Extraction of Lines and Edges by Waleed Abrar (1)

Extraction of edges and straight lines

Waleed abrar (895195))

Multimedia Signal Processing (seminar)

April 1, 2014

Extraction of edges and straight lines | Waleed abrar (895195)

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Abstract

This essay throws light on extracting straight lines from an image the technique

explained in this paper is based on the paper by Burns, J. B., Hanson, A. R. & Riseman,

E. M. (1986). Extracting straight lines The main revolutionary idea in this paper was

they have used Line orientation along with their magnitude to determine the line

segments that should be incorporated for Line support Region (LSR). Using the

Orientation and magnitude along with some additional parameters that Burns, J. B.,

Hanson, A. R. & Riseman have identified during their experiment the line localization

is pretty fast and false likely hood is also decreased. In the later stages of the paper I

have added an addition experiment based on their model to check the parameter

explained by them and to see the visual effect on edge detection which is the

preliminary step for line detection.


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Background:

For the extraction on Lines from the image there should be as image beforehand, so

lets start with the process of Image Acquisition Fig 1

1

Figure 1: The Process of Image Acquisition

As you can see, for an image to be captured the source of illumination is required. It

throws light on the object .The image system captures the light thats is reflected by

the object and Intensity and brightness of at a spatial coordinate is determine by two

factors illumination component i(x,y) the illumination and r(x,y) the reflectance where

0< i(x,y)


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process of image acquisition is Quantization. Quantization is the number of variations

or grey levels. Below figure illustrate the effect of quantization and sampling in details

Figure 2: Explaining the process of sampling and quantization

As you can see clearly from the image if you move from left to right the number of

samples decrease so is the number of information similarly in second column if you

move from left to right the number of intensity variation decreases.

Classification of processes in DSP

Now we are ready to define an image which can easily be represented as a two

dimensional signal f(x, y) where x and y represent the spatial coordinates and value

of the function f represent intensity level or grey level as far as classification is

required we can generally classify them in three types according to the processes

related to them which are low-level processes, mid-level process and High level

processes.


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Low-level processes are those where input is an image and output is also an image

similarly Mid-Level processes are those where input is an image and output are the

attributes rather than the image. The High-Level processes are those which are

mostly related to machine vision and cognations. Table 1 explain the concept in detail.

LOW-LEVEL

Input is image with noise

output (right) is the image

without noise,

MID-LEVEL

Input is the image and

output (right) is the image

with the edges.

HIGH-LEVEL

Input is image and output

is constant detection and

feedback to the

microcontroller

Table 1: Classification of the Processes related to image

Operations related to the images:

Mainly three process are related to the processing of images, this concept is necessary

because its one of the most important process while extracting edges or straight lines.

The three processes are


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A) Point/Pixel operations:

The output value at a specific coordinate is dependent on the input value at (x, y) of a

specified image.

Fig 3: The Blue is the original point in image and red is enhanced point in the output

B) Local operations:

The output value at any point p(x y) is dependent upon the input values of the neighboring

pixels not on the individual pixels.

Fig 4: The Blue is the original point the point shows its composed to neighbors in image and red is output

C) Global operations:

The output value at point (x, y) is dependent upon the whole image

Fig 5: The Blue is the original point the point shows its composed to neighbors in image and red is output


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Introduction:

Neighbors and connectivity are the most important aspect whenever any kind of

information is extracted from the image so basically neighbors are the surrounding

pixel of any given pixel. Basically there is always some problem while performing

those processes at the boundaries, for that reason based on the type of neighbor some

rows horizontally and some rows vertically are skipped another option would be the

padding of zeroes to make it work for boundaries as well so here in this paper I will

just explain 4 and 8 neighbor connectivity as there are many more. When one point

P(x, y) is connected to 4 other point vertically and horizontally its called as 4

neighbors as below figure shows

Similarly when the point P(x, y) is connected to 8 other point vertically, horizontally

and diagonally then they make 8 neighbors as shown in below picture.

And the point is connected if it shares all the connectivity represented by particular

method e.g 4 connectivity or 8 connectivity


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Boundary and region:

Lets take R as a subset of pixels then we call R a region if R is connected set of pixels and

connectivity can be anyone 4, 8, 16. Similarly boundary of a region R is set of pixels in region

that have one or more neighbors that dont belong to R. Following image illustrates the

concept more clearly.

Fig 6: Illustrating the concept of Region and boundary with cricket field example

Discontinuities in the image:

There are mostly three types of grey level discontinuities in a digital image which are:

Point, Lines and Edges

Point is basically any threshold value in the image above, if a value exist above the threshold

value then we can detect the anomalies among the image. Lines are continuities of those

anomalies with a particular orientation as well and edges are basically the set of connected

pixels that lie on the boundary between two regions.


