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Bachelor of Electrical and Electronics Engineering (Hons)

Study on the effectiveness of generalized Hough Transform for fiber alignment classification

Name : Kannapiran Subashini

Student ID : 8479978

Supervisor : Dr Liau Vui Kien

Abstract

The report is presented to estimate the angle position of the fiber in the composite material. The strength of the composite material depends upon the alignment of the fibers in it. The fiber orientation plays a vital role which influences the performance of the composite materials. This orientation provides strength to the material thereby withstand at any load condition. In order to utilize the composite material in an effective manner, alignment and direction of the fiber are important. This paper mainly focused on the angular orientation of the fiber, so the effective metric calculation is carried out to evaluate the angle distribution of the fiber. The Hough transforms is utilized for detecting the accurate edges of the fibers. The Hough transforms is a powerful mathematical tool which converts the image into Hough space, where lines are visible as a single point. The process is taken over in a graph where the horizontal axis represents the angle of fibers and the vertical axis represents the distance of the line from the center of the image. These processes are implemented in the MATLAB program which takes input an image and processes it. It produces a distribution chart as an output through this the researcher can analyze the angle position of the fiber in the composite material. My method is successfully applied to the composite materials and retrieves the angle position of the fiber and display in a graph.

TABLE OF CONTENTS

1 Introduction ................................................................................................

1.1 Introduction ..................................................................................................

1.2 Objective ......................................................................................................

1.3 Composite Materials .....................................................................................

1.4 Fiber Alignment ............................................................................................

2 Literature survey ........................................................................................

3 Proposed work ..........................................................................................

3.1 Frame work .................................................................................................

3.2 Description ..................................................................................................

3.3 Input Image ...............................................................................................

3.4 Conversion of RGB image to gray image ....................................................

3.5 Binary Image .................................................................................................

3.6 Edge Detector ..............................................................................................

3.7 Hough transform ..........................................................................................

3.8 Angle distribution ..........................................................................................

3.9 Algorithm ......................................................................................................

3.10 Hough Space Accumulator ..........................................................................

3.11 Methodology .................................................................................................

3.12 MATLAB software ............................................................................................

3.13 Starting MATLAB ...........................................................................................

3.14 Applications of MATLAB ...................................................................................

4 Project Management ..........................................................................................

4.1 Gantt chart ............................................................................................................

5 Experimental Results .........................................................................................

5.1 Experimental Results and Discussion .................................................................

5.2 Parameters in calculation ....................................................................................

5.2.1 Theta .....................................................................................................................

5.2.2 Rho ........................................................................................................................

5.2.3 Threshold ..........................................................................................................

5.2.4 Nhoodsize ...........................................................................................................

5.2.5 Direction ..............................................................................................................

5.2.6 Is packed ............................................................................................................

5.2.7 Strel ......................................................................................................................

5.2.8 Peaks ...................................................................................................................

5.2.9 Hough Lines ..........................................................................................................

5.2.10 Fill Gap ...................................................................................................................

5.2.11 Min Length ..............................................................................................................

5.2.12 Norms .....................................................................................................................

5.3 Test images and its angle distribution values .........................................................

5.4 Fiber as Input image and its angle distribution values ...........................................

5.5 Benefits of the proposed system .........................................................................

6 Future work ........................................................................................................

7 Conclusion .......................................................................................................

8 References ............................................................................................................

1. Introduction

1.1 Introduction

Composite materials provide rigid support to different applications it is the combination of two or more phases (materials). The primary need for creating composite materials due to its high operating temperature, stiffness, reliability, and affordability. The composite material is the combination of binders and cluster of fibers. The binders bind the materials and make it as a rigid one which improves the mechanical strength of the composite material. The main advantage of adding different constituent of materials is that they can combine together at the microscopic level which prevents the solubility of two different materials. The FRP (Fiber Reinforced Plastic) material is a combination of reinforcement and matrix. The composite material can be used for any type of application. Composite materials are divided into two categories they are fiber reinforced composites and particularly reinforced composites. Normally the composite is made up of different material combinations where metal matrix composite, ceramic matrix composite are common in the composite type. The Fiber Reinforced Composites are classified into continuous or discontinuous fibers. Continuous fibers represent the long fibers whereas discontinuous fibers are short fibers. The fibers have to align in a proper direction to obtain the maximum strength for the materials. The fiber orientation plays a vital role in composite material for acquiring an optimism strength and stiffness for handling any kind of loads. The alignment should be parallel to the direction of loading. When the anisotropic material is subjected to load in the perpendicular direction it performs in a poor manner. In order to attain strength in all direction, the method is used to produce more isotropic composite where the multiple piles of continuous fiber aligned in a different manner with a particular angle. The angle difference between each fiber varies by 90, 45 or30 degrees. This will manage the loads which applied in all direction. The fibers should be flexible and normally it is several times stronger than the matrix. It poses higher elastic properties than the matrix. Through the Hough transform, we can establish the isolated features of the input image such as extracting the shape of the image. It normally detects the regular curves like a circle, lines, ellipse, rectangle etc.Hough transform techniques can detect gap between each fiber and provide a feature boundary description. The researcher analysis the different papers and understood the structure and design of the fibers in the composite materials [12]-[15]. Through these studies it analysis the long fiber and discontinues natural fiber and its parameters [9]. The mechanical properties of the fiber are evaluated [8]. Fiber orientation modulus through Young modulus and short fiber alignment is calculated [6]. The angle of different fiber is analyzed [16]. By combining the proper reinforcement and the matrix we can use it for a specific requirement. The material can be subjected to different shapes, we can mould it into complex shapes. There is much application which uses this material for the manufacturing process such as surfboats, bike frames etc.

The rest of the paper is prepared as observe section ii evaluation the literature survey of the paper. Section III discussed the proposed work of this paper. Section IV explained the project management of the researcher. Section V analysis the experimental result of the proposed method. After that, the paper is organized as a conclusion, Future work, and Reference of the paper.

1.2 Objective

· To use MATLAB to design and implement Hough transform function to convert 2D gray scale images to the Hough space

· Finally to obtain the distribution angle of the image, through which lines position and angle get detected

1.3 Composites Materials

A composite fabric is made from or greater individual constituents. The reinforced constituents are integrated into a matrix for forming the composite material. In composite material the combination of two different materials whose physical and chemical property differs in nature. Among the materials, contains two phases one is the reinforcing phase it is consists of fibers, sheets or particles. The another phase is matrix phase. These two material it can be metal, ceramic or polymer.

