2. Agenda
O What is an edge.
O What is edge detection
O Usage of edge detection.
O Type of edges.
O Background.
O Edge detection methods
O Gradient based methods.
O Zero Crossing based.
O Proposed Algorithm.
3. Edges
O Abrupt change in the intensity of pixels.
O Discontinuity in image brightness or
contrast.
O Usually edges occur on the boundary of
two regions .
4. Edge Detection
O Process of identifying edges in
an image to be used as a
fundamental asset in image
analysis.
O Locating areas with strong
intensity contrasts.
5. Edge Detection Usage
O Reduce unnecessary information in the image
while preserving the structure of the image.
O Extract important features of an image
O Corners
O Lines
O Curves
O Recognize objects, boundaries, segmentation.
O Part of computer vision and recognition.
7. Edge Detection Background
O Classical Gradient Edge detection.
O Sobel, Prewitt, Kirsch and Robinson.
O Gaussian based filters
O Marr and Hildreth.
O Canny
O Shunck, Witkin and Bergholm.
O Wavelets used for different scales.
O Heric and Zazula and Shih and Tseng.
O Fuzzy Logic and Neural Networks.
8. Edge Detection Steps
O Smoothing: Noise Reduction.
O Enhancement: Edge sharpening.
O Detection: Which to discard and which to
maintain.
O Thresholding.
O Localization: determine the exact location
of an edge.
O Edge thinning and linking are usually
required in this step.
9. Methods of Edge Detection
O Gradient methods (First Order Derivative)
O local maxima and minima using first
derivative in an image.
O Compute Gradient magnitude horizontally
and vertically.
O Zero-crossing methods (Second Order
Derivative)
O locate zeros in the second derivative of an
image.
O Laplacian of an Image.
10. Gradient based Edge
Detection
O Best used for abrupt discontinuities.
O Perform better in less noised images
O Magnitude of the gradient - strength
of the edge .
O Direction - opposite of the edge
direction.
Gy
G Gx 2
Gy 2
Gx Gy tan 1
Gx
11. Cont. Gradient based Edge
Detection
O Roberts Edge Detector.
O Prewitt Edge Detector.
O Sobel Edge Detector,
O Canny Edge Detector.
12. Cont. Gradient based Edge
Detection - Roberts
O 2X2 Convolution Mask
O Convolution Mask
O Gx Gy
1 0 0 -1
0 -1 1 0
O Differences are computed at the
interpolated points [i+1/2, j+1/2] and not
[i, j].
O Responds to edge with 450.
13. Cont. Gradient based Edge
Detection - Prewitt
O 3X3 Convolution Mask
O Convolution Mask
O Gx -1 0 1 Gy 1 1 1
-1 0 1 0 0 0
-1 0 1 -1 -1 -1
O The differences are calculated at the
center pixel of the mask.
14. Cont. Gradient based Edge
Detection - Sobel
O 3X3 Convolution Mask
O Convolution Mask
O Gx -1 0 1 Gy 1 2 1
-2 0 2 0 0 0
-1 0 1 -1 -2 -1
O The differences are calculated at the
center pixel of the mask.
15. Cont. Gradient based Edge
Detection
O Simple to implement
O Capable of detecting edges and their
direction
O Sensitive to noise
O Not accurate in locating edges
16. Cont. Gradient based Edge
Detection - Canny
O First derivative of a Gaussian filter will
approximately optimize the signal-to-noise
ratio and localization.
17. Cont. Gradient based Edge
Detection - Canny
O Three conditions for optimal detector
O Error rate: Respond to edges not noise.
O Localization: edges detected near true
edges.
O Response - Not identify multiple edge
pixels.
19. Cont. Gradient based Edge
Detection – Canny Algorithm
O Step 3
O Edge Direction
1 Gy
tan
Gx
O Step 4
O Resolve Edge Direction
20. Cont. Gradient based Edge
Detection – Canny Algorithm
O Step 5
O Non-maxima suppression: keep all local
maxima in the gradient and remove
everything else.
