exploring methods to improve edge detection with canny algorithm

Exploring Methods to Improve Edge Detection withCanny Algorithm

A.Mehta, H.Lehri, P.Thakur & S.TambeJanuary 2015

1 Introduction 1.1 Image as a Signal1.2 Theory of Edge Detection1.3 Edge Detector Types

1.3.1 Gradient Based Edge Detection1.3.2 Second Ordered Derivative Based Edge Detection1.3.3 The Canny Edge Detector

1.4 Problems with Standard Edge Detection Method2 Literature Survey 3 Methods Explored

3.1 Recursive Method for Edge Detection3.1.1 Basics of Recursion3.1.2 Using Recursion with Canny Algorithm

3.2 Edge Filtering by determining Conditional Probability of a point being an Edge3.2.1 Polynomial Regression3.2.2 Edge Linking3.2.3 Algorithm for the Edge Filtering Technique

3.3 Results4 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

INTRODUCTIONEdge 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 likeGaussian 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 allscales

• 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

SpatialDomain

FrequencyDomain

FourierTransform

InverseFourier

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:

=

introduction

Intensity changes can be detected by either finding the maxima or minimaof the first derivative or finding zero crossings in the second derivative of the imageHence we can write it as:

f(x, y) = ( G(x, y) I∗ (x, y) )Gaussian

Kernel Image

Second order directional derivative

Theory of Edge Detection introduction

Edge Detector Types

• Gradient BasedDetects edges by looking for the maxima or minima of the first derivate of the image

• Laplacian basedDetect 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

Sobel Operator

Prewitt Operator

Filter out noise

Convolve Image inhorizontal & verticalDirection using gradientoperators

Gaussian Operators used

For all pixels If magnitude>threshold then pixel=edgeElse pixel edge

introduction

Edge Detector Types

Second Order Derivative Based Edge Detection

Filter out noise

Convolve Image inusing LaplacianKernel

Laplacian of Gaussian matrix

For all pixels If then pixel=edgeElse pixel edge

Marr Hildrith Operator

• Isotropic in nature • Utilizes only one mask• Cheaper to implement

introduction

Edge Detector TypesThe Canny Edge Detector

Remove noiseusing Gaussianfilter

first order derivativesof the Image using operatorslike Sobel operator

For every pixelcalculateNon Maximalsuppression

For every pixelPerformhysteresis thresholding

The process

Canny is Optimal because:• Less sensitive to noise• It removes streaking by using two thresholds • 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

introductionProblems 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


Edge Detection Depends on

Edge linking that may lead to detection of false edges

Difficult to generalize themethod of thresholding


How Canny deals with these problems

Canny EdgeDetection

• Adaptively sensitive to digital noise• Detects sharper and thinner edges• Used as a benchmark

LITERATURE SURVEYModern 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 setsthat fuse into edge image

LITERATURE SURVEYResearch 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 SURVEYResearch 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 SURVEYOther 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 EXPLOREDRecursive 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



Mathematical Reasoning

NxN ImageW

Gaussian FilterKernel

(N −W2 )(N −W2 )Convolutions required




WGaussian Filter

Kernel

(S−W2 )(S−W2 )Convolutions required per block

Block size

S




We have, such blocks

Hence total number of convolutions

S > 1 number of operations have decreased

METHODS EXPLOREDBasics of Recursion

f(x)=

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+ O()Time complexity of recursive algorithms is give as

The solution to this problem is given by the Master’s Theorem as:

T(n) =

METHODS EXPLOREDUsing Recursion with Canny Algorithm

EDGEDETECTION (Image)

1. Divide the image into four regions into , i {0, 1, 2, 3}

2. For Each Region do:

a) IF sizeof is less than Base Case:

i. Filter and Perform Canny Edge Detection on it

b) Else Call EDGEDETECTION()

3. Join the results obtained from each region

4. Return the joint Image

METHODS EXPLOREDEdge Filtering by determining Conditional Probability of a point being an Edge

Noise and

Intensity

changesInput image

CannyNo

unnecessary edges

Edge detected image

Edge FilteringBy determining conditional probability of points being on an edge

Post Processing

Noise and

Intensity

changesInput image

CannyIrrelevant

AndSmalledges

Edge detected image

Our Observation

Our Approach

METHODS EXPLOREDEdge 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

METHODS EXPLOREDEdge Linking

In Global Processing the voting is done by points on a curve

y = mx + c or c = -xm+yc and m are Variablesx 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.


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


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

OriginalImage

Canny

RecursiveCanny

Edge Filtering

OriginalImage Cann

y

RecursiveCanny

Edge Filtering

ANALYSIS OF RESULTSCanny 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 RESULTSCanny 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 scaleTrade off between noise filtering and true edge filtering

ANALYSIS OF RESULTSEffects of variable kernel size

Kernel size=5

Kernel size=7

Kernel size=9

Kernel size=11

ObservationsOutlines (important edges) become more significant as kernel size increasesFalse Edges decrease with increase in kernel sizeLoss 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 RESULTSEffects 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 RESULTSEffects 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 RESULTSEffects of variable truth values

Canny Output

Canny Truth value = 0.4



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 RESULTSEffects 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 = 0.5truth value = 0.7window 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

Thank You

exploring methods to improve edge detection with canny algorithm

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