D:\binu\Documentation\Fiber alignment\im.png

Fig 1.1: Composite material

The combination of fiber and matrices produce a composite structure. Normally composite material is made up resin and fiber to attain the rigidity which is illustrated in fig 1.1 The resins are usually a mixture of the organic compound which can be converted into the polymer and the resin is insoluble in water. There is a different kind of resin available for combining the fibers and produce the composite materials. They are polyester, epoxy, phenolic, and vinyl ester. The filament reinforcement should consist of very powerful, excessive stiffness, and occasional density. The matrix need to pose suitable shear residences and coffee density. Similar to filament reinforcement, composite materials should pose a good shear property

Types of Composites

· Particle Reinforced Composite

· Fiber Reinforced composite

· Structural composite

Particle Reinforced Composite:

It uses particles for creating the composite such as ceramic, glasses and metal particles. The particles normally rise the modulus of matrix and reduce the ductility of the matrix that’s provide the less expensive composites.

Eg: concrete

Fiber Reinforced composite

Normally fibers growth the modulus of the matrix materials which provide strong covalent bond along the length of the fiber because the fiber has to break or extend the bonds provide a connection for it. The metal, ceramic, glasses or polymers turned into graphite is known as carbon fiber.

Structural composite

The structural composite properties depend upon the constituents and the Geometrical design. The stack and bonded fiber reinforced sheets stack sequences in 90 degree which provides plane stiffness. Sandwich panel provides a low-density honeycomb core and provides benefits of small size and large bend stiffness.

D:\binu\Documentation\Fiber alignment\classification.jpg

Fig 1.2: Classification of natural and Man-made textile fiber

For example, the tree is made up of cellulose fibers in a matrix of lignin. This provides the strength to the tree if the grain is in a particular direction it increases the strength of the wood if the grain across the tree then it reduces the strength of the tree. This is an example of the natural composite materials. The man-made composite material is glass or carbon fiber in a plastic resin. The resin is either made up thermoset or thermoplastic materials. The carbon fiber and glass are stronger than the plastic matrix. This cause the stiffness and strength to the manmade composite materials which is illustrated in fig1.2. The dry carbon fiber and the wet resin are used for manufacturing the composite material. The resin also gets solidified when it is subjected to the heat during the manufacturing process.

D:\binu\Documentation\Fiber alignment\Classification of Composites.jpg

Fig 1.3: Classification of composite Material

The composite material further classified into Reinforcement, Perform and matrix which is illustrated in fig 1.3. Based on the requirement, the composite materials will be created with different combinations.

D:\binu\Documentation\Fiber alignment\images\fig2.JPG

Fig 1.4: Classification of Reinforced composite

The Reinforced composite is classified into Fiber and self which is illustrated in fig 1.4. This diagram explained the fiber matrix interface difference between the fiber-reinforced composite and Self-reinforced composite.

D:\binu\Documentation\Fiber alignment\images\composite-materials-20-638.jpg

Fig 1.5: Classification based on Matrix

Matrix is a monolithic material where reinforcement get integrated with it. In matrix from any point, we can set a path for the material. The matrix is a lighter steel along with aluminum, magnesium or titanium this presents help to the reinforcement. Cobalt and cobalt- nickel alloy is common in a high-temperature application. In above fig 1.5, the matrix material classification is illustrated where it further divided into PMC, MMC, and CMC. The PMC is divided into Thermoset, Thermoplastic, and Rubber.

The function of a matrix

· Matrix has to hold the fibers together

· The distribution of the load among the fibers, this will reduce the strain of the material

· It enhances the transverse properties for laminating propose

· It should protect the fiber from the environment

Factor consider for selecting a matrix

· Life expectancy of the matrix should be high

· Smoke requirement

· The matrix should withstand different conditions such as temperature, humidity, UV exposure, Chemical exposure, abrasion by dust particles.

D:\binu\Documentation\Fiber alignment\images\Composite-material-with-fiber-and-matrix.png

Fig 1.6: Combination of Matrix and fiber Materials

In fig 1.6, show the normal view of the composite material where fiber and matrix get combined together and provide rigidity to the surface which is illustrated in fig.

D:\binu\Documentation\Fiber alignment\images\cm1.gif

Fig 1.7: Evaluating the elastic properties, yield strength and density of isotropic matrix and isotropic fiber

In fig 1.7, the isotropic matrix and isotropic Fiber’s mechanical strength is evaluated based on its elastic properties, yield strength and, density.

D:\binu\Documentation\Fiber alignment\images\Density-properties-in-Natural-Fiber-Composite-Materials.png

Fig 1.8: Evaluating the density of the different fibers

Types of Fibers

· Glass Fiber

· Kevlar Fiber

· Carbon fiber

· Extended Chain Polyethylene Fibers

· Boron Fibers

· Ceramic Fibers

Factor that affects the mechanical performance of the composite materials

The composite material depends upon the belongings to reinforcing and the matrix phase. There are some widely used terminologies in the composite materials they are,

· Staple fibers- It represents the discontinuous fiber

· Filament- It refers to the single continuous fiber

· Strand- represent the unwind fibers approximately 100 to 200 in numbers

· Tow- represent the unwind fibers in big number approximately 2000 to 12000 in numbers

· Yarn- Bundle of wind fiber

· Size –Thin coating provided to the surface of the filament which prevents the fiber from damage and environmental effects.

· Coupling agents- provide good connecting between fiber and matrix

Factor controlling the property of the fibers

· Length- the length of the fiber may be tall or shortened. The tall fiber can able to orient and process whereas shortened fiber can’t able to control proper orientation. Compare to the shortened fiber, tall fiber provides more benefits. It consists of tensile strength, effect resistance, low shrinkage, and dimensionality stability. However shortened fibers are easy to fabricate and low in price.

· Orientation- The orientation of fibers decides the stiffness and strengthens of the material. If the fiber oriented in one direction then it provides strength in that direction. Consider a mat it has a high stiffness and strength in numerous direction due to its fiber orientation.

· Shape- Most of the fibers is manufactured in a circular shape. But the fibers are available in different forms such as square and rectangle.