O Gives a thin line for edge
O Step 6
O Double / hysteresis thresholding
21. Cont. Gradient based Edge
Detection – Canny Algorithm
O Better localization
O Improved signal-to-noise ratio.
O Works fine under noisy conditions.
O Complex to implement and time
consuming.
23. Zero Crossing based Edge
Detection
O Indicates the presence of a maxima.
O Pixel value passes through zero (changes its
sign).
24. Cont. Zero Crossing based
Edge Detection
O Laplacian of Gaussian
1 1 1
1 8 1
1 1 1
-1 2 -1
2 4 2
-1 2 -1
25. Cont. Zero Crossing based
Edge Detection - LOG
O Defined as:
O Greater the value of , broader is the
Gaussian filter, more is the smoothing
26. Cont. Zero Crossing based
Edge Detection - LOG
O Steps:
O Smoothing: Gaussian filter
O Enhance edges: Laplacian operator
O Zero crossings denote the edge location
O Use linear interpolation to determine the
sub-pixel location of the edge
27. Cont. Zero Crossing based
Edge Detection - LOG
O Computationally cheaper to implement
since we can combine the two filters into
one filter but it.
O Doesn’t provide information about the
direction of the edge.
O Probability of false and missing edges
remain.
O Localization is better than Gradient
Operators
29. Proposed Algorithm
O Evaluate an Image using a Gradient filter.
O Evaluate an image using a Zero crossing
filter.
O Fuzzy Logic.
30. Cont. Proposed Algorithm
Fuzzy Logic
O Fuzzy Logic
O Problem-solving methodology.
O Draw definite conclusions from
vague, ambiguous or imprecise
information.
O Resembles human decision making with its
ability to work from approximate data and
find precise solutions.
31. Cont. Proposed Algorithm
Fuzzy Image Processing
O Collection of all approaches that
understand, represent and process the
images, their segments and features as
fuzzy sets.
O The representation and processing
depend on the selected fuzzy technique
and on the problem to be solved.
33. Cont. Proposed Algorithm
O Step 1
O Calculate gradient of an image using Sobel
filter.
O Step 2
O Calculate zero crossing using three
different values of standard deviation σ in
gausian of laplacian.
O Step 3
O Apply fuzzy rules on the two steps above.
34. Cont. Proposed Algorithm
Step 1 - Sobel
O The resulted Gradient are mapped from
[0-255]
O Divide into four regions:
O Low class GL from [0-GL].
O Medium class GM
O from [GL-GM] .
O From [GM-GH] .
O High class GH from [GH-255].
38. Cont. Proposed Algorithm
Step 3 – Fuzzy sets
O Pixel (PG), zero crossing value (PZ), and
probability of a pixel corresponds to an edge
{EL, EM, EH}.
O If PG is in GL and PZ equals to 1, then P belongs to EL.
O If PG is in GL and PZ equals to a zero, then P belongs to EL.
O If PG is in [GL-GM] and PZ equals to 1, then P belongs to EM.
O If PG is in [GL-GM] and PZ equals to zero, then P belongs to
EL.
O If PG is in [GM-GH] and PZ equals to 1, then P belongs to EH.
O If PG is in [GM-GH] and PZ equals to zero, then P belongs to
EM.
O If PG is in GH and PZ equals to 1, then P belongs to EH.
O If PG is in GH and PZ equals to zero, then P belongs to EM.
39. Cont. Proposed Algorithm
Result
O All pixels in the EH will be considered as
an edge.
O All pixels in the EL will be discarded.
O All pixels in the EM, the gradient value will
be evaluated against a threshold value in
order to discard any pixel with value (0)
that may result from false zero crossing.
