Exploring Methods to Improve Edge Detection with Canny Algorithm

Exploring Methods to Improve Edge Detection with
Canny Algorithm
A.Mehta, H.Lehri, P.Thakur & S.Tambe
January 2015

1 Introduction
1.1 Image as a Signal
1.2 Theory of Edge Detection
1.3 Edge Detector Types
1.3.1 Gradient Based Edge Detection
1.3.2 Second Ordered Derivative Based Edge Detection
1.3.3 The Canny Edge Detector
1.4 Problems with Standard Edge Detection Method
2 Literature Survey
3 Methods Explored
3.1 Recursive Method for Edge Detection
3.1.1 Basics of Recursion
3.1.2 Using Recursion with Canny Algorithm
3.2 Edge Filtering by determining Conditional Probability of a point being an Edge
3.2.1 Polynomial Regression
3.2.2 Edge Linking
3.2.3 Algorithm for the Edge Filtering Technique
3.3 Results
4 Future Work
5 Conclusion
CONTENT

INTRODUCTION
Edge detection is the process of finding the set of pixels that
represent the boundary of disjoint regions in an image.
Edge detection

INTRODUCTION
Edge detection is important for image segmentation, since many image
processing algorithms are first required to identify the objects and then
process them.
Image Medical Imaging
Finger print detection
Face recognition
Traffic control
processingpre-processing
Edge detection

INTRODUCTION
• Edge detection is not without its challenges
• The image on which the detection is carried out has noise, due to random
variation of brightness, color or electronic noise like
Gaussian noise, Salt pepper noise, Shot noise, Gradient noise etc..
• Noise leads to false edge detection
Gradient noise = False edges

Image as a Signal
• An Image is described as a function of x and y
• A captured image must be treated as a discrete signal rather than a
continuous functions since the image can be recorded on a 2D grid
• The conversion is done by a process called sampling
• Uniform rectangular sampling is the most common
Original Image Spectrum Sampled Image Spectrum
Ld(n, m) = L(n∆x, m∆y)
sinc(x) = sinc(x)/x
introduction

Theory of Edge Detection
• Difficulty: Changes in intensity occur over a wide range of scales in
an image and no single filter can optimally reduce noise at all
scales
• Reason: Physical phenomena that give rise to intensity changes like
illumination and surface reflectance are spatially localized
• Uncertainty Principle: The two requirements lie in different
domains, we cannot achieve both at the same time
Spatial
Domain
Frequency
Domain
Fourier
Transform
Inverse
Fourier
Transform
IlluminationSurface Reflectance
introduction

Theory of Edge Detection
• Possible solution
• Take local averages of the image at various
resolutions and then detect the changes in intensity that occur
at each of the resolutions.
• Determine the optimal smoothing filter to reduce the range of
scales over which the intensity changes take place
• There is only one distribution that optimizes this relationship
• Gaussian distribution:
𝐺(𝑥) =
1
𝜎(2𝜋)
1
2
𝑒
−𝑥2
2𝜎2
introduction

Intensity changes can be detected by either finding the maxima or minima
of the first derivative or finding zero crossings in the second derivative of
the image
Hence we can write it as:
f(x, y) = 𝐷2
( G(x, y) ∗ I(x, y) )
Gaussian
Kernel
Image
Second order directional derivative
Theory of Edge Detection introduction

Edge Detector Types
• Gradient Based
Detects edges by looking for
the maxima or minima of the
first derivate of the image
• Laplacian based
Detect edges by searching for
the zero crossing of the
second derivate of the image
introduction
Edge
Edge

