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Advanced Aspects of Engineering Research

Vol. 3

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Advanced Aspects of Engineering Research

Vol. 3

Advanced Aspects of Engineering Research

India

.

United Kingdom

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Professor,

Department of Mechanical Engineering, California State Polytechnic University, Pomona, USA.

Email: [email protected];

FIRST EDITION 2021

ISBN 978-93-90768-20-2 (Print) ISBN 978-93-90768-21-9 (eBook) DOI: 10.9734/bpi/aaer/v3

_________________________________________________________________________________

© Copyright (2021): Authors. The licensee is the publisher (Book Publisher International).

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Chapter 1

Multiple License Plates Detection in Videos and Still Images Using Various Geometrical Properties and Filtering Techniques

Narasimha Reddy Soora

1-25

Chapter 2

Detailed Study on a Robust and Efficient Fault-Resilient Rad Hard ADPLL Varsha Prasad and S. Sandya

26-40

Chapter 3

Assessment and Prediction of Canal Erosion on Tidal Swamp Delta Telang I, Banyuasin Regency, South Sumatra

Achmad Syarifudin, Henggar Risa Destania and Yunan Hamdani

41-49

Chapter 4

Recent Advancements on Design and Development of Multi Drop Auto-Walk G. Swaminathan, S. D. Kumar and A. Mathivanan

50-58

Chapter 5

Transmission of Avian Influenza Virus by Humpback Whale and Its Stranding along the Atlantic Coast with CO2 Emissions

Tai-Jin Kim

59-81

Chapter 6

Recent Study on Heat Transfer Analysis for a Sphere of Combustible Material of Variable Thermal Conductivity

Ramoshweu Solomon Lebelo

82-91

Chapter 7

Impact of Green House Gases from Thermal Power Plants

K. Sujatha, R. Krishnakumar, R. S. Ponmagal, N. Jayachitra, Nallamilli. P. G. Bhavani, B.

Deepa Lakshmi, A. Raja, B. Rengammal Sankari and V. Karthikeyan

92-103

Chapter 8

Advanced Study on Electrically Operated Multipurpose Trolley Al Sult Al Kharusi, Dinesh Keloth Kaithari and Parimal S. Bhambare

104-113

Chapter 9

Vlasov's Physics: From Plasma to Solid V. I. Talanin and I. E. Talanin

114-119

Chapter 10

Evaluation of Indigenous Knowledge and Fuel Value Index of Some Selected Sudano-Sahelian Fuelwood Species in Damaturu, Yobe State of Nigeria

A. M. Dadile and O. A. Sotannde

120-129

Chapter 11

Automated Guided Vehicle for Physically Handicapped People – A Cost Effective Approach

G. Arun Kumar and S. Lakshmisankar

130-139

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Chapter 13

Recent Study on Design and Development of a Wearable Device to Monitor Vital Signs of Preggers

L. K. Hema, R. Mohana Priya, K. L. Shunmuganathan and S. Velmurugan

151-158

Chapter 14

Research on Experimental Behaviour of Water Hyacinth Ash as Partial Replacement of Cement on Short Column

V. Murugesh, A. Thirumurugan, M. Sadhasivam and M. Sudharsanan

159-167

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This book covers key areas of engineering research. The contributions by the authors include distance based clustering, line based clustering, height based clustering, license plate detection, missed characters extraction, infinite thinning and thickening, analog loop filters, CMOS technologies, SOBEK program, sedimentation dynamics, network performance, multidrop autowalk, CO2 emissions, avian influenza virus, mutant virus, migration, thermal conductivity, exothermic chemical reaction, variable thermal conductivity, heat transfer, green house gas, combustion quality, flue gas emissions, particle swarm optimization and feature extraction, colony optimisation, photovoltaic cell, Vlasov’s model for solids, diffusion model, Vlasov's equation, fuelwood utilization, amelioration, microcontroller, path planning, temperature sensor. This book contains various materials suitable for students, researchers and academicians in the field of engineering research.

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_____________________________________________________________________________________________________

Multiple License Plates Detection in Videos and Still Images Using Various Geometrical Properties and Filtering Techniques

Narasimha Reddy Soora1*

DOI:10.9734/bpi/aaer/v3/1527F ABSTRACT

Most of the existing license plate (LP) detection systems have shown significant development in processing of images, with restrictions related to environmental conditions and plate variations. The environmental conditions include different illumination, weather, and background conditions. The plate variations include location of the plate anywhere on the vehicle, many plates in single image, different combination of vehicles with different plate orientations, different sizes of plates, background colour of plates, plates with dirt, rotated plates, LPs having two lines of characters and tilted plates. With increased mobility and internationalization, there is a need to develop a universal LP detection system, which can handle LPs of any country and any vehicle, including motor cycles, in an open environment and all weather conditions. This paper presents a novel LP detection method using different clustering techniques, based on geometrical properties of the LP characters and proposed new character extraction method, for missed character components of LP due to presence of noise between LP characters and LP border. The proposed method detects the number plate of any type of vehicle (including vans, cars, trucks, motorcycles etc.), having different plate variations, under different environmental and weather conditions because of geometrical properties of set of characters in LP.

The proposed method is independent of colour, rotation, and scale variances of LP. The concept is tested using publicly available standard media-lab and Application Oriented License Plate (AOLP) benchmark LP recognition databases. The success rate of the proposed approach for LP detection using media-lab database is 97.3% and using AOLP database is 93.7%. Results clearly indicate that the proposed approach is comparable to the previously published papers, which evaluated their performance on publicly available benchmark databases.

Keywords: Distance based clustering; line based clustering; height based clustering; license plate detection; missed characters extraction; infinite thinning and thickening.

1. INTRODUCTION

LP recognition system plays a key role in intelligent transportation systems (ITS), such as traffic control, parking lot access control, electronic toll collection, and information management etc. Typical LP recognition system contains four processing steps. The first step is to get the image or video from the camera. The second step is LP detection from the image. The third step is to extract the characters from the LP and the final step is to recognize the extracted characters using different classifiers. These four steps can be achieved by the combination of different techniques of image processing and pattern recognition. Out of these four steps, the LP detection step is very crucial for the success of LP recognition systems.