· Materials- The base of the composite fiber is materials if the materials not in a proper manner then it affects the mechanical performance of the fiber. Generally right fiber ought to have excessive elastic moduli and strength than the matrix material. It additionally affords some useful properties including high thermal resistance, fatigue resistance, and impact resistance.

· matrix elements- matrix fiber have low mechanical properties.

Fiber matrix Interface

When the load is applied to the composite material then the load is carried by the matrix and switch to the fibers via the fiber-matrix interface. This interface created based totally on chemical, mechanical and response bonding. Maximum of the instances, more than one kind of bonding occurs.

Chemical Bonding- In chemical bonding coupling agents are used to couple the matrix and the fiber. Coupling agents are chemical bonds which are added over the surface of the material.

Mechanical bonding- the mechanical bonding is done by interlocking the fiber and the matrix. Every material has a roughness over the surface which is utilized for this kind of bonding.

Reaction Bonding-During the interface the molecules of the fiber and the matrix are bond together. But using the reaction bonding, it creates a thin layer and it can cause cracks in further, these cracks may affect the strength of the fibers.

Fillers

The fillers are the solid materials which improve the physical or functional property of the materials. It reduces the cost of the material. It normally increases the modulus and reduces the strength of the materials, there always be optimal filler content. Filler doesn’t react with the matrix material, which creates an adequate bond between the matrixes. Filler doesn’t absorb any liquid items. In advanced materials no one use fillers. If we are supposed to use fillers it can reduce material strength. Better need avoid fillers.

Example for fillers is polyester resin and epoxy resin.

Additives

The additives are added to the polymer matrix for altering some properties of the materials. The additive doesn’t affect the mechanical property of the material because it gets added as a small quantity.

Pigments

The composite products are created by adding the pigments with the materials. There are two types of pigments organic and inorganic materials.

Fiber Reinforced Polymeric Composite

Fiber Reinforced Polymer Composite is also known as FRP which is one of the most widely used composite material. It utilizes one or more discontinuous phases which integrated into the continuous phase. The specific gravity ranges between 1.2 and 1.5. Matrix is used as a continuous phase.

Reinforced material or fiber is used as a discontinuous phase. It is so stronger than the matrix. It provides high modulus and stiffness and high strength.

The density of the different fiber is evaluated in fig 1.8. Through this analysis, we can understand the highest and lowest density of the different fibers which can be utilized for making the composite materials.

D:\binu\Documentation\Fiber alignment\images\v.jpg

Fig 1.9: Evaluating the different parameters for the different fibers

The different parameters are evaluated for different fiber which is depicted in fig 1.9. The density, tensile strength, Young modulus, Elongation at break, specific tensile strength, and specific young modules. From this, it is easy to analyze the suited fiber for producing the composite material.

The standards propose alignment with rules and rules for the surroundings, protection issues. There are numerous opposing elements that needs attention, consequently optimizing a stabilized solution that meets earlier than the layout is tested a success for provider.

a. Lightweight

Minimizes greenhouse gasoline production and increase fuel efficiency for automobiles. For each 10% of weight decreased from a automobile, a total weight of advanced gas financial system is recorded at 7%, main to a kilogram of weight loss in a automobile

According to 20 kg of carbon dioxide reduced

b. Cost

Cost is a standout amongst the highest essential factors that investigate and decides whether any new material included in vehicle components. Cost consists of three kind of variables and they are the cost of raw material, manufacturing cost, and cost to design and test.

c. Safety and crashworthiness

The ‘‘crashworthiness’’ of the structure in a vehicle is the ability to withstand and survive impact energy applied for the crash test.

d. Recycling and life-cycle considerations

Securing nature builds focus of pollution and decreased impact of co2 emissions’, with ‘recycling’ being issues earlier than inclusion into the car components.

1.4 Fiber Alignment

(a)

(c)

(b)

Fig 1.10: Evaluating the density of the different fiber

In fig 1.10, a represent the fiber which is aligned and continuous, b represent aligned and discontinuous and c represent random continuous of the fiber. If the fiber is taller than the critical length then it can withstand the load applied over it. The entire load is distributed among the matrix to the fibers. If the fiber is shorter than the critical length then it can hold and transmit only some of the load over it. The fiber length is greater than 15times the critical length then it is considered as an optimal one. Normally aligned and continuous fiber provides an effective strength to the fiber composites.

D:\binu\Documentation\Fiber alignment\image7.png

Fig 1.11: Angle vs Tensile strength

The graph is plotted between the angle between fiber and stress with the tensile strength which is depicted in fig 1.11. From this, it is analyzed that the alignment of fiber determines its tensile strength of the material. If the fibers aligned horizontally then the tensile strength is less whereas the vertical alignment of the fiber improves the strength of the composite materials.

Over view-Short fiber alignment

Polymer composites with oriented fibres have high reinforcement performance. Commonly, fibre reinforcements are both in regular or irregular shape. Non-forestall fibrereinforced composites carry out better because of the non-stop load course and fibre continuity also lets in clean alignment within the favored path in comparison to short fibres [21].

But, irregular fibre reinforced polymer composites have become extra appealing with majorbenefits together with the potential to fabricate complicated structural factors due to their higher ductilityin all direction [21,2 2]. There are considered one of a type strategies created via experts so that you can manufacture aligned brief fibre bolstered polymer composites (sfrpcs). Those strategies may be substantially labeled as wet techniques and dry procedures [23]. Generally, within the former, fibres are suspended in a liquid medium and are forced through a converging nozzle for fibre alignment alongside the fluid go with the flow path [22,2 4] whilst inside the latter, generally, dry fibres on the aspect of polymer powder are aligned thru electric or pneumatic manner to shape the aligned fibre preforms. Despite the truth that dry alignment techniques reap quicker production quotes and control over orientation of fibres, the degree of fibre alignment acquired has been higher with moist alignment techniques [22, 23,2 5]. These days, growing environmental troubles have recommended traits and usage of brief natural plant fibre polymer composites (snpfpcs) with true mechanical residences (precise energy and unique stiffness) [26]. Similar to artificial short fibre polymer composites, the aligned snpfpcs display off higher mechanical homes even as the fibre is aligned to the loading route. However, acquiring alignment with short herbal fibres is greater complicated than with quick artificial fibres due to their variability in diameter alongside their duration. This paper provides an define of the principle alignment strategies for sfrpcs described in the literature and also describes a currently followed alignment technique i.E. Dynamic sheet forming which has been employed correctly to offer aligned natural fibre mat. Those aligned mats may be incorporated with polymer matrices to fabricate aligned snpfpcs.