Edge Detector Types
Gradient Based Edge Detection
Roberts Operator
𝐷 𝑥 =
1 0
0 −1
𝐷 𝑦 =
0 1
−1 0
Sobel Operator
𝐷 𝑥 =
−1 0 +1
−2 0 +2
−1 0 +1
𝐷 𝑦 =
−1 −2 +1
0 0 0
−1 +2 +1
Prewitt Operator
𝐷 𝑥 =
−1 0 +1
−1 0 +1
−1 0 +1
𝐷 𝑦 =
+1 +1 +1
0 0 0
−1 −1 −1
Filter out noise
Convolve Image in
horizontal & vertical
Direction using gradient
operators
Gaussian Operators used
For all pixels
If magnitude>threshold then pixel=edge
Else pixel ≠ edge
introduction

Edge Detector Types
Second Order Derivative Based Edge Detection
Filter out noise
Convolve Image in
using Laplacian
Kernel
Laplacian of Gaussian matrix
For all pixels
If 𝐷2
𝑐𝑜𝑛𝑣𝑜𝑙𝑣𝑒𝑑 𝑝𝑖𝑥𝑒𝑙 = 0 then pixel=edge
Else pixel ≠ edge
Marr Hildrith Operator
0 0
0 −1
−1 0 0
−2 −1 0
−1 −2
0
0
−1
0
16 −2 −1
−2
−1
−1 0
0 0
• Isotropic in nature
• Utilizes only one mask
• Cheaper to implement
introduction

Edge Detector Types
The Canny Edge Detector
Remove noise
using Gaussian
filter
first order
derivatives
of the
Image using
operators
like Sobel
operator
For every pixel
calculate
Non Maximal
suppression
For every pixel
Perform
hysteresis
thresholding
The process
Canny is Optimal because:
• Less sensitive to noise
• It removes streaking by using two thresholds 𝑡ℎ𝑖𝑔ℎ 𝑡𝑙𝑜𝑤
• Offers good localization of edges and utilizes gradient of the
edge to generate thin, one-pixel wide edges
introduction

Illumination when the
image is taken
introduction
Problems with Standard Edge Detection Method
(x-1,y+1) (x,y+1) (x+1,y+1)
(x-1,y) (x, y) (x+1,y)
(x-1,y-1) (x,y-1) (x+1,y-1)
Intensity difference
between two
neighboring pixels
Edge Detection Depends on
Smoothing to filter out
noise also spreads the
edges

introduction
Edge Detection Depends on
Edge linking that may lead to
detection of false edges
Difficult to generalize the
method of thresholding

introduction
How Canny deals with these problems
Canny Edge
Detection
• Adaptively sensitive to digital noise
• Detects sharper and thinner edges
• Used as a benchmark

LITERATURE SURVEY
Modern Non-Canny Approaches
Wavelet transform
• Similar to Canny’s Kernel
• Selectivity is high
• Difficult to select Wavelet functions
Mathematical Morphology
• Deng Caixia et al[13]. proposed a technique,
wherein they use 2 structural elements, one of
size 3x3 and the other of size 5x5 and orient them
along different directions
• Gives them two edge sets
that fuse into edge image

LITERATURE SURVEY
Research on Canny Edge Detector
T Rupalatha et al[15] & Qian Xu et al
Distributed Canny Edge detector on Field
Programmable Gate Array(FPGA) based architecture.
Ogawa K
Canny Edge Detection algorithm on CUDA(Compute
Unified Device Architecture)

LITERATURE SURVEY
Research on Canny Edge Detector
Philip Worthington
Canny Edge detector using Curvature Consistency
Ping Zhou et al[5]
Canny Edge Detection algorithm on Otsu method for
Adaptive Thresholding

LITERATURE SURVEY
Other Approaches
Aleksandar Jevtic and Bo Li[7
Ant Based Approach for adaptive edge detection
Piotr Dollar and C.Lawrence Zitnick[10]
Edge detection algorithm using Structured Forests

METHODS EXPLORED
Recursive Method for Edge Detection
Original Image Canny output for 300 x 300
Canny output for 400 x 400 Canny output for 600 x 600
Our Observation - Canny
seems to work better with
smaller size images
Our Approach –
• Recursively divide the image
into sub-images
• Apply Canny on sub-images
• Merge sub-outputs to obtain
result

