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Vehicle Detection Using Normalized Color and

Edge Map

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Abstract

In this thesis, a novel approach for detecting vehicles using color and edge

information from static images is presented. Different from traditional methods

which use motion features to detect vehicles, the proposed method introduces a new

color transform model to find important vehicle color for the quick finding of

possible vehicle candidates. Since vehicles have various colors under different

weather and lighting conditions, seldom works were proposed for the detection of

vehicles using colors. The proposed new color transform model has extremely

excellent capabilities in identifying vehicle pixels from background ones even

though the pixels are under varying illuminations.

After finding possible vehicle candidates, three important features including

corners, edge maps, and coefficients of wavelet transform are used for constructing a

cascade and multi-channel classifier. According to this classifier, an effective

scanning is performed to verify all possible candidates. The scanning can be

quickly achieved because most background pixels are eliminated by the color feature.

Experimental results show that the integration of global color feature and local edge

feature is powerful in the detection of vehicles. The average accuracy rate of

vehicle detection is 94.5%.

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(Moti o n

features)

corners(edge maps)

(multi-channel)

94.5

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CONTENT

CHAPTER 1 INTRODUCTION................................................... ..................................................... 1

1.1MOTIVATION.....................................................................................................................1 1.2REVIEW OF RELATED WORKS .........................................................................................2

1.3OVERVIEW OF THE PROPOSED SYSTEM ..........................................................................5

CHAPTER 2 CONVENTIONAL METHODS FOR DATA ANALYSIS ........................................ 7

2.1KARHUNEN-LOE`VE TRANSFORM ...................................................................................8

2.2BAYESIAN CLASSIFIER....................................................................................................10

2.3NEAREST NEIGHBOR CLUSTERINGALGORITHM .......................................................11

CHAPTER 3 VEHICLE COLOR DETECTOR ....................................................... .....................13

3.1COLOR FEATURES FOR DIMENSIONALITYREDUCTION................................................15

3.2PIXELS CLASSIFICATION USING BAYESIAN CLASSIFIER...............................................19

3.3PIXELS CLASSIFICATION USING NEURAL NETWORK....................................................20

3.4COLOR CLASSIFICATION RESULT..................................................................................25

CHAPTER 4 VEHICLE VERIFICATION..................... ................................................................ 27

4.1VEHICLE HYPOTHESIS ...................................................................................................27

4.2VEHICLE FEATURES .......................................................................................................28

4.2.1 Contour feature....................................................................................................28

4.2.2 Wavelet Coefficients .............................................................................................33

4.2.3 Corner Features ...................................................................................................36

4.3INTEGRATION AND SIMILARITY MEASUREMENT ..........................................................37

4.4VERIFICATION PROCEDURE...........................................................................................39

CHAPTER 5 EXPERIMENTAL RESULTS................................................................ ...................42

5.1DATA SET ........................................................................................................................42

5.2PERFORMANCE ANALYSIS OF PIXELS CLASSIFICATION ...............................................42 5.3DETECTION RESULT IN VARIOUS ENVIRONMENTS .......................................................44

CHAPTER 6 DISCUSSIONS AND CONCLUSIONS .............................................................. ........47

6.1DISCUSSIONS ..................................................................................................................47

6.2CONCLUSIONS ................................................................................................................47

REFERENCES................................................................ ............................................................ .........49

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List of Figures

Fig. 1 Details of the proposed vehicle detector...........................................................5

Fig. 2 Two-dimension data representation of ten-dimension data set.........................8

Fig. 3 Bayes classifier (adapted from Tou and Gonzlaez[1974]) .............................10

Fig. 4 Effect of the threshold and starting points in a simple cluster seeking scheme.