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Types of Edges:

There are many types of edges in the image but I will discuss two most important

types that are ideal and Ramp edge.

Ideal edge is the one where there is sudden altering of values at a particular region

where as Ramp edge is the normal or real life edge when edge start and mesh up till

its end following image explain the two edge types in detail

In the Left image one can see that there is sudden or sharp change from dark pixels

to light Pixel ad the localization of the edge is fairly easy as one can see from the

graph as well there is a sudden change from low pixel value to maximum suddenly.

Whereas the image on the left side the change from dark to light pixels are very slow

and there is a large region for pixel mesh up and edge localization is hard, The

increase in slope slowly with respect to time shows the problem


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Edge detection methods and problems:

There are many methods to detect the edge from the image like canny and more but

two most basic methods are explained by me in this paper as these methods are

used by Hanson and Burns in the paper.

The two most popular methods of edge detection is first and second derivatives. By

using the first derivative we get the peek where the edge start and where it end.

Whereas while using second derivative we can get more information regarding

edge, which is not only we can detect the edge by maxima and minima but the rise

and fall of peeks can also tell us rather the change is from brighter pixels to darker

or darker pixels to lighter pixels.

The above image is of a ramp edge as you can see from the plot on the right side of

image. Then when we take first derivative you can see where the edge is located is a

constant positive square wave, whereas if we take the second derivative of the same


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image we get the relative maxima and minima at some points and the direction of

wave also tell the direction of change as first peak is high and second peak is in ve y

direction this tells us that the pixels are changed from dark to bright as seen in the

above image.

The problem in localization of the edge starts when its added with a little bit of noise

for further explanation we can use an image to illustrate the effect as shown below

From the figure we can easily see that that when there is no noise the localization is

very easy (the top right picture with noise 0) then 0.1 of Gaussian noise is added to

the image and the edge localization is difficult (noise 0.1) then in 1.0 and 10 the edge

is nearly impossible to find and if one is using these two methods to detect edge from

the image then the results are totally wrong so for these methods to be used, the

image should be normalized or smoothed to remove the noise effects before applying

the derivatives for edge localizations.


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Simple line detection methods:

As you know that the line is represented by the equation of line as Y=MX+C where M is the

gradient or slope whereas C is the y intercept or the crossing point of line. Convolving he

image with a simple mask can help to detect the lines from a particular image

So if the image is convolved by horizontal mask from the above image it intensify the

Horizontal lines from the image as it double there pixel value and compress the other pixels

which are not following the same order. Same is the case for other masks .The vertical mask

will enhance the vertical lines from the image and suppress the other lines.

The above image show the effects of line detection and line detection the above image

is the original one and the bottom left is convolved with -45 degrees and one can see

that those lines are enhanced and bottom left is parsed with threshold of pixel values

and certain pixels above threshold are allowed to pass from the filter others low


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frequencies are blocked by the filter or mask. In this one can detect line from the

image.

The process of straight line detections proposed by BURNS and Hanson:

The algorithm proposed by them is very effective even though its given in 1986 even

now many modern algorithms are using their method because its not only effective

but computationally very fast and the number of false alarm are very less. The

algorithm is explained as under.

Magnitude and Direction:

Gradient is basically directional change in the intensity of the pixels. Gradient magnitude is

the sum of movement in the point G(x) x axis and G(y) y axis directions as explained in

Pythagoras theorem .we assume its the sum to save the number of calculations that are

needed to calculate the magnitude of the image. Or in simple worlds change in x-y direction

Similarly the gradient orientation can be obtained by taking the tan-1 of G(y), y direction by

x direction G(x).where G(x) and G(y) tell the gradient in x direction and y direction. Or in

simple words angle of change of the particles.


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So the Algorithm works by computing the magnitude and gradient of the image firstly it

create a coarsely quantized buckets which will serve as labels as to which block these points

belong to.

Figure: showing buckets with labels.

So buckets here are 45 degree interval as 45*8 =360 so pixels in the second step are

assigned the bucket number it belongs. Then connected component algorithm is

applied to create a line support region for the pixels and based on some additional

attributes defined in the paper the like steepness orientation and length of pixel

segments a line is formed. The whole process is explained in detail in the following

Figure


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(a) Shows the intensity profile plot showing gradient magnitude orientation and

steepness. (b) Explain the process of adding the bucket to those pixels and if more the

bucket is only assigned when we have more than 50% of confidence otherwise the

bucket number will not change. (c) Shows the process of applying CCA (connected

component analysis and line support region. (d) Explain the process of fitting the line

in line support region with planar intersection.