2.Literature Survey

C.J Creighton et al [1] proposed a method for analyzing the characteristic of fiber alignment in composite material where image get analyzed based on the low magnification micrographs and evaluate the direction of fibers by the direction of expanded light and dark features. They utilized 7µm diameter based fiber for this analysis. It well suited only for a composite material which showing long-range spatial variation in the waviness. They used counter map for display this result. Tom et al [2] put forth a paper where he overviews the alignment of short fibers. He analyzed that the wet process-based manufacturing provides a high degree of alignment. In this method, he found that the dynamics sheet forming (DFS) is a method to align the fiber mat with the natural fiber. Till many method types of research are carried out to improve the alignment of fibers in fiber mat. Potter et al [3] proposed a method for manufacturing the aligned discontinuous fiber composite. This method utilizes low viscous medium such as air and orientation head which consist of a parallel plate with the narrow gaps. It can produce a highly aligned short fiber composite materials.

Pickering et al [4] proposed a method to review the development in natural fiber composite and their mechanical performance. In this paper, they viewed on the improving power, stiffness, performance. Aruan et al [5] studied the Structure and mechanical performance of PLA reinforced materials. It is found that the harakeke and hemp fiber composite volume is lower than the injected molded composites due to the better efficiency. This efficiency is due to the proper fiber alignment. LE et al [6] analysis the high performance of aligned short fibers. These composite materials attain a high tensile property due to the addition of epoxy resin in it. HeyiGe et al [7] proposed a method to establish the properties of the water-soluble of the carbon fibers. Raja et al [8] evaluate the mechanical properties of the fiber reinforced composites. This paper showed that the natural fiber reinforcement for polymeric composite provides positive feedback over the mechanical behavior of the polymers. Byoung-Ho et al [9] put forth a paper for fabricating long and discontinues fibers where the natural fibers get combined together and form the biocomposite materials. The carding and punching method is used to manufacture the bio-composite through compression molding. It is understood that the too shortened fibers may affect processing of carding operation. Mustafa et al [10] proposed a method to select and verify the kenaf fibers by weight decision matrix. It understood that the kenaf fiber is cheapest compared to the other natural fibers. Zini et al [11] proposed a review of the green composite materials. The green composite is lightweight in nature and it can be used from waste materials also. Hoi et al [12] proposed a paper where usage of the bio-degradable composite to provide a safe environment for some extends. The bio-engineering and bio-medical field the natural fiber gets integrated with bio-degradable and bio-resorbable polymers which can be used to treat the patients who are all affected by joint and bone fractures. Madsen et al [13] proposed a paper to evaluate the physical and mechanical properties of the one directional plant fibers. Here composite porosity content and fiber anisotropy are mixed in a correct manner which improves the axial property of the material. Joshi et al [14] proposed a method to analyze the natural fiber composite is superior to the glass fiber reinforced composites. It is analyzed that the natural fiber composites are cheaper and lighter in nature. Harper et al [15] proposed a paper to predict the mechanical property of carbon fiber. Kongkew et al [16] proposed a paper where he analyzed the different orientation pattern of the fibers. They are random, continuous unidirectional and weaving patterns. The adhesion between the fiber and the matrix were analyzed through a scanning electron microscope. It showed that the weaving pattern provides a good performance than the continuous unidirectional and randomly oriented fiber composite. Sriyono et al [17] analysis the fiber orientation and the volume fraction in composite ramie fiber. Ozarslan et al [18] proposed a paper on generalized diffusion tensor imaging. Maria et al [19] proposed a method for estimating the 3D fiber orientation in volume images, where analysis takes over for fiber data sets and fiber-based materials. Bakir et al [20] proposed a method to analyze the effect of fiber orientation for fiberglass Reinforced composite materials on mechanical properties where they use 45-degree alignment for glass fiber which provides good tensile strength for the materials. [27] many researchers founded that the orientation of fibers had a main characteristic in growing some houses, in this field. [28] express that it developing the creep resistance. Lee & jyongsik [29] said that as fiber content material multiplied, the tensile and flextural modulus of the glass fiber composite confirmed a linear increment. N. Rajesh mathivanan j. Jerald [30] have a look at effect reaction of woven glass fiber epoxy matrix composite laminates. Salah s. Al-rawi [31] have a examine a pattern of glass fiber strengthened epoxy composite modified into subjected to a tensile load to observe the impact of fiber instructions at the tensile elasticity theoretically best by using the use of finite detail technique (fem). Ahmad bakhtiar b. Mukhtar [32] examine the mechanical properties of epoxy resin bolstered coconut fiber. and describes the effect of construct orientation or affiliation parameters primarily based on tensile finding out of the process situations on this critical composite function, it modified into decided that the addition of the coconut fiber into polymer matrix had elevated the tensile electricity of the composite. However, the tensile strains of the composites are diminishing while the fiber is covered into the polymer grid.

3.Proposed Work

3.1 Frame work

In proposed framework comprises of a number of steps there are RGB to Gray conversion, Binary image, Edge detector, Hough transform and Angle distribution.

Input Image

Binary image

RGB to GRAY conversion

Edge Detector

Hough Transform

Angle Distribution

Fig 3.1: Block diagram of the Proposed Method

3.2 Description

The input images get fetched into the workspace through imread command. The input images get converted into a grayscale image. After that, the morphological operation is taking place on the Grayscale image. Then the picture is changed into a binary picture using threshold value.

The Sobel operator is need to detect the edges in the binary image. Now the edges of the image are detected which is subjected to the Hough transform. The Hough transform image is displayed in a specified color where the longest fibers are highlighted. Finally, angle distribution is evaluated from the final image. This angle distribution displays the alignment of the fibers in an image which is depicted in fig 3.1.

3.3 Input Image

Here the input image is a fiber-based image which fetched into the workspace of the Mat lab through reading command. Normally imread is used to study the input image from the source file to the workspace of the Mat lab. Let Iin be the Input image.