LP detection systems have shown significant development for past few decades with good performance reports, but most of these systems evaluation is carried on proprietary data sets, having

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controlled conditions on environment and plate variations. To assess the performance of the LP detection methods, there is a need for a common benchmark data set, which should contain videos and images taken in open environment and with different LP variations aforementioned. A common publicly available benchmark data set, for performance evaluation of LP recognition systems is initiated by Anagnostopoulos et al. [1], contains 741 still images of Greek LPs with several open environmental conditions and different plate variations at [2]. For evaluation of the proposed approach, we have used 741 still images of media-lab Greek LP database, 159 Indian and Israeli LPs from videos and still images. As media-lab Greek LP database missed motorcycles, vehicles with rotated LPs, combination of different types of vehicles, and more than one motorcycle in a single image, appropriate care is taken while selecting Indian LP images, to achieve all the combinations of missed LP variations.

In this paper, we have proposed a new approach, for finding LP/LPs in an image, using various clustering techniques on geometrical properties of LP characters, and a new approach for finding and extracting missed characters of LP/LPs, due to the presence of noise such as dirt or screw between LP characters and LP border. For the clustering techniques proposed in this paper, we have used geometrical properties of the components of LP characters, such as distance between the components, angle between the components, and height of the component, to find the probable LP.

This is the first time that different clustering techniques are applied on geometrical properties of the LP components of an image for finding the probable LP/LPs in an image. The proposed approach is taking relatively more processing time for the images with too many components for detecting the LP, as it is using different clustering techniques on geometrical properties of the components of the image. Hence, the proposed approach is not suitable for applications with strong real time requirements. The method proposed for finding the vehicle LP/LPs is scale and rotational invariant, and is suitable for many countries LP detection, for any type of vehicles and motorcycles having different plate variations.

The performance of the proposed LP detection method is more prominent when compared with other competitive LP detection methods from literature, by taking into consideration publicly available media-lab and AOLP benchmark LP recognition databases. It is inappropriate to declare which methods are better, because in most of the previously published methods, evaluation was carried on proprietary data sets having restricted conditions and are not revealed to the public, to assess their performance. In this paper, we have proposed new methods for LP detection, missed character extraction, and LP characters rotation correction. New findings in this paper are as follows:

 Proposed a new method for LP detection, using distance based, line based, and height based clustering techniques, on geometrical properties of LP components.

 Proposed a new method to remove the unwanted clustered components, using infinite thinning and resizing technique.

 Proposed a new method for correcting LP rotation of the probable LP cluster components, using the average angle amongst successive probable LP cluster components top left coordinates and x-axis.

 Proposed a new method to extract the missed characters of the probable LP, because of the presence of noise.

Remaining sections of the paper are planned as follows. Section II exhibits the existing similar research. Section III describes proposed approach. Section IV elaborates on the proposed methodology for LP detection. Section V describes the extraction of missed LP characters due to presence of noise between LP characters and LP border. This section also describes the rotation of the probable LP characters if the vehicle LP is rotated. Experimental results are discussed in Section VI and Conclusion in Section VII.

2. EXISTING SIMILAR RESEARCH

Many LP detection algorithms have been proposed in literature, for the past ten years and even today, LP detection remains challenging due to different environmental conditions and plate variations. In literature, there is no LP detection method, which will work for LP detection of all countries, for all

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types of vehicles and motorcycles, without any constraint. LP detection and character extraction are challenging and crucial in LP recognition systems, which influences the recognition rate. Most of the existing LP detection papers in literature are based on edge information, morphological operations, template matching, and LP background colour.

Authors in the paper [3], proposed LP recognition strategy for motor cycles, for checking annual inspection status. The data set considered by this paper contains only motorcycles having the LP characters falling in only one line. The method proposed in this paper, finds the LP using search window, with help of horizontal and vertical projections, and reported an average LP detection rate of 97.55%.

Authors in the paper [4], proposed two methods to find the LP. These two methods are based on Connected Component Analysis (CCA) model. Before applying these methods, input image is binarized using improved Bernsen algorithm, to remove shadows and uneven illumination. Method1 is used to find the candidate regions based on prior knowledge of LP. The frame is detected using CCA methodology. If the frame is broken, the LP cannot be detected correctly. When the frame of license is not detected using Method1, then Method2 is adopted. This method extracts the LP using large numeral extraction technique. This paper reported a success rate of 97.16%.

In the paper [5], a new method, based on fixed colour collocation is used to locate the LP. This method uses the colour collocation of the plate’s background and characters, to recognize the LPs.

This paper reported 95% success rate for LP detection.

Authors in the paper [6] proposed a new approach for LP detection based on Principal Visual Word (PVW) discovering and visual word matching. In visual word matching, it will compare the extracted SIFT features of test image with all discovered PVW and locate the LP based on matching results.

This method published 93.2% success rate on proprietary data set and 84.8% success rate on Caltech dataset.

In paper [7], plate’s background colour is extracted from input image. For more stable colour extraction, a neural network is used. Fixed ratio of horizontal and vertical length of a plate is used for LP extraction. Template matching and post processing techniques are used to recognize characters of a plate. This paper reported 91.25% success rate for LP detection.

A hybrid LP localization scheme is presented in paper [8], based on the edge statistics and morphology. The proposed approach had four sections. Section 1 handles the vertical edge detection, section 2 takes care of the edge statistical analysis, and section 3 finds the hierarchical-based LP location and section 4, the morphology-based LP extraction. The overall success rate for detecting the LP out of 9825 images is 99.6%.

Paper [9] proposed RELIP algorithm, which performs a global search for probable LP, using multiple templates, 3-D cross-correlation function, and Principal Component Expansion. This paper uses corner detection to remove deformation of LPs. RELIP reported 97% LP detection success rate.

Paper [10], proposed a new approach for detecting LP candidates, using Expectation-Maximization clustering method on vertical edges of gray scale images. This paper reported 93.33% success rate on AOLP proprietary benchmark LP recognition data set and reported 92.1% success rate on media- lab benchmark LP recognition data set, for LP detection. It is mentioned in the paper that, the LP recognition solution is designed primarily based on LPs of Taiwan and is not optimal for other countries.

In Paper [11], a real time and robust method for license plate location (LPL) is used. LPL has several stages, with combination of Sobel mask, histogram analysis and morphological operations. Overall success rate for detecting the LP is 83.5%.

In paper [12], a new image segmentation method called sliding concentric windows (SCW) is proposed for LP detection. The SCW method works based on local irregularities in the image. The

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method uses statistics such as standard deviation and mean value, for possible plate location. SCW uses two concentric windows A and B, with different sizes, to scan the image from left to right and top to bottom, to find the mean and standard deviation of the regions, of concentric windows. If the ratio of the statistical measurements exceeds a threshold value set by the user, then the central pixel of the two concentric windows is considered to be part of the LP. This paper reported a success rate of 96.5% for LP detection using media-lab proprietary data set.