METHODS EXPLORED
Our Observation - Canny seems to work better with smaller size images
Mathematical Reasoning
NxN Image
W
Gaussian Filter
Kernel
N −
W
2
N −
W
2
Convolutions required

METHODS EXPLORED
W
Gaussian Filter
Kernel
S −
W
2
S −
W
2
Convolutions required per block
Block size
S

METHODS EXPLORED
We have,
N
S
N
S
such blocks
Hence total number of convolutions S −
W
2
2 N
S
2
= N −
WN
2S
2
Since
N
S
> 1 number of operations have decreased

METHODS EXPLORED
Basics of Recursion
f(x)=
g x , if x satisfies the base case
a∗ f(x/b) + c otherwise
Problem can be divided into multiple independent problems(Image) unlike dynamic programming. Recursion is part
of the Divide and Conquer strategy. Recursion is usually of the following format:
T(n) = a ∗ T
𝑛
𝑏
+ O(nk
)
Time complexity of recursive algorithms is give as
The solution to this problem is given by the Master’s Theorem as:
T(n) =
O nlogba , If a > 𝑏 𝑘
O nk
. logn , If a = 𝑏 𝑘
O nk
, If a < 𝑏 𝑘

METHODS EXPLORED
Using Recursion with Canny Algorithm
EDGEDETECTION (Image)
1. Divide the image into four regions into Si, i ∈ {0, 1, 2, 3}
2. For Each Region do:
a) IF sizeof Si is less than Base Case:
i. Filter Si and Perform Canny Edge Detection on it
b) Else Call EDGEDETECTION(𝑺𝒊)
3. Join the results obtained from each region 𝑆𝑖
4. Return the joint Image

METHODS EXPLORED
Edge Filtering by determining Conditional Probability of a point being an Edge
Noise
and
Intensity
changes
Input image
Canny
No
unnecessary
edges
Edge detected image
Edge Filtering
By determining
conditional
probability of
points being on
an edge
Post Processing
Noise
and
Intensity
changes
Input image
Canny
Irrelevant
And
Small
edges
Edge detected image
Our Observation
Our Approach

METHODS EXPLORED
Edge Filtering by determining Conditional Probability of a point being an Edge
noise
and
intensity
changes
Input image
Canny
For every pixel detected by the Canny
algorithm:
1. Analyze Surrounding
2. Measure Order in the neighborhood of the
pixels
• Determine if the pixels can be aligned
along a particular line using regression
fitting
• Get conditional Probability of pixel
falling on the line
3. Probability whether the pixel is part of an
edge or not
4. Filter out pixels based on certain threshold
Post-Processing
No
unnecessary
edges
Edge detected image

Exploring Methods to Improve Edge Detection with Canny Algorithm

METHODS EXPLORED
Edge Linking
In Global Processing the voting is done by points on a curve
y = mx + c or c = -xm+y
c and m are Variables
x and y are Parameters
To find he straight line that best fits given n-points, we can
work in the m-c domain instead of the x-y domain and
apply Hough transform.
The point through which maximum number of lines pass
through gives the m and c of the best fitting line.

METHODS EXPLORED
Edge Linking
In localized algorithm for each edge point, we find the approximate direction of the edge in one of the eight
directions (0o, 45o, 90o, 135o, 180o, 225o, 270o, 315o)
Canny List L = Edges Endpoints While is not empty
• Analyze the 8-neighborhood
of L0 and find the direction
(from the 8 directions) of the
edge
• If reflection(ir,jr) of Lk(i,j) is not
in the list L:
• Add (ir,jr) to List L
• Mark (ir,jr) as white
• Remove Lk from List L
END

METHODS EXPLORED
Edge Linking
Algorithm for Edge Filtering Technique
Canny For each point detected as an edge by Canny algorithm:
1. Analyze the neighborhood around the point.
Using regression, determine a line ax+b which
best fits all the points in the neighborhood which
are white. Once we determine a and b, we find
the number of points (x,y) for which y = ax+b. We
then compute Probability P(i,j).
2. Determine the probability Pr. If Pr > 0.5 the
we retain (i,j) else we set pixel (i,j) as black
Remove small
edges and perform
edge linking