CCA (connected component Analysis) Process:

There are basically two passes for the CCA to work during the first iteration all the elements

are labeled. All the pixels are scanned and checked if they belong to background or not if

they are not from the background then their neighbors are checked and a label is assigned

to those component if its not previously labeled otherwise parent label is maintained Fig

below explain the process.

During the second iteration which can be called as aggregation, all pixels are scanned again to see if

all pixels are labeled if the pattern belong to the list add to existing list otherwise assigned to new

list. Figure explain the second iteration of CCA algorithm.


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Following is the snippet of the result obtained by CCA algorithm:

Line Creation Process and Attributes of Lines:

Some of the attributes that are discover while using the orientation along with the

magnitude for improving the line detection results are Contrast which is intensity

change in an image, Width of line which is basically the ratio about the edge and its

propagation to the image so that the line is according to the edge or the size of the

interval of the profile across which the bulk of intensity change occurs and steepness

is basically the slope within each interval

Input image in 2 D

Result

Output CCA Aggregated distinct classes


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The above image explain the process of line drawing after localization in the top left

(a) of the image gradient region is formed based on grouping of those pixels. Then in

(b) top right, shows pixels included in the line support region highlighted by dots.

Then in (c), (d) straight line is obtained by intersecting the weighted planar fit to the

intensities with horizontal plan representing averages. In the end line is overlaid on

those pixels.

Results:

Below Table explain the results obtained by applying Burns and J. B., Hanson techniques

A) In this image all those elements are

taken that have line support >=0.5

or 50 or 50% elements fall in similar

bucket.

B) In this image the addition

parameters Gradient Steepness is

used and Gradient steepness>2.5 GL

(grey level). So you can see the that

darkness is lessened in image


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C) Length >= 5 grey level or steepness

greater than 10 GL

D) Steepness >10 GL are shown in this

picture and the straight lines are

now more visible as low

frequencies are blocked.

E) All line segments with length >=5

are shown .Now only big lines are

visible mostly.

F) In this image the orientation 3-28

degrees are passed rest are blocked

G) In this image the orientation 165-

177 degrees are passed rest are

blocked


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H) In this image the orientation 81- 95

degrees are passed rest are

blocked. By their process we can

not only get lines but also filter

them with respect to orientation

from the image.

My Experiment:

I have done small experiment to see the effect of the parameters find out by them in the paper

and see their effect on live video feed and see how they effect in edge detection and line

detection, for my experiment I have used Action script 3 and pixelbender as there Libraries

are precompiled over there2

Figure Description

In this figure left side is the original

feed from the camera with 3 frames PS

And high frequency component from

the edges are allowed to pass. Edges

are bold as well

2 author: eugene, libraries can be found at http://blog.inspirit.ru/?p=297


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Then in this figure again 3 frames PS

are utilized and all low frequencies are

allowed to pass and image is binary so

lots of dark region is seen and

extremely high frequencies are

allowed to pass

In this figure on left one is the input

and right one is the result and one can

see all the low frequencies are blocked

and only the extremely high frequency

components are allowed to pass.

This figure left input right out put

shows the effects of normalization of

the contrast .As the edges are

everywhere because the information is

gained by normalization of the

contrast values.

This figure shows the bold edges .As I

explained earlier the ramp edge where

it start and end so the slope is taken as

whole for edge formation thats why

we get bold edges

Applications of Edge and line Detection:

Some of the applications for the line and edge extraction processes are


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Robotics and machine vision.

Autonomous Road follower

GIS Systems

Missile Technologies and many more.

Conclusions:

This paper involves a new direction on line extraction method by focusing on gradient

orientation along with gradient magnitude and while finding line support region other

interesting attributes related to line detection are also identified which enhance the existing

process of edge and line detection and perform those operation with great accuracy. Many

modern research are still based on the work of Burns, J. B., Hanson because there

algorithm for straight line detection is not only accurate but computing efficient as

well. My experiment helps me to understand the process of extraction of edges

based on those parameters and to see there result and to alter them to see their

effects.

Bibliography

Rafael C. Gonzalez, R. E. (2002). Digital Image Processing.

ftp://217.219.170.14/Electronic%20Group/Hashemi%20kamangar/Image%20Processing/(E

book)%20Prentice%20Hall%20-%20Digital%20Image%20Processing%20By%20Gonzalez%

202nd%20Edition%202002.pdf. New Jersey, USA: Tom Robbins. Retrieved from New Jersey.


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Extraction of Lines and Edges by Waleed Abrar (1)

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