(Adapted from [23]).........................................................................................12

Fig. 5 Vehicle detection procedure. (a) Vehicle hypotheses generation. (b) Vehicle

verification. ....................................................................................................14

Fig. 6 Road color distribution and (u, v) feature plane. ............................................15

Fig. 7 Parts of vehicle training samples. (a) Vehicle training images. (b) Non-vehicle

training images...............................................................................................17

Fig. 8 Results of color transformations of background pixels. (a) Result of color

transformation using the (u, v) domain. (b) Result of color transformation

using the (s, t) domain.(c) Vehicle pixels plotting : result of color

transformation in the (u, v) domain................................................................18

Fig. 9 The basic perceptron model............................................................................21

Fig. 10 Vehicle color detection result. (a)~(b) Original images.(c)~(d) Color

classification result using Bayesian classifier. (e)~(f) Color classification

result using perceptron.................................................................................24Fig. 11 Another vehicle color classification results. Compared with another

images, (b) is duskier but can still perform well. (a)~(b) Original

images.(c)~(d) Color classification result using Bayesian classifier. (e)~(f)

Color classification result using perceptron ................................................26

Fig. 12 A 3x3 averaging mask often used for smoothing .........................................29

Fig. 13 2-D Gaussian distribution with mean (0,0) and =1 ....................................29

Fig. 14 Discrete approximation to Gaussian function with=1.4.............................30

Fig. 15 The Sobel mask in x-direction and y-direction. ...........................................31

Fig. 16 Edge detection by Canny operator................................................................31

Fig. 17 The value ofy is nonlinearly increased whenx increases. ...........................32

Fig. 18 Result of distance transform. (a) Original Image. (b) Distance....................33

Fig. 19 Block diagram of discrete wavelet transform...............................................34

Fig. 20 Wavelet decomposition of three scales.........................................................35

Fig. 21. Corner detection of vehicles (a)Vehicle contains many corners

(b)Comparison with background, vehicle contains more corners than

background thus corners features can be adapted as features......................37

Fig. 22. The cascade classifier used for vehicle detection........................................38

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Fig. 23. Image pyramid structure. Assume the original image size is 320*240,

processing the image at each resolution rescaling the original size with 0.8

ratios until pre-defined resolution is achieved.............................................39

Fig. 24 Red points represent the possible vehicle candidates with stronger responses.

These points should be clustered by nearest-neighbor algorithm. (a)

Original image (b) The white area denotes the region of possible vehicle

pixels............................................................................................................41

Fig. 25. Result of vehicle color detection. (a) Original image. (b) Detection

result of vehicle color...................................................................................44

Fig. 26. Result of vehicle color detection. (a) Original image. (b) Detection result

of vehicle color.............................................................................................44

Fig. 27. Result of vehicle detection in a parking lot .................................................45

Fig. 28. Result of vehicle detection in a parking lot with different orientation. .......45

Fig. 29. Result of vehicle detection on road. ............................................................46

Fig. 30. Result of detecting vehicles from highway. Although these vehicles were

with different colors, all of them were correctly detected. ..........................46

Fig. 31. Result of vehicle detection in road with occlusion......................................46

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CHAPTER 1INTRODUCTION

1.1 Motivation

Due to the development of the scientific and technological civilization, automobiles

have already become an indispensable tool in replacing walking in the modernized

society. The problem resulting from city civilization is the lacking of parking lot, i.e.,

fewer and fewer parking spaces are available especially in the city. It is difficult to

find vacant parking spaces within a short period, which results in the wasting of

precious resources and the problem of environmental pollution.

To fully utilize the precious space, it is a trend to construct the parking lot of every

building upwardly or down into underground in many floors. However, the supply

of the needing parking space still can not meet the urgent requirement comparing with

the speed of the fast growth of vehicles. If we can save the time in finding parking

space, the problems of fuel wasting, traffic violation, labor resource pending, and the

pollution of surrounding air can all be resolved even can improve the mobility of

transportation and the productivity economics. On the other hand, the problem of

traffic jam in city roads usually occurs in rush hour or vacation. Part of the reason is

due to the unawaring of road information, such as the information of nearby available

parking space. The detection of vehicles in parking lot can accurately provide the

information of available parking spaces. Hence, the providing of useful road

information to vehicle drivers may somewhat alleviate the traffic jam problem.

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Moreover, the accurate detection of vehicles is also indispensable to the

measurement of various traffic parameters, such as vehicle count, speed, flow, and

concentration.

