kuliah 10 deteksi tepi canny edit print

1Deteksi Tepi Canny

Yeni Herdiyeni

Departemen Ilmu Komputer IPB

Canny Edge Detector 1

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.

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 3 Canny Edge Detector 4

Deteksi Tepi (edge)

Perubahan mencapai maksimum pada

saat nilai turunannya pertamanya

mencapai nilai maksimum atau nilai

turunan kedua (2nd derivative) bernilai

0.

5

The Canny edge detector

original image (Lena)

2The Canny edge detector

Gradient magnitude


thresholding


thinning

(non-maximum suppression)

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

Low, high edge-strength thresholds

Accept all edges over low threshold that are connected to edge

over high threshold

Matlab: edge(I, canny)


Gradient

At each point convolve with

Sobel also can be applied to compute gradient

magnitude and orientation of the Gradient are computed as

Avoid floating point arithmetic for fast computation

11

11xG

11

11yG

22 ],[],[],[ jiQjiPjiM

]),[],,[(tan],[ 1 jiPjiQji

Sobel Edge Detector

Detecting Edges in Image

Image I

101

202

101

121

000

121

*

*

Idx

d

Idy

d

22

Idy

dI

dx

d

ThresholdEdges

3Teknik Konvolusi


Example:

Non-Maximum Suppression

courtesy of G. Loy

Original image Gradient magnitudeNon-maxima suppressed

Edge Smearing

from Forsyth & Ponce

0

0

0

0

2

2

2

2

20

20

20

20

2

2

2

2

Sobel filter example: Yields2-pixel wide edge band

We want to localize the edge to within 1 pixel

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8

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00

00

00

00

-8

-6

-6

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Input

Result


Non-Maxima Suppression

Thin edges by keeping large values of Gradient

not always at the location of an edge

there are many thick edges

12010232

10100232

01001230

00112310

01121200

13121000

31110000


Non-Maxima Suppression (2)

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

12010232

10100232

31001230

00112310

01121200

13121003

31110000

gaps

false

edges

Edge Streaking

Can predict next pixel in edge orthogonal to gradient to make edge chain Can also just use 8-connectedness to define chains

Streaking: Gaps in edge chain due to edge strength dipping below threshold

courtesy of G. Loy

Original image Strong edges

gap

4Example: Canny Edge Detection

courtesy of G. Loy

gap is gone

Originalimage

Strongedges

only

Strong +connectedweak edges

Weakedges

Non-Maximum Suppression

Suppress the pixels in Gradient Magnitude

Image which are not local maximum

edgean tonormaldirection thealong

in of neighbors theare and Sx,yy,xy,x

otherwise0

,,&

,, if,

, yxSyxS

yxSyxSyxS

yxMyx ,

yx,

yx ,


Gradient Orientation

Reduce angle of Gradient [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


local

maxima

removed

depends

on condition

12010232

10100232

01001230

00112310

01121200

13121000

31110000


The suppressed magnitude image will contain many

false edges caused by noise or fine texture

02010030

10100030

00000230

00000300

00021200

03120000

30000000

false edges


Thresholding

Reduce number of false edges by applying a

threshold T

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

5Canny Edge Detector 25

Double Thresholding

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


T2=2 T1=1

02000030

00000030

00000230

00000300

00020200

03020000

30000000

02010030

10100030

00000230

00000300

00021200

03120000

30000000

gaps

filled

from

T1

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)


Line Detection

Model of a line: two edges with opposite polarity in distance less than the size of the smoothing filter

edge detection filters respond to step edges

they do not provide meaningful response to lines

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

Tugas

Buat program deteksi tepi Canny

menggunakan matlab, tidak boleh

menggunakan fungsi dari matlab : edge(I,

canny)

Sertakan penjelasan teori dan kode

programnya pada laporan terpisah dengan

kode program (*baca referensi yang diberikan)

Tugas dikumpulkan tgl 4 Desember 2009


kuliah 10 deteksi tepi canny edit print

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