Editor's Notes
Step edge:– the image intensity abruptly changes from one value to one side of the discontinuity to a different value on the opposite side.Ramp edge:– a step edge where the intensity change is not instantaneous but occurs over a finite distance.Ridge edge:– the image intensity abruptly changes value but then returns to the starting value within some short distance– generated usually by linesRoof edge:– a ridge edge where the intensity change is not instantaneous but occurs over a finite distance– generated usually by the intersection of surfaces
Classical: gradient of pixels and succeeded in computing both magnitude and direction of gradient and used a threshold to locate edges. These methods are simple techniques that use differential masks but they lack image smoothing as a pre-processing step that made these methods more vulnerable to noise.Gaussian: Gaussian filters as a pre-processing filter. Gaussian filters proved that when applied over an image, it never creates new zero crossing and therefore it is possible to detect true edges over different scales. The use of a combination of Laplacian and Gaussian filters achieved the conditions of optimal smoothing filter in which an image should be smoothed in the frequency domain and then localized in the spatial domain. less reliable in locating true edges when the signal-to-noise ratio in an image is very high Shunck, Witkin and Bergholm based on multiple scales of segma. Wavelet: with regions of low contrast separated by high-contrast edges. Wavelets maps an image using two variables that are Scale, which either stretch or compress functions that is done in the frequency domain and Shift that corresponds to the translation function in the spatial domain. Low scale shows the abrupt change in the intensity with high frequency while high scale shows a slow change in intensity with low frequency.
Smoothing: suppress as much noise as possible, without destroying the true edges.Enhancement: apply a filter to enhance the quality of the edges in the image (sharpening).Detection: determine which edge pixels should be discarded as noise and which should be retained (usually, thresholding provides the criterion used for detection).Localization: determine the exact location of an edge (sub-pixel resolution might be required for some applications, that is, estimate the location of an edge to better than the spacing between pixels). Edge thinning and linking are usually required in this step.
Provides an approximation to the gradientis susceptible to noise
less susceptible to noise. But it produces thicker edges. So edge localization is poor
less susceptible to noise. But it produces thicker edges. So edge localization is poorEdge is several pixels wide for Sobel operator– edge is not localized properly
Error rate: the edge detector should only respond to edges and not miss any.Good detection– The filter must have a stronger response at the edge location (x=0) than to noiseLocalization: the location of the edge as detected by the edge detector should be accurate as possible. Good Localization– The filter response must be maximum very close to x=0Response - the edge detector should not identify multiple edge pixels. Low False Positives– There should be only one maximum in a reasonable neighborhood of x=0
The larger the filter the lower noise in the image can be accomplished but with increase error in localization.S=Gσ* I, were σ is the standard deviation.
the purpose here is to turn the blurred edges into a sharp one. trace along the edge direction and suppress any pixel value not considered to be an edge. Gives a thin line for edgeedges responding to a certain threshold and linking them. Two thresholds are used T1 and T2 with T1 > T2. Tracking can only begin at a point on a ridge higher than T1 then continues in both directions out from that point until the height of the ridge falls below T2. This hysteresis helps to ensure that noisy edges are not broken up into multiple edge fragments.
It uses a Gaussian filter for smoothing an image in order to reduce high frequencies in the image and then apply a laplacian filter.
It uses a Gaussian filter for smoothing an image in order to reduce high frequencies in the image and then apply a laplacian filter.
The fuzzification and defuzzification steps are due to non availability fuzzy hardware.Therefore, the coding of image data (fuzzification) and decoding of the results(defuzzification) are steps that make possible to process images with fuzzytechniques.After the image data are transformedfrom gray-level plane to the membership plane (fuzzification), appropriate fuzzy techniques modify the membership values.
Subtraction to determine the width of the edge.Then, we will detect the zero crossing in an image by finding the maximum and minimum among all pixels in the neighborhood of a pixel under consideration. If the maximum is greater than zero and the minimum is smaller than zero, the pixel is a zero-crossing. To exclude false zero crossing resulting from noise, we will check whether the difference between the maximum and the minimum is greater than a threshold value. If so the pixel is on an edge, otherwise the zero-crossing is assumed to be caused by noise and suppressed.