Iin=Input image;

3.4 Conversion of RGB image to GRAY image

RGB image also called true color image which saved in Mat lab in m-by-n-by-3 format. This data array format defines its red, green, blue color components of each individual pixel in the image. This RGB image does not use the palette. The color of any images determined based on this color combination. The color of each pixel decided by red, blue, green intensities which are saved in the color panel at pixel’s location. Graphic based RGB images are 24-bit images where each color components occur 8-bits. The RGB MATLAB array consists of double, uint8 or uint16 classes. Normally the pixels whose color is 0 it produces a black color whereas 1 produces a white color.

Gray Scale images represent only the amount of light over it during the image capturing period. It only contains the intensity information. It is a kind of black and white or gray monochrome where represented as shades of gray. The contrast range of the fray image ranges from black to white where black possess the weakest intensity and the white possess the strongest intensity.

In RGB to gray conversion, the rgb2gray function eliminate the hue and saturation information of input image and retains the luminance intensity of the image. The matrix value consists of 0 and 1 values for grayscale images. The input Image I get converted to gray image (Igray).

3.5 Binary Image

The pixels of the binary images consist of two possible components are black and white. The color in the binary image is classified as foreground and background color. It is also called bi-level or two-level. Each pixel is stored as a single bit i.e. 0 or 1. Mostly binary images are used for segmentation, thresholding and dithering operation. The im2bw change the grayscale image into a binary image based on the threshold value. The Igray image is converted into Ibw.

3.6 Edge Detector

The sudden changes or discontinues of the images called edge detector. It classified into horizontal, vertical and diagonal edges. The edges contain the shape information of the images. The edges are detected using filters and then enhancing and sharpening the images. Prewitt Operator, Sobel Operator, Robinson Compass Masks, Krisch Compass Masks, Laplacian Operator are some of the masks to detect the edges. Sharpening is opposite to the blurring where edge content gets increased and decreased. The sharpening increase the edge content, in order to rise the edge content the edges has to detect properly. Using above mentioned any method we find detect the edges and then sharpened the images. Let the Edge detector output be Iline.

3.7 Hough Transform

The analysis of any digital image, it is difficult to detect the shapes in the images. The shapes may be a line, circle, ellipse etc. The edge detector is used to detect the edges of the images which are processed in pre-processing step. The pre-processing step obtains the image points or image pixels which is available from the image space. Sometimes due to the imperfection in the input images or edge detector, there may be some errors in the image points or image pixels, it leads to provide an inappropriate output which causes a spatial deviation between the ideal data and the obtained output. This problem can be overcome by the Hough transform where the edge points are grouped as object candidates by operating the voting procedure over a set of parameterized image objects. Normally the straight line is represented as y=mx+b where (b, m) is a point in the parameterized space. Through this equation, it is easy to detect the straight line. In Hough transform the image is represented as H.

D:\binu\Documentation\Fiber alignment\images\hough02.gif

Fig 3.2: Conversion of image domain to Hough domain

In fig 3.2, the input image gets converted into the Hough image. The lines and points are evaluated and the edges were detected and without losing any data it gets transform to Hough domain.

3.8 Angle Distribution

In angle distribution, we can see the angle position of each fiber in the images thereby detect the alignment of each fiber in the image.

3.9 Algorithm

Here algorithm is used to detect the straight lines through some following steps they are

• The edge detector is want to analyze the edges in the image- canny edge detector

• The mapped edge points are transformed into the Hough space and stored in the accumulators

• It is necessary to assume the length of the line which gets stored in the accumulator

• The interpretation is carried out by the threshold method or other constraints

• The process of converting infinite line to finite line

• Then the finite line can be superimposed into the original input image

3.10 Hough space Accumulator

The accumulator determines the area where the Hough space lines are intersecting more. The edge points of the image are transformed where bins in the accumulators are get incremented for each line which passes through the points. The resolution of the accumulator regulate the line which detected in a precise manner. The size of the accumulator array gets increased based on the number of parameters involved in the process.

3.11 Methodology

The Hough Space - Representation of Lines in the Hough Space

The lines in the Hough space represented in two parameters they are a and b which is equated in equation 1.

In order to represent the vertical line, it equated in equation 2 and 3. The parameter θ and r determining the angle of line and the distance from the line to the origin respectively.

All lines can be represented in this form when [0,180] and r R(or) where and r represent as dimensions of Hough space.

D:\binu\Documentation\Fiber alignment\Mapping-of-one-line-in-Cartesian-space-to-a-point-in-the-Hough-space.png

Fig 3.3: Mapping one line unique to the Hough space

The line to point mapping illustrated in fig 3.3. The first step in the mathematical calculation of Hough transform is to represent the line as a single point, without losing any data from it.

D:\binu\Documentation\Fiber alignment\hough_mc_space.jpg

Fig 3.4: Lines to Points

The xy and mc space is illustrated in fig 3.4 where clop and intercept are calculated through the graph representation. The above figure mentioned that the every line is consist of two quantities there are slope and intercepts. Through this it is easy to describe the complete data of the single line.

D:\binu\Documentation\Fiber alignment\hough_mc_space_point1.jpg

Fig 3.5: Point to Lines

Figure 3.5 represents the analyzing of the point to lines where x and y are the points in the xy space. The point in the xy space is equal to the line in the mc space which is calculated through the equation c=-xm+y;

D:\binu\Documentation\Fiber alignment\1-1.jpg

Fig 3.6 : Mapping of lines to point

The Line get converted into points in Hough space where get calculated which is illustrated in fig 3.6.

D:\binu\Documentation\Fiber alignment\hough-2point_transform.png

Fig 3.7 (a) Transformation of double points (p0, p1) to lines in the Hough space. The Hough space represents all the possible lines through p0 and p1.

The input image consists of two points where each point get converted into lines in Hough space where most Hough space lines intersect is interpreted as true lines in the edge map which is depicted in fig 3.7.

D:\binu\Documentation\Fiber alignment\line2.jpg

Fig 3.8 Principle of the Hough transform. Individual points in (x,y)-space are represented by lines in Hough space. If all points lie on a line y = Mx + N, all lines in Hough space will meet at point (M,N).

These diagrams represent the multiple lines which have a common direction this cause the junction of the lines together in the Hough space which is illustrated in fig 3.8. The Hough transform is to convert the points into the parameter space. The Line in the Cartesian (x,y) co-ordinate system explained in the equation

Where m and n are slope and intercept of the line. Each line is separately identified by the value of m and n in it.