In paper [13], a new approach is proposed, in which, a colour image is converted to gray scale and then adaptive threshold is applied on gray scale, to convert it into a binary image. ULEA method is applied on gray scale image, to enhance the quality, by removing the noise. Next, VEDA is applied to detect LP. In order to detect the true LP, some statistical and logical operations are applied. The success rate reported in this paper is 91.65%, for LP detection.

Most of the LP detection methods, which used edge information and morphological operations mainly focuses on finding the components, which are rectangular in shape with specific aspect ratio. Such type of LP extraction methods will fail to identify the LP, if the LP does not follow a rectangular shape, with proper aspect ratio. The problem with template matching LP detection methods is that, it will not work for all types of plate variations. The colour based LP extraction methods use the background colour of the LP, to identify the probable LP candidate region, because some countries use particular background colour in their LPs. Such type of LP recognition systems will fail to recognize the LP properly, if the body colour of the car matches with the LP background colour. The above categorized LP detection methods use the features of LP in an image, to extract the LPL from an image. These categories have limitations in extracting LP/LPs from an image, for any country, because of the features adopted to extract LPs.

In this paper, we have proposed for the first time, a new LP detection method based on geometrical properties of LP characters and filtering techniques, which will work for LP of many countries, having any shape. The advantage of using different clustering techniques on geometrical properties of character components of LP is that, they are independent of scale, rotation, pan, and orientation.

There are very few techniques in the literature, which talk about LP detection methods, which will work for any type of vehicle and motorcycle, for any country having any LP shape.

3. PROPOSED APPROACH

In this paper, we have proposed a new method for LP/LPs detection and missed characters extraction, for any type of vehicle and motorcycle, having different plate variations, under different environmental and weather conditions, for any country. The proposed method can be articulated as a generalized method for identifying the LP/LPs, because it is independent of LP variations under different environmental and weather conditions, and can be applicable to any country and for any vehicle, having any number of lines in LP. In the proposed approach, we have not used any type of edge detection, template matching, and background colour of the LPs, which are extensively used by previously published papers from the literature to detect the LP.

We have used CCA to label the components and applied different clustering techniques on geometrical properties of the labelled components, such as location of components, angle between components and height of components, to extract the probable LP/LPs. In most of the countries, the LP characters are near to each other, are positioned along one or multiple lines, and are of similar height. Based on these properties of LP characters, clustering techniques can be applied on geometrical properties of LP characters to identify the LP. Most of these properties are followed by many nations while designing their LPs. That is why; the proposed approach can be applicable to detect the LP of many nations. The proposed method contains the steps shown below.

 Apply pre-processing steps on input image. If it is video, convert the video into different frames and then apply pre-processing steps. After completing the pre-processing steps, label the components of the image using CCA. From each component, extract the geometrical properties such as, top left coordinates, width and height.

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 Apply newly proposed distance based clustering algorithm on each component top left coordinates. This algorithm divides the image components into clusters, which are closer to each other. Let Nd be the no. of distance based clusters.

 Re-cluster each Nd distance based cluster into different line based clusters. If the components of distance based cluster subtend similar angle between the lines joining left top coordinates of the components with x-axis, then construct line based clusters from such components. The algorithm re-clusters each distance based cluster components into Nl line based clusters, which are in line and close to each other.

 Re-cluster each Nl line based clusters, based on cluster components height. This is height based clustering, which re-clusters each Nl line based cluster into Nh height based clusters.

 After distance, line, and height based clustering, the resultant clustered components have the properties such as, near to each other, positioned along a line, and having similar height.

These properties belong to LP characters of any vehicle and motorcycle in the world.

 There may be few non LP components which follow the properties of LP characters. Apply infinite thinning and re-sizing technique to remove such unwanted clusters, resulting from different clustering techniques. Let Ntr be the number of probable LPs in the image, after applying thinning and re-sizing technique.

 Refine Ntr clusters further, by finding the border of the cluster components. If the border percentage for each cluster is less than pre-defined threshold, remove such clusters from the list of probable LPs. After this step, let N be the number of probable LP clusters.

 Apply newly proposed character extraction technique to extract missed characters of the LP, on each of 'N' probable LPs, due to presence of noise such as screw or dirt or stamps between LP characters and border of LP.

 After extracting the missed characters, rotate the probable LP characters using average angle between the lines joining adjacent components left top coordinates and x-axis, so that all the probable LP characters will be horizontal to x-axis.

The above mentioned outlined procedures are explained in detailed in the following sections.

4. METHODOLOGY

This section describes, in detail about the methods to find the probable LP/LPs in an image with the help of various clustering, thinning and re-sizing techniques. This section also explains the method and the need to further refine the probable LP/LPs, by finding the border of the LP/LPs.

A. Pre-Processing stage Steps:

1. Due to effect of illumination in open environment and presence of shadows, it is very difficult to process an image with the help of traditional threshold binarization methods and will not give satisfactory results. In this paper, we have used Bernsen algorithm, to overcome the illumination and shadow problems in an image. Let f(x, y) denotes gray value at a point (x, y) of an image. Let (x, y) be the centre of a block of size (2w+1) X (2w+1) in the image. Threshold T(x, y) at the point (x, y) can be computed using the equation below.

(1) 2. Convert the input image (shown in Fig. 4 (pp1)) into gray scale. If it is video, convert it into frames

and then convert each frame into gray scale. Apply the Bernsen algorithm to overcome from uneven illuminations or shadows present in gray scale image. Complement the binarized image, whose output is shown in Fig. 4 (pp2). Remove components, whose height is less than three pixels, from the complemented binary image, because no LP character has less than three pixels height. Fig. 4 (pp3) shows the output after removing components that are less than three pixels in height from Fig. 4 (pp2).

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3. To implement the rest of the operations on individual components, such as distance based clustering, line based clustering, and height based clustering, extract the geometrical properties of components such as top left coordinates, width, and height.

4. Geometrical properties of individual components described in step 3, can be extracted using the following procedure.

a. To find the number of components present in an image, use CCA method to apply labelling to preprocessed image.

b. After labelling, find left top coordinates, width and height of the individual connected component.

c. Crop each individual component from pre-processed image using left top coordinates, width, and height.

d. Save individual cropped component as separate image components.

e. Table 1 shows the individual components saved for input image1. Geometrical properties of individual components such as left top coordinates are saved as 2D array with name 'Input Image1 Left Top', width and height are saved as 2D array with name 'Input Image1 W H'. N1 shows the number of individual components in the image.

f. The description of the individual variable names are as follows:

In 'Input_Image1_C1' variable, the presence of first '1' indicates the image and the second '1' indicates the label of the component in the image.

