Lowpass filter 19 19 19 HighPass Filter 1

Low-pass filter 1/9 1/9 1/9 画像平滑化

High-Pass Filter -1 -1 9 -1 -1 画像鮮鋭化

Edge Types u Different edge models: 屋根 凹形 傾斜 階段 棒 Roof edge Concave roof edge Ramp edge Step edge Bar edge

有名なGradient operators (a): Roberts’ cross operator (b): 3 x 3 Prewitt operator (c): Sobel operator (d) 4 x 4 Prewitt operator

Sobel operatorのエッジ検出例 -1 0 1 -1 -2 0 2 -0 0 0 -1 0 1 1 2 1

ノイズの影響（ Effects of noise ） u Consider a single row or column of the image • Plotting intensity as a function of position gives a signal １Ｄ u Where is the edge? 微分するとノイズを強調される

エッジ抽出前、まずフィルタhより平滑化 １Ｄ Gaussian u Where is the edge? u Look for peaks in

Laplacian of Gaussian u Consider １Ｄ Laplacian of Gaussian operator u Where is the edge? u Zero-crossings of bottom graph

2 D エッジ検出フィルタ Laplacian of Gaussian derivative of Gaussian ノイズを抑制しながらエッジを検出 u is the Laplacian operator:

Laplacian operatorのエッジ検出例 0 1 0 0 -1 0 1 1 -4 1 -1 4 -1 1 -8 1 0 0 -1 0 1 1 1

Canny Edge Detector Derivative of Gaussian

次のエッジ点を予測 (Forsyth & Ponce) Assume the marked point is an edge point. Then we construct the tangent to the edge curve (which is normal to the gradient at that point) and use this to predict the next points (here either r or s).

Canny Edge Detector Non-Maximum Suppressionの処理結 果 2値化処理 Step 3 Step 4

Canny Edge Detector ５． “Hysteresis Threshold”処理を行う u Scan the image from left to right, top-bottom. u If the gradient at a pixel is • above “High”, declare it an ‘edge pixel’ • below “Low”, declare it a “non-edge-pixel” ‘edge pixel’ High Gradient magnitude • “non-edge-pixel” ヒステリシス閾処理 low

Canny Edge Detector ５． “Hysteresis Threshold”処理を行う u If the gradient at a pixel is • between “low” and “high” • Consider its neighbors iteratively then declare it an “edge pixel” if it is connected to an ‘edge pixel’ directly or via pixels between “low” and “high”. ‘edge pixel’ High Gradient magnitude • “non-edge-pixel” ヒステリシス閾処理 low

Canny Edge Detector “Hysteresis Threshold”処理を行う u Connectedness x x x 4 connected 8 connected 6 connected

Canny Edge Detector Hysteresis Threshold処理結果例 Step 5

Effect of (Gaussian kernel size) original u The Canny with choice of • large • small Canny with depends on desired behavior detects large scale edges detects fine features

Canny Edge Detector gx(x, y) Gradient magnitude Non-maximum suppression Image gy(x, y) Gradient direction Hysteresis thresholding

Gaussian - image filter Gaussian delta function Laplacian of Gaussian