Once a vehicle can be accurately tracked through a road network,

more complex traffic parameters, such as linked-travel-time, can be computed.

Therefore, vehicle detection is critical to traffic management systems and intelligence

transport systems for collision avoidance or traffic flow control.

In this thesis, we plan to develop an intelligent vehicle detection system based on

the techniques of computer vision with an eye to effectively managing the parking

spaces in the indoor/outdoor parking lots or along the roads.

1.2 Review of Related Works

Vehicle detection [1]-[2] is an important problem to be resolved in many related

applications, such as self-guided vehicles, driver assistance system, intelligent parking

system, and measurement of traffic parameters like vehicle count, speed, and flow.

One of the common approaches to vehicle detection is the using of vision-based

techniques to analyze vehicles from images or video sequences. However, due to the

variations of vehicle colors, sizes, orientations, shapes, and poses, the developing of a

robust and effective vision-based vehicle detection system is challenging. To

alleviate the above problems, different approaches using different features and

learning algorithms for locating vehicles have been investigated. For example, many

researchers [2]-[5] used background subtraction to extract motion features for

detecting moving vehicles from video sequences. However, this kind of motion

features is no longer usable in static images. To deal with static images, Wu et al. [6]

used wavelet transform to extract texture features for locating possible vehicle

candidates from roads. Then, each vehicle candidate is verified by using a PCA

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colors, sizes, and shapes changing, due to different viewing angles and lighting

conditions. All the variations will increase the difficulties and challenges in

selecting a general feature for describing vehicles. In this thesis, a novel vehicle

detection method using colors from still images is proposed. Once a general color

transform can be found to accurately capture the visual characteristics of vehicles

(even under different lighting conditions), color feature will become a very useful and

powerful cue to narrow down the search areas of possible vehicles. The main

contribution of this thesis is the presentation of a statistic linear color model that

makes vehicle colors be more compact in the specific feature space such that vehicles

pixels will be distributed sufficiently concentrating on a smaller area. The model is

leaned by observing how the vehicle colors change in static images under different

lighting conditions and cluttered backgrounds. The model is global and does not

need to be re-estimated for any new vehicle or new image. Without prior knowledge

of surface reflectance, weather condition, and view geometry in the training phase, the

model can still perform very well in separating vehicle pixels from background ones.

After that, three features including edge maps, corners, and wavelet coefficients are

devised to form a multi-channel classifier. The classifier is modeled using a Gaussian

model and can be automatically learned from a set of training examples. Since the

classifier records many vehicle appearance changes, it possesses good discriminative

properties in verifying the correctness of each vehicle candidate. Due to the usage of

color feature that can filter out most of background pixels in advance, only very few

candidates are still needed to be checked and thus the verification process can be

accomplished efficiently. Moreover, vehicle still can be detected successfully even

with occlusions because of the filtering effect and discriminative capabilities of the

proposed method. Experiments were conducted in various real cases and the

experimental results verify the superiority of the proposed method in detecting

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vehicles.

Fig. 1 Details of the proposed vehicle detector.

1.3 Overview of the Proposed System

A novel system using edges and colors from static images to detect vehicles is

presented in this thesis. The flowchart of the proposed system is shown in Fig. 1.

At the beginning, a specific color transformation is proposed to project all the colors

of input pixels on a new feature space such that vehicle pixels can be easily

distinguished from non-vehicle ones. Here, a Bayesian network is adopted for

identification.

Since vehicles have different sizes and orientations, different vehicle hypothesis are

generated from each detected vehicle. Three kinds of vehicle features including

edges, coefficients of wavelet transform, and corners are employed to eliminate

non-vehicle candidates. Using the proper weights obtained from training samples,

these features can be combined together to form an optimal vehicle classifier. Then,

vehicles candidates can be verified robustly and accurately from static images.

The rest of the thesis is organized as follows. Chapter 2 introduces three

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conventional methods for data analysis. The details of our proposed novel color

transform in finding vehicle colors are described in Chapter 3. Chapter 4 discusses

the details of feature extraction and the proposed multi-channel classifier.

