Edge Detection Method • The First Derivative - Gradient: The gradient method detects the edges by looking for the maximum and minimum in the first derivative of the image.
Deteksi Tepi Canny
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Yeni Herdiyeni Departemen Ilmu Komputer IPB
The Second Derivatives - Laplacian: The Laplacian method searches for zero crossings in the second derivative of the image to find edges. An edge has the one-dimensional shape of a ramp and calculating the derivative of the image can highlight its location.
Canny Edge Detector
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Canny Edge Detector
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Canny Edge Detector
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Canny Edge Detector
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Deteksi Tepi (edge)
The Canny edge detector
• Perubahan mencapai maksimum pada saat nilai turunannya pertamanya mencapai nilai maksimum atau nilai turunan kedua (2nd derivative) bernilai 0.
• original image (Lena) 5
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The Canny edge detector
The Canny edge detector
Gradient magnitude
thresholding
The Canny edge detector
Canny Edge Detection •
Steps 1. Doing Convolution :Apply derivative of Gaussian (to compute Gradient Magnitude) 2. Non-maximum suppression •
Thin multi-pixel wide “ridges” down to single pixel
3. Thresholding • •
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Low, high edge-strength thresholds Accept all edges over low threshold that are connected to edge over high threshold
Matlab: edge(I, ‘canny’)
thinning (non-maximum suppression)
Gradient
Detecting Edges in Image
• At each point convolve with Gx
1 1 1 1
Gy
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• Sobel Edge Detector
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• Sobel also can be applied to compute gradient • magnitude and orientation of the Gradient are computed as
M [i, j ] [i, j ]
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P[i, j ]
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Q[i, j ]
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2 0
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1 0
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d I dx d I dx
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• Avoid floating point arithmetic for fast computation
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d I dy
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Edges Threshold
Image I
tan 1 (Q[i, j ], P[i, j ]) Canny Edge Detector
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Example: Non-Maximum Suppression
Teknik Konvolusi
courtesy of G. Loy
Original image
Canny Edge Detector
Non-maxima suppressed
Gradient magnitude
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Edge “Smearing”
Non-Maxima Suppression • Thin edges by keeping large values of Gradient
Input
0 0 0 0
0 0 0 0
2 2 2 2
2 2 2 2
2 2 2 2
Result
0 0 0 0
6 8 8 6
6 8 8 6
0 0 0 0
-6 -8 -8 -6
from Forsyth & Ponce
Sobel filter example: Yields 2-pixel wide edge “band”
We want to localize the edge to within 1 pixel
– not always at the location of an edge – there are many thick edges 0 0 0 0 1 1 1 0 0 0 1 2 1 3 0 0 2 1 2 1 1 0 1 3 2 1 1 0 0 3 2 1 0 0 1 2 3 2 0 0 1 0 2 3 2 0 1 0 2
3 1 0 0 0 1 1
Canny Edge Detector
Edge “Streaking”
Non-Maxima Suppression (2)
• Can predict next pixel in edge orthogonal to gradient to make edge chain
• Thin the broad ridges in M[i,j] into ridges that are only one pixel wide • Find local maxima in M[i,j] by suppressing all values along the line of the Gradient that are not peak values of the ridge
false edges
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Canny Edge Detector
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– Can also just use 8-connectedness to define chains
• Streaking: Gaps in edge chain due to edge strength gap dipping below threshold
gaps courtesy of G. Loy
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Original image
Strong edges
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Example: Canny Edge Detection
Non-Maximum Suppression
gap is gone
Strong + connected weak edges
Original image
• Suppress the pixels in „Gradient Magnitude Image‟ which are not local maximum M x, y
x,y Strong edges only
S x, y 0
if
S x, y
S x,y
& S x, y S x ,y otherwise
x, y
Weak edges
x ,y
x ,y and x ,y are the neighbors of x,y in
S
along the direction normal to an edge courtesy of G. Loy
Gradient Orientation 0 0 0 0 1 1 1 3
• Reduce angle of Gradient θ[i,j] to one of the 4 sectors • Check the 3x3 region of each M[i,j] • If the value at the center is not greater than the 2 values along the gradient, then M[i,j] is set to 0
0 0 0 1 2 1 3 1 0 0 2 1 2 1 1 0 0 1 3 2 1 1 0 0 0 3 2 1 0 0 1 0 2 3 2 0 0 1 0 1
local maxima removed depends on condition
2 3 2 0 1 0 2 1 Canny Edge Detector
0 0 0 0 0 0 0
0 0 0 0 3 3 3
0 0 2 3 2 0 0
0 0 1 0 0 0 0
0 2 2 0 0 0 1
0 1 0 0 0 1 0
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0 3 0 0 0 0 2
3 0 0 0 0 1 0
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Thresholding • Reduce number of false edges by applying a threshold T false edges
– – – – –
• The suppressed magnitude image will contain many false edges caused by noise or fine texture Canny Edge Detector
Canny Edge Detector
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all values below T are changed to 0 selecting a good values for T is difficult some false edges will remain if T is too low some edges will disappear if T is too high some edges will disappear due to softening of the edge contrast by shadows Canny Edge Detector
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Double Thresholding
T2=2
• Apply two thresholds in the suppressed image – T2 = 2T2 – two images in the output – the image from T2 contains fewer edges but has gaps in the contours – the image from T1 has many false edges – combine the results from T1 and T2 – link the edges of T2 into contours until we reach a gap – link the edge from T2 with edge pixels from a T1 contour until a T2 edge is found again Canny Edge Detector
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Line Detection
0 0 0 0 0 0 0 3
0 0 0 0 2 0 3 0
0 0 0 0 2 1 3 0
0 0 2 0 2 0 0 0
gaps 0 0 3 0 0 0 0 0 filled 0 3 2 0 0 0 0 0 from T1
0 0 2 1 2 0 0 0
0 3 0 0 0 0 0 0
0 3 0 0 0 1 0 1
0 3 0 0 0 0 2 0
0 3 0 0 1 0 2 0
0 0 3 0 0 0 0 0 0 3 2 0 0 0 0 0
• A T2 contour has pixels along the green arrows • Linking: search in a 3x3 of each pixel and connect the pixel at the center with the one having greater value • Search in the direction of the edge (direction of Gradient) Canny Edge Detector
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Tugas
• Model of a line: two edges with opposite polarity in distance less than the size of the smoothing filter
• Buat program deteksi tepi Canny menggunakan matlab, tidak boleh menggunakan fungsi dari matlab : edge(I, ‘canny’)
– edge detection filters respond to step edges – they do not provide meaningful response to lines
• Sertakan penjelasan teori dan kode programnya pada laporan terpisah dengan kode program (*baca referensi yang diberikan) • Tugas dikumpulkan tgl 4 Desember 2009
• Apply nonmaxima suppression on the smoothed output – a line is the derivative of a step the derivative step of the Canny algorithm is not necessary Canny Edge Detector
T1=1
0 0 0 0 0 0 0 3
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Canny Edge Detector
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