3.12 MATLAB Software

MATLAB mostly used for technical computing where high-performance languages are utilized to perform the operations. It can provide a proprietary programming language which is developed by Mat work. Normally mat lab allows to calculating the matrix manipulation, plotting of function and data, implementing the algorithm and creating a user interface environment. The program in Mat lab can be done using an inbuilt function or by math calculation. The mat lab also supports some other languages such as C, C++, Java C#, Fortran and Python. Usage of the Mat lab includes they are,

● Math and computation

● Algorithm development

● Modeling, simulation, and prototyping

● Data analysis, exploration, and visualization

● Scientific and engineering graphics

● Application development, including Graphical User Interface building

● An interactive numerical computing environment

● Matrix Computations

● Graphics

● Programming (M-files)

● Toolboxes (signal processing, statistics, optimization, symbolic math)

The Mat lab is n interactive system where data get stored in the form of an array which doesn’t require any dimensions for this process. The matrix and vector formulations based problems have occurred which can be easily solved out by writing a program in C or Fortran.

In Mat lab, a user can utilize a toolbox in it which allows the user to learn and apply the specialized technology. The m-files is used to store the files in the mat lab. Normally signal processing, control system, neural networks, fuzzy logic, wavelet, simulation etc these are the area where utilizing the toolbox.

3.13 Starting MATLAB:

Here in we used (MATLAB 2014a) version for coding, the Mat lab major tools are

· The Command Window

· The Command History

· The Workspace

· The Current Directory

· The Help Browser

· The Start button

3.14 Applications of MATLAB:

· Mathematical Calculations

· Data Analysis & Visualization

· Software Development

· Simulation

4. PROJECT MANAGEMENT

Project Management covers in usage of various principles, procedures, and policies which a necessary tool to guide a project from its conception stage to the completion stage. If the project without any planning and organization then it leads to the failure result. This management skill improvises time management skill of each person who is involving on the project creation. The project management enhances the individual’s leadership skill, strategic alignment, clear focus and objectives, project planning, Quality control, Risk Management, Orderly process, and continuous oversight.

4.1 Gantt chart

D:\binu\Documentation\Fiber alignment\7 feb\Project Outline.png

Fig 4.1: Gantt chart

Gantt chart is a prominent tool in project management which shows the activities and task worked against time. It is also called visual presentation of the project where the activities are broken down and display on the chart. It is easy to understand the implementation of the project.In simple Gantt chart is a horizontal bar which visually represents the project plan over time. We prepared the project in the time duration of Dec 15-20. We analysis many works and started to develop the project from Dec 21 to Jan 19. We initially prepared the first two modules of the project at the period of Dec 22-Dec 31. Final module gets completed on Jan 17. The report work started on Jan 21and continued till Jan 28. We execute the project on Jan 30.

5. Experimental Results

5.1 Experimental Results and Discussion

In this section, we discussed the experimental results and analysis take over on the fiber composite material. This discussion compares the efficiency of our proposed system with the existing system. Result images are displayed in this section from fig 5.1 to fig 5.7. In all method for image processing, they use mat lab as a system for analyzing the problem and providing the solution for it. In our proposed system we used MAT LAB 2014a is used. In MATLAB, it is easy to test any algorithm immediately without any constraint. For quick analysis, we can check in the command line which helps the researcher to test the algorithm in a fast manner. It also creates a good interactive environment for users. Here we used composite fiber as an input image. We took six images of the fibers and measure the angle distribution of it. The analysis of six images provides a different output through which it is understood that the angle distribution of fiber gets differ for each fiber. The result of the angle distribution is tabulated for different input images.

Fig 5.1: Input Image

The experiment is conducted between two test images for calculating the angle distribution of the fiber in the composite material which is illustrated in fig 5.1.

Fig 5.2: RGB to Gray Image

In order to reduce the difficulties in the calculation and reduce the complexity of the code, because RGB image consists of three different values based on the color components. But the grayscale image provides only 0 and 1. So it easy to calculate the value in the process.

G (i, j) = 0.2989 * R(i, j) + 0.5870 * G(i, j) + 0.1140 * B(i, j);

Based on the equation the conversion process is carried out in the MATLAB where the coordinates of each component are measured and determine the value for Grayscale images without losing any data the RGB images get converted into Gray image which is depicted in fig 5.2

Fig 5.3: Gray to Binary Image

Then we have to find the edges of the images, these edges stored all the data because this edges are the connectivity in the images. It is necessary to find the edges for that the gray scale image. This can be done by converting the gray scale into binary image which is illustrated in (fig 5.3). Converting the Gray image into a binary image using a pixel value of the gray image. Then the threshold value is calculated for the gray image. Based on the threshold value the image gets converted into a binary image. Now the image consists of foreground and background images with the lines and borders in it.

Fig 5.4: Edge Detection of Image

Sobel operator is used as an edge detector which detects the edges of the fibers in the images which is depicted in fig 5.4. Compare to other operators Sobel provides a great accuracy in detecting the edges in the images. The sobel operator provides either corresponding gradient vector or normal to the vector at each pixel of the image. It computes the gradient magnitude and direction of the input image. The sobel operator uses 3*3 two kernels they are, And E

Compare to other operators it is less sensitive to the noise. So the edges get easily detected through these operators.

Fig 5.5: Hough Transform

The Hough transform use to represent the line:

D:\binu\Matlab\pic6.jpg

Where is the distance between the origin to the line along the perpendicular direction. The angle of is

Here we represent the Hough transform of

The number of is calculated based on the resolution parameters. Then the rows and column value is calculated.

Where -values range from -diagonal to diagonal

n = length()

Hough transform is applied on fig 5.5 and the lines are converted into points which holding all the valuable information. This process where takes place in Hough space.

Fig 5.6: Highlighting the longest line in the Binary image

In order to see the longest fibers, we highlight the longest fiber with a different color in fig 5.6. This help the researcher or user can visualize the longest fiber in the composite material. The red colored small blocks represent the longest line in the materials which is displayed in fig 5.6. From the above-mentioned figure, it is analyzed that there are many long fibers and small fibers are available in the given image, it is clearly understood from the figure that the longest fibers are marked as red in the image and fibers are marked as green in the image.

After that we have to find the angle distribution of each fiber in it, each fiber alignment is represented in fig 5.7. It is also analyzed that the fiber orientation in the horizontal or vertical direction. Through this discussion, it is understood that the alignment and direction of the fiber have to be studied to develop or manufacture of any composite material at any condition.