Table 1. Individual components after step 4

Name of the variable Value

Input_Image1_C1 <56x122 double>

Input_Image1_C2 <3x11 double>

Input_Image1_C3 <8X7 double>

… …

… …

Input_Image1_C43 <7x6 double>

Input_Image1_C44 <4x5 double>

N1 44

Input_Image1_Left_Top <44X2 double>

Input_Image1_W_H <44X2 double>

B. Clustering Stage

The purpose of the clustering stage is to prepare the probable LP clusters. In this stage, the proposed system performs three types of clustering techniques, one after the other. First clustering technique is distance based clustering, whose purpose is to group the components which are near to each other.

Second clustering technique is line based clustering, whose significance is to divide distance based clusters into array of line based clusters, where the components of the line based clusters are in line with each other from view point of left top coordinates. Third clustering technique is height based clustering, whose significance is to regroup the line based cluster components which are similar in their height. After all these clustering techniques, resultant cluster components in each cluster are close to each other, positioned in a line and alike in their heights, which are the probable LP/LPs of an image.

Context dependent variable: cluster_size=Alpha

Variable cluster_size is a context dependent variable, which indicates minimum number of characters in a row of a LP and can be tuned to satisfy country specific LP constraints. Proposed clustering stage has following steps.

Steps:

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1. After pre-processing stage, cluster all the components of the image, based on the distance between top left coordinates of each individual component, using distance based clustering algorithm, whose pseudo code is shown in Table 2.

2. Distance based clustering algorithm prepares a matrix of size N_IXN_I, whose 1st row indicates the distance between 1st label component top left coordinates and rest of the components top left coordinates, 2nd row indicates the distance between 2nd label component top left coordinates and rest of the components left top coordinates and so on. Distance based clustering algorithm prepares maximum N_I clusters, one for each component, using distance matrix.

Fig. 1. Components of image after distance based clustering

3. Remove clusters whose size is less than cluster_size and which are subset to other. Retain clusters with large number of components in it, when performing subset removal operation. At this stage, the components of the image are clustered into groups, based on distance between the top left coordinates of each individual component.

4. Fig. 1 shows the components of an image which are clustered using distance based clustering technique. In Fig. 1, image components C1...C13 are clustered into two distance based clusters.

Components C1...C9 form first cluster and C10...C13 as second cluster.

5. After distance based clustering, there will be at most N_I clusters from the list of components of each image, which is shown in Table 7. Fig. 4 (clust1) shows, the resultant image after distance based clustering. Let Nd be the number of distance based clusters.

6. Distance based clusters are maintained for each input image, with nomenclatures as ‘Input Image1 distance Cluster2’, ‘Input Image1 distance Cluster14’ etc., and distance cluster list is maintained for each input image as ‘Input Image1 distance Cluster List’, which is shown in Table 7. The variable ‘Input Image1 distance Cluster2’ indicates, distance cluster for component 2 in input image 1 (here, '1' indicates first '1' in variable name).

7. Now, apply line based clustering technique on each Nd distance based clusters, to find those components which are in line with each other. Table 3 shows, pseudo code for line based clustering.

8. In line based clustering, consider individual distance based clusters and take each component and draw a line, from its top left coordinates to the top left coordinates of the next component in the list. Find the angle between x-axis and the line that is drawn between two top left coordinates of components. In the same way, find the angle between rest of the components and x-axis, as a matrix (angle matrix) of size NXN, where N is the number of individual components, in each distance based cluster.

9. Cluster those components, which subtends similar angle (<= 35) with the x-axis and which are close to each other, for each row of the angle matrix. Now, remove those angle based clusters, which are less than cluster_size components in count and which are subsets to other clusters.

This is line based clustering.

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10. Line based clustering is used to re-cluster distance based cluster components, based on the property of having similar angle and closeness of the cluster components. After this stage, the components of an image are clustered, using distance based clustering and line based clustering techniques which is shown in Table 8.

11. Fig. 2 shows how the distance based clusters are divided into line based clusters. In Fig. 2, first distance based cluster with components C1…C9 is divided into two line based clusters with components C1…C5 and C6…C9, indicated with green rectangular boxes. The second distance based cluster with components C10…C13, resulted into a line based cluster with components C10, C11 and C13 and the component C12 is removed from the resultant list, because C12 is not in line with other components.

12. Fig. 4 (clust2) shows resultant image after line based clustering. A value of an 'angle cluster' variable indicates an index of the component inside 'distance cluster' variable. For each distance based cluster, there is an array of angle based clusters and their 'include list' which is shown in Table 8.

13. After line based clustering, apply height based clustering technique, to remove few unwanted/junk components, which are very close to and in line with the components, but shows much difference in height as compared with other components in the cluster. Remove such unwanted components from the list, by using height based clustering technique, whose pseudo code is shown in Table 4.

Fig. 2. Components of image after line based clustering

Fig. 3. Components of image after height based clustering

14. In Fig. 3, as component C3 (indicated by arrow) is showing much difference in height as compared to rest of the components, it will be removed from angle based cluster and will result

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in height based cluster, with components C1, C2, C4 and C5. Fig. 4 (clust3) shows image after height based clustering.

15. After height based clustering, few clusters from the final cluster list may contain all unwanted components, which obey all the characteristics based on distance, line and height based clustering. Such junk component clusters can be removed by thinning and re-sizing technique.

16. Apply infinite thinning and re-sizing technique to each cluster of an image. Thinning is a morphological operation, used for skeletonization of the binary image components. When we apply thinning and re-sizing operations, junk components will retain its shape, but the LP characters will fade away completely. Remove those clusters from the cluster list, which retain its shape after thinning and re-sizing operations. This technique removes all junk cluster components, from the final cluster list. Let N1 be the number of clusters in the cluster list, after removing junk clusters, using thinning and resizing technique.

17. Table 9 shows retained variables, after thinning and resizing. Fig. 4 (thin_res1) shows image after thinning and re-sizing technique.