Experimental results are demonstrated in Chapter 5 to verify the validity of the

proposed method. Finally, conclusions are given in Chapter 6.

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CHAPTER 2

CONVENTIONAL MEHTODS FOR

DATA ANALYSIS

In this chapter, three conventional methods used for constructing the vehicle color

detector are firstly described including their basic theories, mathematical models, etc.

As we know, feature extraction, classification and clustering are significant issues that

were intensively discussed in pattern recognition. Feature extraction concentrates on

the looking of a subset that contains the critical information but can not destroy the

nature from the original vast data set. This subset can be utilized to replace the

original data set to avoid noise jamming. Dimensionality reduction is often

performed for feature extraction in reducing computational load. In addition, fewer

and critical features are remained in designing the classifier that decreases the

confused judgment. With the prior knowledge of the data distribution, Bayesian

classifier is adopted to separate the desired features from unconcerned ones and

clustering technique is employed to aggregate the critical features for recognition.

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Fig. 2 Two-dimension data representation of ten-dimension data set

2.1 Karhunen-Loe`ve Transform

Dimensionality reduction is a useful skill in pattern recognition. Too many features

lead to more computation load and create confusion such as to decreasing the

classifier performance. The main idea of Dimensionality reduction is selecting a

subset of feature from original data and generating the lower dimension data still

preserving distinguishing characteristics. That is to reduce the dimensionality of a

high dimensional data without significant loss in accuracy. In practice,

high-dimensional data are often loose without tight clusters. By projecting data onto

an appropriate lower-dimensional space (feature space), data clusters would have a

local structure that makes the close neighborhood meaningful.

Human beings can not realize the shape, density of the data in high dimension.

Projecting data into lower-dimension space makes data clusters easy to observe by

human eyes. Fig. 2 shows a 10D data set projecting into 2D space. Obviously, this

data set contains four clusters in high-dimensional space through projecting into 2D

plane.

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Karhunen-Loe`ve transform (K-L transform) is a well-know and widely used

technique for statistical analysis. It has various names, such as Principal component

analysis and Hotelling transform. This method usually was adopted in feature

extraction, data compression, image processingetc. K-L transform is a linear

projection from m-dimension space to n-dimension space (n m). It has to

compute a transformation matrix H which is constructed by the eigenvector of the

covariance matrix R. Suppose we have an input data set X = { nxxx ,...2,1 }, the

computation of the transformation matrix is as the following algorithm:

Step 1 : Let m denote the mean and C denote the covariance matrix

Step 2 : Compute the eigenvalues nddd ,...,, 21 and construct the associate

eigenvector ofC . Sort them as

Step 3 : form the matrix H = Tn ]...[ 2,1

After transformation, the covariance matrix of the feature becomes a diagonal

matrix. This matrix projects the input data into a subspace whose axes are in the

direction of the largest variation as follow:

Step 4 : NiforHxy ii ,...1==

=

=

=

=

n

i

T

ii

n

k

k

mxmxn

C

xn

m

1

1

))((1

1

n ...21

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Fig. 3 Bayes classifier (adapted from Tou and Gonzlaez[1974])

2.2 Bayesian classifier.

In statistical pattern recognition, we focus on how to developing decision or

classification strategies which form classifiers. The design of classifier attempts to

integrate all available information such as measurement of a priori probabilities of

data. Then, the classifier minimizes the total expected loss and using Bayes formula

as the optimum measure of performance. The class-conditional density function of

probability of a patternx, whenxbelongs to class iw , can be given as follow:

Kiwxp i ,...,2,1),/( =

All the class-conditional densities are completely know a prior, the decision

boundary between pattern classes can be established using the optimal Bayes decision

rules (as shown in Fig. 3)[24].

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By way of introduction, consider a vector x with Gaussian distribution, the

probability density function ofx is:

m and are mean and variance respectively. We can get the decision boundary

function is:

C is covariance matrices. The Bayes classifier assigns a patternx to class iw if

The detail derivate procedure can be found in [23].