Fig 5.7: Final Output- Angle Values

The above test figure explained each process in detailed manner. Similar to above figure we took additionally five test images and evaluate the angle distribution for each images.

5.2 Parameters in the calculation:

Hough Transform is normally use to detect the lines in the images.

5.2.1 Theta(θ)

Theta is used to represent the angular position of the vector. It is also defined as the calculation of the declined angle in the passage of time. Theta normally displays the angle values of the lines in the images. It displays the vector of Hough transform. The theta value is calculated for the outer value of the output matrix (H). Theta value is from -90°≤θ<90°. The default value will be -90:89.

5.2.2 Rho (ρ)

Based on the values of ρ and θ the Hough matrix is created from the edge detected image.

5.2.3 Threshold

Nonnegative scalar value that point out the threshold at which values of H are considered to be peaks. The threshold can vary from 0 to Inf. Default is 0.5*max(H(:)).

5.2.4 NHoodSize

The 2-element vector of high quality atypical integers: [M N]. 'nhoodsize' specifies the dimensions of the elimination community. This is the neighborhood round every top this is set to 0 after the height is recognized. Default: smallest peculiar values more than or equal to length (h)/50.

5.2.5 Direction

It is a representation of the angle position in a horizontal or vertical direction.

5.2.6 Is packed

IM is treated as a packed binary image as produced by bwpack. IM must be a 2-D uint32 array and SE must be a flat 2-D structuring element. If the value of PACKOPT is 'ispacked', PADOPT must be 'same'.

5.2.7 Strel

It creates the morphological structure element for the given image. It consists of the flat and non-flat structuring element. The flat structure element is arbitrary, pair, diamond, periodic line, disk, rectangle, line, square, and octagon. Non-flat elements are arbitrary, and ball.

5.2.8 Peaks It generates the peak values in the Hough matrix which is evolved by the hough functions. The numpeaks is a scalar value that find the maximum number of peaks to identify. If you omit numpeaks, it defaults to 1. The function returns peaks, a Q-by-2 matrix, where Q can range from 0 to numpeaks. Q holds the row and column coordinates of the peaks.

5.2.9 Hough lines

It extracts the road segment from the pics in which bw related to specific packing containers in a hough remodel. Theta and rho are vectors again with the aid of function hough. Peaks is a matrix back with the aid of the hough peaks characteristic that includes the row and column coordinates of the hough remodel packing containers to apply in attempting to find line segments.

The hough strains characteristic returns strains, a structure array whose period equals the wide variety of merged line segments located.

Element vector [X Y] specifying the coordinates of the give up-point of the line segment

5.2.10 Fill Gap

Positive real scalar value that specifies the distance between two line segments associated with the same Hough transform bin. When the distance between the line segments is less the value specified, the Hough lines function merges the line segments into a single line segment. Default: 20

5.2.11 MinLength

Positive real scalar value that specifies whether merged lines should be kept or discarded. Lines shorter than the value specified are discarded. Default: 40

5.2.12 Norms

norm(X) returns the 2-norm of input X and is equivalent to norm(X,2). If X is a vector, this is equal to the Euclidean distance. If X is a matrix, this is equal to the largest singular value of X.Determine the endpoints of the longest line segment The endpoint of the line segment is calculated by the max length of the line and surface area of the image.

5.3 Test images and its angle distribution values:

(a) (b)

(c) (d)

(e)

(f)

(g)

Fig 5.8 Test Image 1,

(a) (b)

(c) (d)

(e)

(f)

(g)

Fig 5.9 Test Image 2

(a) (b)

(c) (d)

(e)

(f)

(g)

Fig 5.10 Test Image 3

(a) (b)

(c) (d)

(e)

(f)

(g)

Fig 5.11 Test Image 4

(a) (b)

(c) (d)

(e)

(f)

(g)

Fig 5.12 Test Image 5

(a) (b)

(c) (d)

(e)

(f)

Fig 5.13 Test Image 6

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.14 Test Image 7

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.15 Test Image 8

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.16 Test Image 9

(a) (b)

(c) (d)

(e)

(f)

(g)

Fig 5.17 Test Image 10

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.18 Test Image 11

Angle distribution of Test images

Test Image1

84

31

0

84

87

81

30

-3

3

Test Image2

-90

-90

46

89

89

46

-87

47

-90

Test Image3

-90

-90

-51

0

-51

-54

-48

87

-87

Test Image4

-90

-90

0

0

0

0

0

0

-90

Test Image5

0

0

Test Image 6

-90

Test Image 7

0

Test Image 8

-90

0

0

0

0

-90

0

0

-89

Test Image 9

0

0

1

1

Test Image 10

-90

-90

Test Image 11

-45

-45

4

-53

-4

4

-88

-49

-42

Table 5.1

From table 5.1, the angle distributions of the different shapes are evaluated and the values get tabulated.

5.4 Fiber as Input Image and its angle distribution values:

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.19 Fiber Test Image 1

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.20 Fiber Test Image 2

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.21 Fiber Test Image 3

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.22 Fiber Test Image 4

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.23 Fiber Test Image 5

(a) (b)

(c) (d)

(e)

(f)

(g) Fig 5.24 Fiber Test Image 6

Angle distribution of Fiber Test images

Fiber Image1

-90

88

-89

-87

-81

87

-90

-82

80

Fiber Image2

0

-11

3

-14

-2

0

73

-3

0

Fiber Input Image3

0

-4

5

5

-3

-2

-2

-6

-1

Fiber Image4

-90

89

87

-90

-80

-84

85

-88

-84

Fiber Image5

1

0

-1

2

-9

-10

5

6

-11

Fiber Image 6

-85

-89

88

-88

-88

85

-90

80

89

Table 5.2

After the evaluation of the six test images, we obtained an angle distribution of the fibers. It is analyzed that the number of fibers aligned in a vertical and horizontal direction. The fibers aligned in the same direction will provide rigidity to the composite materials which are tabulated in Table 5.2. During the analysis and test process, it provides 100 data for each image. Among them, the first ten data get tabulated in the table. As already mentioned the orientation of the fibers plays a vital role in providing the mechanical strength to the composite materials. The alignment of each fiber should be the same direction, this causes the rigidity and stiffness to the materials. Consider the Test Image 6 where the fiber get aligned in the horizontal direction where all the fibers are aligned in the horizontal direction this provides good mechanical strength to the composite materials. Based on the alignment and compactness of the fibers create a good tensile strength to the materials.