Table 2. Pseudo Code for new distance based clustering

/*Let the number of individual components of each image I (Input Image) be N_I; Find the distance between each individual component as matrix Distance_I of size N_IXN_I; max_distance is the maximum distance between the cluster components which is equal to length of image/cluster_size.

cluster_size indicates min no of characters that can present in LP of vehicle, which is pre-defined */

for each image I for J=1:N_I

/* prepare the cluster list of components which are closer to each other using Distance_I matrix and whose cluster size is greater than cluster_size*/

1 start_index = J; res_list = { };

2 start_index1 = start_index+1;

3 while 1

4 if start_index >= N_I 5 break;

6 end if

7 min1= find minimum distance between start_index and rest of the cluster components except the components in {start_index, res_list, j};

8 find1 = find the component which is having min1 distance with component start_index;

9 if min1 > max_distance 10 if start_index1 < N_I

11 start_index1 = start_index1+1;

12 if start_index1 >= N_I 13 break;

14 else 15 continue;

16 end if 17 end if 18 end if

19 if the find1 is not in res_list, put it in res_list else increase find1 till it is not there in the res_list 20 start_index = find1;

21 start_index1 = start_index+1;

22 end while

23 res_list = union(res_list, j);

24 res_list = sort(unique(res_list));

25 if count(res_list) >= cluster_size

26 store the above cluster in distance cluster list for image I and cluster as J 27 end if

28 end for 29 end for

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Table 3. Pseudo Code for line based clustering

/*The logic mentioned below is used to prepare angle based clusters from angle matrix for each distance_cluster.

dist_cluster_j contains distance cluster components for jth label component.

Input_ImageI_Left_Top contains left top coordinates of Ith image components.

dist_cluster_j_size is size of dist_cluster_j. */

1 for each distance based cluster of size dist_cluster_j_size

2 Prepare angle matrix of size dist_cluster_j_size*dist_cluster_j_size, where each row indicates the angle between the component, with label as row number and rest of the components of the distance cluster using the below formulae.

θ = (180

π) * tan-1((y2-y1) (x2-x1))

3 In above equation, (x1, y1) and (x2, y2) are the top left coordinates of the distance based cluster components. This equation is used to find the angle between x-axis and the line joining two left top coordinates of distance cluster components.

4 end for

5 for each distance cluster of size dist_cluster_j_size

6 Prepare angle clusters for each row from angle matrix, which subtends similar angle with other components and which are close to each other.

7 If the size of newly prepared angle cluster is greater than pre-defined size, then consider the angle cluster and include the same in angle cluster include list.

8 end for

Table 4. Pseudo code for height based clustering

/* Variable Retained_Height_Diff holds a value, which indicates that the algorithm retains only those components, whose height difference is less than the value of the variable.

Pre-defined cluster size is the minimum number of LP characters.

*/

1 for each angle based cluster include list 2 for each angle based cluster component

3 Prepare component list diff_j_list, which indicates the array of angle cluster components, whose height difference with jth component is less than pre-defined Retained_Height_Diff.

4 If the number of components in the above list is below the pre-defined cluster size, then remove jth component from array of angle cluster components.

5 end for

6 If the no. of components in angle cluster components after removing differed components, is less than pre-defined cluster size, then remove the entry of the particular angle cluster component from the angle cluster include list.

7 end for

C. Finding Border of the Number Plate

Contrasting to a typical LP recognition system, the proposed system first finds the probable LP characters and then finds the border of the components. The reason for finding the border of LP is that, there can be group of non LP characters in the image with similar properties of LP characters without border. In order to avoid such type of characters, the system proposes to find the border of the LP.

Pre-defined border percentage: Beta

Beta is a user defined variable, which decides the percentage border that a LP can have.

Steps:

1. At this stage, there can be N1 clusters after distance, line, height based clustering techniques, and thinning and resize technique. Now, find the border/LP region for the components, of each of the clusters.

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2. Take each individual component from the cluster and traverse from top left coordinates of each individual component towards upward direction, till the traversal reaches the border point or three times the height of each individual character component.

3. Apply the same procedure for downward direction, to find the bottom border point for each individual component.

4. Save the top and bottom border points for all the components, of each cluster.

5. Find the percentage of the borders for each cluster. Retain a cluster, only when the percentage is greater than or equal to pre-defined border percentage. Retained clusters indicate the LP/LPs of an image, and its components indicate the individual characters of the LP.

6. Remove clusters, which fall below pre-defined border percentage. This is another way to further refine the cluster list, to get the required LP region. Fig. 4 (lp1) shows, LP border identification for the image.

7. Table 10 shows, LP cluster in 'Cluster20 Angles Cluster67' and 'Cluster25 Angles Cluster13', which are indexes into 'Input Image1 distance Cluster20' and 'Input Image1 distance Cluster25' respectively, which resulted in same values.

8. Table 5 shows, pseudo code for LP border identification. Fig. 4 (lp1) shows, image after LP border identification.

Table 5. Pseudo code for LP border points identification 1 For each cluster component

2 Take the top left coordinates and traverse the image upward direction till it finds the non zero and non cluster component label or till the traversal reaches three times the height of the component.

3 Record it as top border point of the cluster component.

4 End for

5 Repeat the same procedure for downward direction also

6 Now find and remove those cluster components, whose border percentage is less than user defined border percentage.

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Fig. 4. Results of pre-processing, different clustering stages, thinning and re-sizing and LP identification

5. MISSED CHARACTERS EXTRACTION AND PROBABLE LICENSE PLATE CHARACTERS ROTATION

There may be few LP characters, which may be missed in the clustering stage, because of the presence of noise such as screw or dirt or stamps between border of the LP and the LP characters.

This section proposes a new approach for extracting missed LP characters.

Steps:

1. Pseudo code for missed character extraction is shown in Table 6.

2. The proposed algorithm uses below equations (2), (3) to find the missed characters, which is to find the coordinates (x2,y2) at a distance d with given point (x1,y1) and with slope m.

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(3) 3. At this stage, we have few probable LP clusters. Take each probable LP cluster and find the

average heights and average slopes amongst the subsequent components left top coordinates and x-axis.

4. From each probable LP cluster, take left top coordinates of first component and move in the downward direction to 1/4th of the first components height. Then traverse the image right side, one pixel at a time, using equations (2) and (3) mentioned above, to find any missed LP character components.

5. If any missed LP character component is found, which is not part of the probable LP cluster component and is not a background pixel, then find the left top coordinates and width of the missed component. To find the left top coordinates of the missed component and its width, we have to perform three traversals.