2.3 Nearest Neighbor Clustering Algorithm

Clustering is a data analysis method for discovering patterns and underlying cluster

structures. Its also the formal study of algorithm and methods for grouping data.

It helps to exploring structure of the data and has many applications in engineering

and science. Unfortunately, theres no predominant method that is the best for

different data sets. Various kinds of methods such as Hierarchical clustering,

partitioning based k-means and Self Organizing map (SOM) are wildly used. The

K-means algorithm needs choosing the value k, the number of clusters, at initial step.

Then it divided the input data set into kdistinct cluster by minimizing the sum of the

distances between the input pattern and the each cluster center.

( ) ( )

[ ]MimxCmxCwpxd

ii

T

iiii

,...,2,1,2

1ln

2

1)(ln)( 1 ==

ijMjwpwxpwpwxp jjii => ,,....2,1),()/()()/(

=

2

2

1exp

*2

1)(

mxxP

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Fig. 4 Effect of the threshold and starting points in a simple cluster seeking scheme.(Adapted from [23])

Here, a simple Nearest Neighbor Clustering algorithm similar K-means without

initial value kis described below:

Step 1: set i = 1 and k = 1, assign pattern iX to cluster )1( =kCk

Step 2:i = i + 1. Find the nearest neighbor of iX and assign these patterns

to clusters. Let d denote the distance from iX to its nearest

neighbor.

Step 3: if d t (a pre-defined threshold), then assign iX to kC .

Otherwise, set k= k +1, and assign iX to a new cluster kC

Step4: if every pattern has been assigned to a cluster, stop. Else, go to

step2.

As shown in Fig. 4, the number of clusters kdepends on the parametert. As the

value of t increases, the fewer clusters are generated. The distance d is usually

measured as Euclidean distances.

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CHAPTER 3

VEHICLE COLOR DETECTOR

Like the skin color used for face representation, a new color transform is introduced

in this chapter for projecting all pixels with (R, G, B) colors to a new domain. Then,

a specific vehicle color can be found and defined for effective vehicle detection.

The notion or vehicle color will be briefly introduced in the forthcoming contexts.

Section 3.1 describes the derived procedure of the transformation formula and Section

3.2 presents the classification of vehicle color pixels using Bayesian classifier.

Section 3.3 presents the neural network technique used for classification. Finally,

section 3.4 shows the results of color classification.

As a gray car goes into the general gray road surface, human vision will perceive

that the colors of the two are very similar. That is the feature of color alone is not

enough in distinguishing the two in human eyes. However, the color of an object

can be represented in several different color spaces, such as RGB, HSV, etc., and the

observation of an objects color in images depends on incident light, reflectance of the

object, and viewing angle. In these feature spaces, vehicle color owns the different

and special characteristic to separate from the background even vehicles with various

colors. Thus, the distributions of road and vehicles color can belearned from

training samples. Once the distribution of vehicles color is evaluated precisely, the

difference between vehicles and background color pixels can be easily discriminated.

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(a) (b)

Fig. 5 Vehicle detection procedure. (a) Vehicle hypotheses generation. (b) Vehicleverification.

In general, vehicle detection contains two major steps: vehicle hypothesis and

vehicle verification. In the first step, the location of a vehicle or more vehicles in an

image is generating as shown in Fig. 5(a). Without extra information about vehicle

positions, a time-consuming scanning is performed from left to right, up to down in

the input image. Exhaustive search is the simplest method to verify by testing all

pixels in images and check all of them whether vehicles exist or not. Too many

vehicle hypotheses make the following verification step needing enormous

computation times. In the past, most papers focus on improving the performance of

verification steps but selecting an exhaustive search. Therefore, this paper provides

an efficient method which can quickly find possible vehicle positions reducing the

numbers of vehicle hypothesizes and decreasing the computation time without a full

search.

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Fig. 6 Road color distribution and (u, v) feature plane.

3.1 Color Features for Dimensionality Reduction

In this section, a detail description about what we called vehicle color is given.

Assume that there are N images collected from roads, highways and parking places.