RESULTS
Original
Image
Canny
Recursive
Canny
Edge Filtering

Original
Image
Canny
Recursive
Canny
Edge Filtering

ANALYSIS OF RESULTS
Canny Recursive Canny
Region 1
Region 2
Region 1
Region 2
Good Hysteresis linking preserves edges Reduced scale of Hysteresis linking doesn't preserves
some edges
Recursive Canny helps us analyze Canny without hysteresis linking

ANALYSIS OF RESULTS
Canny Recursive Canny
Region 1
Region 2
Bad Hysteresis linking preserves noise Reduced scale of Hysteresis linking doesn't preserves
noise
Region 1
Region 2
Because linking at lower scales gives fewer false edges than linking on a large scale
Trade off between noise filtering and true edge filtering

ANALYSIS OF RESULTS
Effects of variable kernel size
Kernel size=5 Kernel size=7 Kernel size=9 Kernel size=11
Observations
Outlines (important edges) become more significant as kernel size increases
False Edges decrease with increase in kernel size
Loss of Actual Edges after size = 7

ANALYSIS OF RESULTS
Effects of variable recursion base case (block) size
Block size=8 Block size=16 Block size=32 Block size=64
Jittery and unsmooth output
Approaches to Regular Canny

ANALYSIS OF RESULTS
Optimal Kernel and Block size
block size of 32 and kernel size of
5 improves the quality of output
generated.
• Larger block size the performance suffers
• Smaller block size the recursion leads to a jittery
output with the edges appearing mismatched.
• Larger kernel size smoothen the image, but it
increases the time taken for convolving the image
with the kernel and hence may not b e useful for
practical purposes.

ANALYSIS OF RESULTS
Canny Probabilistic Edge Filtering
Region 1
Region 2
Region 1
Region 2
• No Significant differences since it uses original Canny image used for edge linking
• Marked regions are maintained since they satisfactorily fit on a line unlike in recursive canny
• Noise density is reduced to some extent

ANALYSIS OF RESULTS
Canny Probabilistic Edge Filtering
Noise removal depends on minimum edge length and hence not a fault of refinement process
Region 1
Region 2
Region 1
Region 2

ANALYSIS OF RESULTS
Effects of variable length thresholds
Canny Output Length threshold=1 Length threshold=5 Length threshold=10
Significant-Edge Retention
• However after linking the edges result is similar to Canny
• This is a fault of the linking algorithm as the original Canny is
used for linking broken edges

ANALYSIS OF RESULTS
Effects of variable probability thresholds
Canny Output Probability threshold= 0.5 Probability threshold= 0.6 Probability threshold=0.7
Strong step edges (lines)are retained always, showing the algorithm returns high probability for nearly straight lines
Number of edges decreases

ANALYSIS OF RESULTS
Effects of variable truth values
Canny Output Canny Truth value = 0.4 Canny Truth value = 0.6 Canny Truth value = 0.7
True Edges are lost
False edges increase
• Strong step edges (lines)are not retained
• Because we assume the output of the Canny algorithm itself has very small chance of being true and hence reduces
the overall probability

ANALYSIS OF RESULTS
Effects of variable window size
Canny Output Window Size = 4 Window Size = 14 Window Size = 18
Ineffective neighborhood judgment
Increased processing time & lines
integrate to curves

ANALYSIS OF RESULTS
Optimal probability threshold and truth value and window size
probability threshold = 0.5
truth value = 0.7
window size = 6
• Configuration must be chosen carefully
• Absolute Optimal configuration is not possible

FUTURE SCOPE
• Applying Tsalli’s model
• Color Space Research
• Machine Learning Approach
• Adaptive Thresholding Using
Image Histograms
• 2D Entropy and Probability
application
• Texture Analysis

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