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i. The first traversal is towards top side of the missed character component, to compensate the left top coordinates slope with average slope. The second traversal is to traverse towards left side of the missed component, in the direction of the average slope, till it reaches leftmost pixel of the missed component, within the average height. After reaching the left most side of the missed component, fix the coordinates as left top coordinates of the missed component.

ii. Take newly found left top coordinates of the missed LP character component and move towards right side in the direction of the average slope, till it reaches the right most point of the missed component, within the average height. The difference between the x-coordinates of newly found left top coordinate point and right most point is width of the component.

iii. Crop the missed component using left top coordinates, width, and average height of the cluster components.

6. Repeat the same procedure, till the traversal reaches the last component of probable LP cluster component. Repeat the same procedure, for all the LP cluster components.

7. Rotate each individual component of the probable LP cluster by using average angle, which can be calculated from the average slope amongst the components of probable LP cluster. Consider each component of the binary image as F = {F(i,j), i=1,2,…,I, j=1,2,…,J and can be defined as follows:

(4) Let F(x,y) be the image component before rotation and F(x',y') be the image component after rotation.

Use average angle θ to rotate F(x,y). The equation for each individual pixel of F(x',y') can be obtained by using below equations.

(5) (6) 8. In a rotated image, if average angle of the probable cluster components is above a certain

threshold, then there is a chance that other part of the character component will be present in the target component. In such case, retain the bigger component from the target component and remove the rest of the components.

Table 6. Algorithm for missed character extraction

/* Missed character extraction technique is required to extract the characters, which are missed due to presence of screw or dirt between a character and border of LP. Let Im_x and im_y are the dimentions of Input_Image*/

1 for J = 1:probable_LP_cluster_list

2 cluster_components = get Jth LP cluster components

3 cluster_Heigths = get Jth LP cluster components Heights using Input_ImageI_W_H 4 cluster_Widths = get Jth LP cluster components Widths using Input_ImageI_W_H 5 mean_Height = calculate mean height of Jth LP cluster components

6 mean_Width = calculate mean width of Jth LP cluster components

7 avg_slope = calculate average slope of cluster components, with respect to x-axis from their top left coordinates.

8 comp_first = first component of Jth LP cluster components 9 comp_last = last component of Jth LP cluster components 10 comp = comp_fist

11 First_Comp_Left_Top = get first component left top coordinates 12 pos = 1

13 dist_travelled = 1

14 while comp ~= comp_last

15 traverse from first component left top to right side, till it reaches last component using the below formulae.

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16 X_Left_Top = First_Comp_Left_Top(:,1) + ( dist_travelled

√(1+avg_slope2) ) 17 If avg_slope < 0

18 Y_Left_Top = First_Comp_Left_Top(:,2) + 2 - (avg_slope*dist_travelled

√(1+avg_slope2) ) 19 Else

20 Y_Left_Top = First_Comp_Left_Top(:,2) + 2 + (avg_slope*dist_travelled

√(1+avg_slope2) ) 21 End if

22 If X_Left_Top > 1 && X_Left_Top < im_x && Y_Left_Top > 1 && Y_Left_Top < im_y 23 Val = value of image at X_Left_Top and Y_Left_Top position

24 Find whether Val is present in LP clustered component list

25 If it is present, then increase value of variable 'pos', to track the position of the missed component in the LP

26 If it is not present and is not background pixel value, then traverse to the leftmost part of the missed component, as per the slope direction given in the equations, so that is reaches the leftmost part of the missed component.

27 Same way traverse to the right most side of the component and find its width and height.

28 End if

29 If extracted width is less than the 2/3 of mean_Width or more than 4/3 of mean_Width then 30 Break and continue increase the value of X_Left_Top to reach next component in LP

cluster component list in avg_slope direction as per the equations given.

31 End if

32 Continue till traversal reaches last component 33 End while

34 End for

Table 7. Distance based clusters

Name of the variable Value

Input_Image1_Distance_Cluster2 [1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 15, 17, 18, 19, 20]

Input_Image1_Distance_Cluster14 [3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20]

Input_Image1_Distance_Cluster20 <1x29 double>

Input_Image1_Distance_Cluster25 <1x22 double>

Input_Image1_Distance_Cluster41 [41,42,43,44]

Input_Image1_Distance_Cluster_List [2, 14, 20, 25, 41]

Table 8. Angle based clusters

Name of the variable Value

Input_Image1_Distance_Cluster_List [2,14,20,25]

Input_Image1_Distance_Cluster2_Angles_Cluster_Include_List 1

Input_Image1_Distance_Cluster2_Angles_Cluster1 [1,3,4,6,8,10]

Input_Image1_Distance_Cluster25_Angles_Cluster_Include_List [13,56,76]

Input_Image1_Distance_Cluster25_Angles_Cluster76 [7,13,14,15,17]

Input_Image1_Distance_Cluster25_Angles_Cluster56 [5,6,10,12,16,18,22]

Input_Image1_Distance_Cluster25_Angles_Cluster13 [1, 2, 4, 9, 11, 14, 15, 17, 19, 20, 21]

Input_Image1_Distance_Cluster25 <1x22 double>

Input_Image1_Distance_Cluster20_Angles_Cluster_Include_List [20,67]

Input_Image1_Distance_Cluster20_Angles_Cluster67 [4, 6, 9, 12, 16, 18, 21, 22, 24, 26, 27, 28]

Input_Image1_Distance_Cluster20_Angles_Cluster20 [2,17,19,23,25,29]

Input_Image1_Distance_Cluster20 <1x29 double>

Input_Image1_Distance_Cluster2 [1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 15, 17, 18, 19, 20]

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Name of the variable Value Input_Image1_Distance_Cluster14_Angles_Cluster_Include_List [1,37]

Input_Image1_Distance_Cluster14_Angles_Cluster37 [9,12,15,16]

Input_Image1_Distance_Cluster14_Angles_Cluster1 [1,2,4,6,10]

Input_Image1_Distance_Cluster14 [3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20]

Table 9. Retained list of variables after thinning and re-sizing

Name of the variable Value

Input_Image1_Distance_Cluster_List [20,25]

Input_Image1_Distance_Cluster25_Angles_Cluster_Include_List 13

Input_Image1_Distance_Cluster25_Angles_Cluster13 [4,9,11,14,17,19,20,21]

Input_Image1_Distance_Cluster25 <1x22 double>

Input_Image1_Distance_Cluster20_Angles_Cluster_Include_List 67

Input_Image1_Distance_Cluster20_Angles_Cluster67 [12,16,18,21,24,26,27,28]

