spr 2011 Intro Computer Vision Edges 1. Object boundaries 2. Surface normal discontinuities 3. Reflectance (albedo) discontinuities 4. Lighting discontinuities (shadow boundaries) CSE152, Spr 2011 Intro Computer Vision Edge is Where Change Occurs: 1-D Change is measured by derivative in 1D Smoothed Edge First Derivative Second Derivative Ideal Edge • Biggest change, derivative has maximum magnitude • Or 2nd derivative is zero. CSE152, Spr 2011 Intro Computer Vision Numerical Derivatives f(x ) x X 0 X 0 +h X 0 -h Take Taylor series expansion of f(x) about x 0 f(x) = f(x 0 )+f’(x 0 )(x-x 0 ) + ½ f’’(x 0 )(x-x 0 ) 2 + … Consider Samples taken at increments of h and first two terms, we have f(x 0 +h) = f(x 0 )+f’(x 0 )h+ ½ f’’(x 0 )h 2 f(x 0 -h) = f(x 0 )-f’(x 0 )h+ ½ f’’(x 0 )h 2 Subtracting and adding f(x 0 +h) and f(x 0 -h) respectively yields Convolve with First Derivative: [-1/2h 0 1/2h] Second Derivative: [-1/h 2 2/h 2 -1/h 2 ] Can often drop h or h 2 in denominator Yielding [-1 0 1] and [-1 2 -1]

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2 CSE152, Spr 2011 Intro Computer Vision Implementing 1-D Edge Detection 1. Filter out noise: convolve with Gaussian 2. Take a derivative: convolve with [-1 0 1] We can combine 1 and 2. 3. Find the peak of the magnitude of the convolved image: Two issues: Should be a local maximum. Should be sufficiently high. CSE152, Spr 2011 Intro Computer Vision Canny Edge Detector 1. Smooth image by filtering with a Gaussian 2. Compute gradient at each point in the image. 3. At each point in the image, compute the direction of the gradient and the magnitude of the gradient. 4. Perform non-maximal suppression to identify candidate edgels. 5. Trace edge chains using hysteresis tresholding. CSE152, Spr 2011 Intro Computer Vision Gradients: x y Is this dI/dx or dI/dy? I = I / x I / y Ρਟ Σਿ ΢ਯ Τ੏ Φ੯ Υ੟ CSE152, Spr 2011 Intro Computer Vision We wish to mark points along the curve where the magnitude is biggest.
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