Through a statistic analysis, we can get the covariance matrix of the color

distributions ofR, G, andB fromNimages. Using the Karhunen-Loe`ve transform,

the eigenvectors and eigenvalues of can be further obtained and represented as ie

and i , respectively, for i = 1, 2, and 3. Then, three new color features iC can be

formed and defined, respectively,

for =1, 2, and 3,= + +r g b

i i i iC e R e G e B i (1)

where ( , , )= r g bi i i ie e e e . The analysis of Ohta et al[1] indicated the color feature 1C

with the largest eigenvalue is the one used for color-to-gray transform, i.e.,

1

1 1 1

3 3 3= + +C R G B . (2)

Other two color features 2C and 3C are orthogonal to 1C and can be obtained,

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respectively, as follows:

2

R -

2=

BC and

3

2 - -

4=

G R BC . (3)

All the color features can be obtained by projected a pixel color (R, G,B) with the

vectors (1/3, 1/3, 1/3), (1/2, 0, -1/2), and (-1/4, 1/2, -1/4) respectively. In [17],

Healey pointed out that the colors of homogeneous dielectric surfaces (like roads or

clouds) moved along the axis directed by Eq.(2), i.e., (1/3, 1/3, 1/3). That means the

colors of homogeneous dielectric surfaces have no changes as time passes except

intensity strength. Compared with other metal surfaces, road surface are more easily

modeled. Fig. 6 indicates a RGB color space and the color of road surface

distribution are represented as red points. In [14], Rojas et al. also found that the

colors of roads concentrated around a small cylinder along the axis directed by Eq. (2).

Therefore, projecting all the road colors to a plane which is perpendicular to the axis

pointed by 1C , all the road colors concentrate around a small circle [14]. Once

feature vectors of color distribution of the object are founded, the object color

distribution would form a specific cluster in the feature space by feature projection.

Based on this observation, this paper proposed a new color model to transform all

color pixels on a 2D feature space. On this feature space, all vehicle color pixels

concentrated on a smaller area. By modeling the characteristics of this area, a

Bayesian classifier is developed to accurately identify vehicle pixels from background

ones.

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(a) (b)

Fig. 7 Parts of vehicle training samples. (a) Vehicle training images. (b) Non-vehicletraining images.

At the beginning, thousands of training images are collected from different scenes

including roads, parking lots, building, and natural scenes. Fig. 7 shows some parts

of out training samples. Based on the training samples, using theKL transform, we

found that the eigenvector with the largest eigenvalue of this data set is (1/3, 1/3, 1/3)

(the same as in Eq. (2)). In addition, the color plane ( , )u v perpendicular to the axis

(1/3, 1/3, 1/3) expanded by other two eigenvectors is:

2 p p pp

p

Z G Bu

Z

= and { , }p p p pp

p p

Z G Z Bv Max

Z Z

= , (4)

where ( pR , pG , Bp ) is the color of a pixel p and ( )/3p p p pZ R G B= + + used for

normalization. The color transformation described in Eq.(4) concentrates all vehicle

pixels on a smaller area. There are also other color planes perpendicular to the axis

(1/3, 1/3, 1/3). For example, another color plane (s, t) perpendicular to the axis (1/3,

1/3, 1/3) can be found, i.e.,

-

p p

p

p

R Bs

Z

= and- +2 -p p p

p

p

R G Bt

Z

= . (5)

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(a) (b)

(c)

Fig. 8 Results of color transformations of background pixels. (a) Result of colortransformation using the (u, v) domain. (b) Result of color transformation using the (s,t) domain.(c) Vehicle pixels plotting : result of color transformation in the (u, v)domain

Plotting all background pixels of training images on the (u, v) and (s, t) planes

using Eq.(4) and Eq.(5), respectively, are 8.85384 and 40.1879, respectively. Fig. 8

shows the result of color transform. Clearly, the transformation described in Eq.(4)

makes background pixels more compact than the one in Eq.(5).