Input_Image1_Distance_Cluster20 <1x29 double>

Table 10. Showing the final cluster list containing LP

Name of the variable Value

Input_Image1_Distance_Cluster20 <1x29 double>

Input_Image1_Distance_Cluster20_Angles_Cluster67 [12,16,18,24,26,27,28]

Input_Image1_Distance_Cluster20_Angles_Cluster67_B_B_Pts <8x2 double>

Input_Image1_Distance_Cluster20_Angles_Cluster67_T_B_Pts <8x2 double>

Input_Image1_Distance_Cluster20_Angles_Cluster_Include_List 67

Input_Image1_Distance_Cluster25 <1x22 double>

Input_Image1_Distance_Cluster25_Angles_Cluster13 [4,9,11,17,19,20,21]

Input_Image1_Distance_Cluster25_Angles_Cluster13_B_B_Pts <8x2 double>

Input_Image1_Distance_Cluster25_Angles_Cluster13_T_B_Pts <8x2 double>

Input_Image1_Distance_Cluster25_Angles_Cluster_Include_List 13

Input_Image1_Distance_Cluster_List [20,25]

6. EXPERIMENTAL RESULTS

We have implemented proposed method using MATLAB on Intel core i3 processor machine, having 4 GB RAM. The performance of the proposed LP detection method is compared with some of the competitive LP detection methods, by taking into consideration publicly available media-lab benchmark database, Israeli LP images from web and proprietary Indian LPs, having different plate variations in open environment. Total images from all these data sets are 900. To further assess the performance of the proposed LP detection method, we have considered AOLP benchmark database, having 2049 images with three subsets. Indian, Israeli, and media-lab Greek LPs are divided into following categories.

 Images in open environment

 Images with blur

 Images with shadows

 Images with reflectance and illumination

 Images with dirt and screw

 Images with distorted LP

 Images with LP at different places on vehicle

 Images taken at night

 Images with dirt and shadows taken on difficult tracks

 Images with tilt

 Images with pan

 Images with more than one vehicle

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 Images with more than one motorcycle

 Images with different combinations of vehicles and motorcycles

 Images with rotation

In an open environment, there are many possible ways that we can capture the image from cameras.

Clustering techniques proposed in this paper are invariant to tilt, pan, and rotation. That is why, the proposed approach works properly with extreme observation views. There is no restriction on the size of LP characters, to detect LP. There are very few methods in literature, which talks about the extraction of LP of motorcycles, where LP characters fall in two lines and each line of characters is having different size. The proposed method works for any type of vehicles, motor cycles, vans and trucks having any number of lines of LP characters and also, each line of characters having different sizes. The proposed approach will fail to identify the LP, if the LP characters touch the border of the LP or there are less than cluster_size characters in LP or there are no characters present in LP at all.

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Fig. 5. Images with all possible combinations of plate variations in an open environment Fig. 5 shows the sample results for all categories of LPs, which include images of different plate variations, environmental, and weather conditions from media-lab, Israeli, and proprietary Indian LP databases. First column of Fig. 5 shows, the actual image and second column shows the binarized

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image. Red border in a binary image of Fig. 5 indicates the identification of LP and without a red border belongs to a failed case. Vehicles of many countries including motor cycles, will have single line of characters in their LPs, but there may be a chance that few countries will have LP characters that will fall into more than one line and there may be a chance that the characters in each line of LP may vary in size, as shown in (a11), (a23), and (a24). In such LPs, most of the existing LP detection systems recognize only the line of characters, which are bigger in size. Hence, such type of LP detection systems will not satisfy the real time requirements. Our approach will work in all such conditions.

In Fig. 5, (a1), and (b1), show images in an open environment. In Fig. 5, (a2), and (b2) show images with blur and (a3), and (b3) show images with shadow. In Fig. 5, (a4), (b4), (a5) and (b5), show images with reflectance and illumination. In Fig. 5, (a6), (b6), (a7), and (b7), show images with dirt and screw present in LP. In Fig. 5, (a8), (b8), (a9) and (b9), show images with distorted LP. In Fig. 5, (a10) and (b10), show images with LP at different place. In Fig. 5, (a11), (b11), (a12) and (b12), show images taken at night. In Fig. 5, (a13), (b13), (a14) and (b14), show images with dirt and shadows taken on difficult tracks. In Fig. 5, (a15), (b15), (a16) and (b16), show images with different tilt. In Fig.

5, (a17) and (b17), show image with extreme pan. In Fig. 5, (a18), (b18), (a19), (b19), (a20) and (b20) show images with multiple LPs, with different combination of vehicles. In Fig. 5, (a21), (b21), (a22), (b22), (a23), (b23), (a24) and (b24) show images with different combination of rotations, having different vehicles and motorcycles. In Fig. 5, (a25) and (b25), show LP detection successfully for Urdu language LP. In Fig. 5, (a26), (a27), (b26) and (b27) show images with failed LP detection, due to overlapping of LP characters, with LP edges and presence of lot of dirt. In Fig. 5, (a28) and (b28), show image with close view of LP.

The performance comparison among few of the prominent LP detection methods and the proposed approach is shown in Table 11. The method proposed in [8] is superior to our approach with a remarkable LP detection success rate of 99.6%, which supersedes all other methods. The methods proposed in [3,4,5,9,12] reported 97.55%, 97.16%, 95.3%, 97%, and 96.5% LP detection rates respectively, which are close to our method’s success rate of 95.78%. The papers [7] and [13]

reported 91.25% and 91.65% success rates, but their data set contains only cars. Paper [11] reported lower success rate, as compared to others. Paper [6] reported 93.2% success rate on proprietary data set and 84.8% on Caltech data set. The success rates of above mentioned LP detection systems are based on proprietary data sets.

It is impractical to compare the performances of different LP detection systems which evaluated their performances using proprietary data sets. There should be a common, true benchmark database, openly available to assess the performance of the proposed LP detection systems. A common, publicly available media-lab benchmark database, for research community, is initiated in [1], which contains Greek vehicles LP images. As the media-lab benchmark database is not satisfying all plate variations mentioned in this paper, we coupled the images of Israeli and Indian LP images having cars, vans, trucks and motor cycles, with media-lab benchmark database, to attain all plate variations mentioned. Table 12 shows the performance comparison between SCW method [12], AOLP method [10] and our proposed approach, using media-lab and AOLP benchmark databases. Using media-lab benchmark database, our method’s success rate of 95.14% is close to SCW method’s success rate of 96.5% (No. of images taken by SCW method is 1334) and is more than AOLP method’s success rate of 92.1%. Using AOLP benchmark database, the success rate of the proposed approach is 93.7%, which is close to the success rate of 93.33%, of the AOLP approach and better than 81.67%, which is the success rate of SCW method. The average success rate of our approach which is, based on both the benchmark databases is 94.66% and is close to the average success rate of 92.72% for AOLP and better than the average success rate of 89.09%, for the SCW’s approach.