Test image as input

Images

Point1

Point2

theta

rho

Test image1

[3,157]

[70,150]

84

155

Test image2

[121,79]

[289,79]

-90

-78

Test image3

[12,130]

[163,130]

-90

-129

Test image4

[21,211]

[26,211]

-90

-210

Test image5

[5,1]

[5,187]

0

4

Test image6

[1,190]

[185,190]

-90

-189

Test image7

[2,1]

[2,205]

0

1

Test image8

[36,10]

[225,10]

-90

-9

Test image9

[4,4]

[4,261]

0

3

Test image10

[1,115]

[365,115]

-90

-114

Test image11

[207,15]

[210,17]

-45

136

Table 5.3

Fiber image as input

Images

Point1

Point2

theta

rho

Fiber image1

[28,66]

[34,66]

-90

-65

Fiber image2

[7,139]

[34,141]

-85

-137

Fiber image3

[138,1]

[138,32]

0

137

Fiber image4

[256,5]

[256,37]

0

255

Fiber image5

[65,80]

[108,80]

-90

-79

Fiber image6

[12,162]

[24,163]

-88

-161

Fiber image7

[213,1]

[213,4]

1

212

Fiber image8

[167,18]

[167,58]

0

166

Table 5.4

The angle distribution of the two images is evaluated in table 5.1 and 5.2. The lines parameter is evaluated using the equation where point1, point2, theta, and rho is determined and tabulated in table 5.3 and 5.4. These two tables are compared based on the values and evaluate the better performance between the test image and fiber image. By comparing the angle distribution, theta and rho value it is understood that the fiber-based input image provides a good accuracy than the shape based normal input images. The fiber alignment calculation plays a vital role in this paper, the alignment of the fiber is easily calculated through the fiber-based image. The fiber input utilized the Hough transform in a better manner than the normal input image.

5.5 Benefits of the Proposed System

· By analyzing the orientation of the fiber, it is easy to meet the application requirement

· The mechanical strength of the composite material get calculated easily

· The long fibers and short fibers approximation can be evaluated in the composite material through the MATLAB analysis process.

· Future enhancement can be done for aligning the fiber in a specific direction.

6. Conclusion

In this paper, wide research and analysis are carried out for evaluating the orientation of fibers in composite materials which increase and decrease the performance and mechanical strength of the material. The composite materials are utilized in a different application, different appliances are build using this concept. So it is essential that the fiber should pose highly tensile strength and rigidity or else it is necessary to find the good tensile based fiber for manufacturing the composite materials. The main objective of this paper is to obtain the Angle distribution of the fiber through the Hough transform method. The Hough transform estimates the line and point value and determines the angle and position of the fibers in the composite material. Through this analysis, we can improve the stiffness and tensile strength of the reinforced composite material. This scrutiny provides a good result compared to the traditional method. By examining the orientation and angle of the fibers we can increase the quality of the products in the future. In Angle distribution, the fiber orientation is calculated for each test images, the data are check for six different test images. From the table itself it is easy to understand the fiber angles. We can implement the manufacturing equipment which can detect this angle position and then using those fibers for creating composite materials. Thereby we can distribute the load equally among the materials and improved the mechanical strengths. Our proposed method provides a promising solution for enhancing the mechanical strength of the composite material through a Hough transform.

7. Future Work

Fiber orientation and alignment of the composite material influences the load manipulation. To enhance this alignment of the fibers we can integrate the proposed method with comprehensive image analysis tool (AFM). AFM is developed as a MATLAB package which is a standalone application where a researcher can easily analysis the structural parameters of the composite material. Atomic force microscopy (AFM) is utilized for promoting the angle of fibers, it can be visualization at each stage of processing. By this combination, we can upgrade the research work to the next level.

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Binary Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-300

-200

-100

0

100

200

300

00.20.40.60.81

0

0.5

1

1.5

2

2.5

3

3.5

4

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-400

-300

-200

-100

0

100

200

300

400

-91-90.5-90-89.5-89

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-400

-300

-200

-100

0

100

200

300

400

-100-50050100

0

10

20

30

40

50

60

70

80

90

100

(degrees)

No

Angles value

X: 243 Y: 143

RGB: 30, 24, 12

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-300

-200

-100

0

100

200

300

-100-50050100

0

10

20

30

40

50

60

70

80

90

100

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-250

-200

-150

-100

-50

0

50

100

150

200

250

-100-50050100

0

10

20

30

40

50

60

70

80

90

100

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-400

-300

-200

-100

0

100

200

300

400

-80-60-40-200204060

0

10

20

30

40

50

60

70

80

90

100

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-300

-200

-100

0

100

200

300

-60-40-20020406080

0

10

20

30

40

50

60

70

80

90

100

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-300

-200

-100

0

100

200

300

-100-80-60-40-200204060

0

10

20

30

40

50

60

70

80

90

100

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

hough transform Image

(degrees)

-80-60-40-20020406080

-300

-200

-100

0

100

200

300

highlight the longest line in Binary Image

-100-50050100

0

10

20

30

40

50

60

70

80

90

100

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-250

-200

-150

-100

-50

0

50

100

150

200

250

-20020406080100

0

1

2

3

4

5

6

7

8

9

10

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

-100-50050100

0

1

2

3

4

5

6

7

8

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-200

-150

-100

-50

0

50

100

150

200

-100-50050100

0

2

4

6

8

10

12

14

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-400

-300

-200

-100

0

100

200

300

400

-100-50050100

0

5

10

15

20

25

30

35

40

45

50

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-250

-200

-150

-100

-50

0

50

100

150

200

250

-1-0.500.51

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-250

-200

-150

-100

-50

0

50

100

150

200

250

-91-90.5-90-89.5-89

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-250

-200

-150

-100

-50

0

50

100

150

200

250

-1-0.500.51

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(degrees)

No

Angles value

Input Image

Gray Image

Binary Image

Edge detection in Image

highlight the longest line in Binary Image

hough transform Image

(degrees)

-80-60-40-20020406080

-300

-200

-100

0

100

200

300

-100-50050100

0

5

10

15

20

25

(degrees)

No

Angles value

Input Image

Gray Image

Edge detection in Image