Image Processing Edge Detection Image Processing Edges in

Image Processing Edge Detection

Image Processing Edges in a picture 2

Image Processing Edge Localization-Zero Crossing Where exactly is the edge ? f Zero crossing of f’’ ’’f 3 Problem: f’’ is very noisy Smooth first !

Image Processing Real edges in pictures f 4 f’ f’’

Image Processing Zero Crossing: Smoothing Example 5

Image Processing The gradient The vector of derivatives The gradient points in the direction of most rapid change in intensity Edge Size Edge Direction 6

Image Processing The gradient Original 7 Gradient

Image Processing Gradient vs. Derivatives Ix = Ix 2 + Iy 2 = Iy =

Image Processing Canny Edge Detection Criteria for edge detection: • Discriminate edges from non-edges (noise, texture etc. ) • Localization • One response per edge Assumption: edges are elongated and continuous 9

Image Processing Canny Edge Detection Approach: • Smooth image to eliminate noise • Find highlights of the image gradient • Connect highlights to lines (Hysteresis) 10

Image Processing Canny Edge Detection 1. Smooth the image by a Gaussian - Parameter: σ (standard deviation) 2. Compute the image derivatives Gx, Gy - 11 Use simple derivative kernels (e. g. Sobel)

Image Processing Canny Edge Detection 3. Compute magnitude and direction: , 4. Quantize the gradient directions: 12

Image Processing Canny Edge Detection 5. Non-maximum Suppressing: - For each pixel (x, y) trace along the gradient direction. - If G(x, y) is not a local maximum, set its value to zero. 13

Image Processing Canny Edge Detection 6. Hysteresis - Define two thresholds T 1 > T 2 - Any pixel with value greater than T 1 is presumed to be an edge pixel - Any pixels that are (1) connected to an edge pixel and (2) has a value greater than T 2 are also selected as edge values 14

Original 15 Example Image Processing Canny