The feature space ( , )u v has better discrimination abilities to concentrate the

vehicle pixels forming a compact cluster with variance 13.2794. It makes us easy to

separate vehicle pixels from background ones. Using this color transformation, the

critical issue becomes a 2-class separating problem in the (u, v) feature space. With

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an input image, the color transformation is performed to project all pixels of input

image into a 2D space. Then, How to find a decision boundary to distinguish these

pixels into two different classes (i.e., vehicles vs. non-vehicles) will be described in

the next section.

3.2 Pixels Classification Using Bayesian Classifier

After transformation, a Bayesian classifier should be designed to accurately identify

vehicle pixels from background ones with colors. We assume that the RGB color

component in the (u, v) color domain are multivariate Gaussian distribution.

Assume vm and nm are the mean of the vehicle and non-vehicle pixels calculated

from collected training images in the (u, v) color domain, respectively. In addition,

v and n are their corresponding covariance matrices in the same color domain

respectively, which yields

t

vux

vvv

vux

v

mxImxIn

xIn

m

=

=

),(

),(

))()()((1

)(1

where n is the total training images. The probability of the point x belongs to

vehicle class is:

1( | ) exp(- ( ))

2v

v

p x vehicle d x

=

, (6)

where ( ) ( )11

( )2

t

v v v vd x x m x m= . Similarly, the probability of pointx

belonging to a non-vehicle class is defined as follows:

1( | - ) exp(- ( ))2

n

np x non vehicle d x= , (7)

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where ( ) ( )11

( )2

t

n n n nd x x m x m= . If a pointxbelongs to vehicle class, the

probability of a pixelx satisfy:

( ) ( )| - |p vehicle x p non vehicle x> , (8)

With the Bayesian rule, Eq.(8) can be rewritten as follows:

( ) ( )| ( le) | - ( - )p x vehicle P vehic p x non vehicle P non vehicle> , (9)

where ( le)P vehic and (non- le)P vehic are the priori class probabilities of vehicle

pixels and non-vehicle ones, respectively. Plugging Eqs. (6) and (7) into Eq.(9),

we can get:

( | ) ( - )exp(- ( ) ( ))

( - | ) | | ( )

n

v n

v

p vehicle x P non vehicled x d x

p non vehicle x P vehicle

= + >

. (10)

Taking the log form of Eq.(10), we have the following classification rule:

Assign a pixelx to class vehicle if

( ) - ( )>n vd x d x , (11)

where = v

n

( - )log[ ]

| | ( )

P non vehicle

P vehicle

. In this way, we can get a binary image that

denotes the vehicle pixels extraction result.

3.3Pixels Classification Using Neural Network

Learning is an extremely important characteristic of the biological or artificial system

full of wisdom and can be divided into two styles: learning from examples orlearning from observation and discovery. The former is supervised learning and the

later is unsupervised learning. This section describes how to use neural network

method to classify vehicle pixels from background ones.

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Fig. 9 The basic perceptron model

The operation of neural network can be divided into two stages: learning and recall.

In the learning stage, network learns from input data using different study rules. In

each repeated training recurrences, network adjusts the weight values in order to reach

the study and recall effects. The results of learning lies in the change of the network

weight values

In this section, a neural network model called perceptron is used for pixels

classification. The basic architecture of perceptron is shown in Fig. 9. The model

contains three layers which are called input layer, hidden layer and output layer,

respectively. Basic components of perceptron are accumulators which combine each

input pattern linearly with some proper weights. Let R denotes the response

activated by the thi neuron and iw is its corresponding weight. The total response is

given by:

xwxwR j

n

j

i

'

1

== =

Input layer Hidden Layer Output layer

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Then, the response are forwarded into a hard limiter or threshold function f(v). In

general, the responds of a neuron are positive causing the output of hard limiter

function 1, otherwise, the negative responds makes the output 0.f(v) can be described

as the following form:

In section 3.1, we used the equation 5 to transform training images containing

vehicle and non-vehicle pixels into (u, v) domain. Here, we plus a label of each

pattern transformed of the two classes (i.e., vehicle is 1 and non-vehicle is -1).