As media-lab database does not have the images which satisfy all plate variations mentioned, we coupled the images of Israeli and Indian LPs to attain all the plate variations reported in this paper.

We considered media-lab, Israeli and Indian LP images as one data set as per different plate variations mentioned. Success rate of our approach on this combined data set is 97.56%, which is close to the success rate of 96.5% of the SCW approach. The success rate of SCW method is

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reported using 1334 images, whereas they made available only 741 images online, as media-lab benchmark database. We do not have clarification on rest of (1334-741) 593 images.

As performance comparison is concerned, it is inappropriate to compare the performances of methods evaluated on different data sets, which are not publicly available. There should be a common standard data set which has to be followed by the research community, for performance evaluation of their proposed methods. In literature, paper [10] evaluated the performance of their LP detection method on common, publicly available data sets. The proposed method is evaluated, using two publicly available media-lab and AOLP benchmark databases and the success rate of the proposed approach is compared with the recently published papers in literature, which have performed their evaluation on these common benchmark databases.

Table 11. Comparison of proposed LP detection method with few of the competitive LP detection methods in the literature

Ref LP detection Rate Types of vehicles

Used

Number of images in data sets Error!

Reference source not found.

97.55% using proprietary data set motor cycles 522

Error!

Reference source not found.

97.16% using proprietary data set cars, trucks 9026

Error!

Reference source not found.

95.3% using proprietary data set Not reported 150

Error!

Reference source not found.

93.2% using proprietary data set Not reported 410

84.8% using Caltech data sets cars 1999

Error!

Reference source not found.

91.25% using proprietary data set cars 80

Error!

Reference source not found.

99.6% using proprietary data set vans, trucks, cars 9825

Error!

Reference source not found.

97% using proprietary data set Not reported 100

Error!

Reference source not found.

92.1% using media-lab data set vans, trucks, cars 741

93.33% using AOLP data set (proprietary) cars and vans 2049

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Error!

Reference source not found.

83.5% using proprietary data set Not reported 400

Error!

Reference source not found.

96.5% using media-lab data set (proprietary data set and only 741 images are available on web)

vans, trucks, cars 1334

Error!

Reference source not found.

91.65% (proprietary data set) cars 664

our approach

97.3% using media-lab data set vans, trucks and cars

741 98.74% using Israeli data set and Indian

proprietary data set

cars, trucks and motorcycles

159 97.56% using media-lab Israeli and Indian

data sets

vans, trucks, cars and motorcycles

900

93.7% using AOLP database cars and vans 2049

Table 12. Comparison of our approach with SCW, AOLP on medialab and AOLP benchmark databases

Database DB details Conditions SCW AOLP Our Approach

media-lab database

741 images having vans, trucks and cars

open environment having different plate variations

96.5% 92.1% 97.3%

AOLP 2049 images

having vans, trucks and cars

open environment having different plate variations

81.67% 93.33% 93.7%

Average of success rates

89.09% 92.72 94.66%

7. CONCLUSION

In this paper, we proposed a new method for LP detection and missed characters extraction, due to presence of noise between LP characters and border of the LP. The proposed method’s performance is evaluated on media-lab and AOLP benchmark data sets and reported success rates of 97.3% and 93.7% respectively which are shown in performance comparison Table 12. Our approach can detect any number of LPs in an image and is not specific to any country; there is no restriction on the number of characters present in LP, size of LP characters, the number of lines present in LPs, and the size of the characters in each line of LP. As demonstrated in the results, our approach is less restrictive as compared with most of the previously published work and it works for any country having different plate variations, under different environmental and weather conditions. The proposed approach fails to identify the LP, if the LP characters are missed, due to presence of noise such as extremely dirty or blur or characters of LP touches the LP border.

In our future work, we would like to propose a new character recognition algorithm, for English alphabets and numerals which will work for different font styles.

COMPETING INTERESTS

Author has declared that no competing interests exist.

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Biography of author(s)

Dr. Narasimha Reddy Soora

Department of Computer Science and Engineering, Kakatiya Institute of Technology and Science, Warangal, Telangana, India.

He received his post-graduate degrees (Ph.D.(CSE)) from VNIT, Nagpur, Maharashtra, India in 2017 and (M.Tech.(CSE)) from JNTU, Hyderabad, Telangana, India in 2007 and his undergraduate degree (B.E.(CSE)) from Osmania University, Hyderabad, Telangana, India in 1999. He has a total of 21 years of experience, nine years of which were in the IT industry and 12 years as an academic. Currently he is working as Associate Professor in the department of Computer Science and Engineering, KITS Warangal. His research interests are in the fields of Image Processing, Machine Learning, Medical Image Processing and Deep Learning. He has published good number of journals and conferences indexed in SCIE and SCOPUS. He has 2 topper certifications from SWAYA-NPTEL along with few mentor certifications. He is a Wipro Certified Faculty (WCF) in Java Programming. He has various certifications from ORACLE Academy. He has good expertise in C, C++, Java, Python, Unix Internals, Shell Scripting, Perl, Matlab, and Oracle (SQL/PL-SQL). He is life member of ISTE, CSI, India and a Fellow of IETE, India. Email ID: [email protected], [email protected]. ORCID: https://orcid.org/0000-0002-2268-0022. Scopus author id: 56766080900. Web of Science ResearcherID: AAF-6622-2019.

_________________________________________________________________________________

© Copyright (2021): Author(s). The licensee is the publisher (Book Publisher International).

DISCLAIMER

This chapter is an extended version of the article published by the same author(s) in the following journal.

Mathematical Problems in Engineering, 1-14, 2016.

Gambar

Table 5. Pseudo code for LP border points identification  1  For each cluster component
Fig. 4. Results of pre-processing, different clustering stages, thinning and re-sizing and LP  identification
Table 11. Comparison of proposed LP detection method with few of the competitive LP  detection methods in the literature
Table 12. Comparison of our approach with SCW, AOLP on medialab and AOLP benchmark  databases
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