Assume we have n examples from two classes

}1,1{),,(...1,),( += iiii yvuxniyx

If we want to classify all input patterns into two classes, the discriminate

hyper-plane is defined as:

= =

k

n

k

kxwxf1

)(

Letx denotes ),( ii yx and is the threshold of hard limit function pre-defined.

If 0)( >xf , we say that the pattern belongs to class 1 ; if 0)(

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Step 2: Calculating the output of the network.

Assume input pattern isx(n) , n denotes the thn recurrence. The outputs

of neuron are:

Step 3: Adjust ninw i ...1,)( = according to the following rules:

Step 4: n=n+1, go tostep 2until the network converges or learning recurrences n

exceed some pre-defined values.

)]()(sgn[)( nxnwnyT

=

+=

01

01)sgn(

vif

vifv

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(a) (b)

(c) (d)

(e) (f)

Fig. 10 Vehicle color detection result. (a)~(b) Original images.(c)~(d) Colorclassification result using Bayesian classifier. (e)~(f) Color classification result using

perceptron

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3.4 Color Classification Result

This section gives some illustration examples to present the effect about color

classification. The results of color classification are given in two ways which are

described in section 3.2 and 3.3. We plot the vehicle pixels with red color and

preserve the original image for comparison. Fig. 10(a) are shot at high way. It is

noticed that the color of vehicle and road surface are both very similar to gray color.

With the view of the human eye, these two kinds of color are very close to a certain

extent. However, these two kinds of color own different property in our experiment

after color classification. The road pixels with similar gray color are rejected and

vehicle pixels passed which drawn with red color. Fig. 10(c)and (e) demonstrate our

argument. In Fig. 10(b), two vehicles are occlusive by trees but there is no miss by

the power of color classification which has shown in Fig. 10(d) and (f).

In fact, color classification process is a supervised learning. There is no guarantee

which kinds of methods are the best. There are many techniques can achieve this

goal such as Support Vector Machine (SVM), Radial basis function network

(RBF)etc. In this paper, we only give two methods including Bayesian and

perceptron to fulfill color classification. Other experimental results are given in Fig.

11 that vehicles are shot at short range. The experimental results proved that the

proposed method is robust dealing with large variety color changes including different

viewing angle, vehicle colors and lighting conditions. Fig. 11(b) was captured at

dusky lighting situation and the color classification still performs well.

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(a) (b)

(c) (d)

(e) (f)

Fig. 11 Another vehicle color classification results. Compared with another images,(b) is duskier but can still perform well. (a)~(b) Original images.(c)~(d) Colorclassification result using Bayesian classifier. (e)~(f) Color classification resultusing perceptron .

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CHAPTER 4

VEHICLE VERIFICATION

In the previous chapter, a novel color model and classifiers (Bayesian and neural

network) were presented to extract vehicle pixels by using colors from static images.

After that, different vehicle hypothesizes are generated to tackle the variations of

vehicle appearances. Then, a verification process is applied to verify whether there

exists a vehicle in the scene or not.

4.1 Vehicle Hypothesis

Here, a vehicle hypothesis ( )IsH X is a sub-image extracted from a static image I

with the size s sw h and the centerX. The minimum size of detected vehicles used

in this paper is assumed to be36 36 . We build a set of classesi

C of vehicle

templates to verify the correctness of ( )IsH X estimating its maximum response at

different orientations. Herei

C is a collection of different vehicle templates whose

orientations are at the same anglei

. The maximum response is defined as the

maximum similarity between ( )IsH X and all vehicle templates.

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4.2 Vehicle Features

In this thesis, three features including vehicle contour, wavelet coefficients and

corners are used to measure the similarity. In what follows, details of each feature

are introduced.

4.2.1 Contour feature

Contour is a good feature to describe vehicles shapes and usually represented by

chain coding. However, chain coding is easily affected by noise. Therefore, this

paper uses a distance transform to convert an object contour to a distance map

different from chain coding. Based on this map, different vehicle hypothesis can be

well discriminated.

4.2.1.1 Edge extraction

Edge detecting is a fundamental technique in image processing. Edges in images are

areas with strong intensity and characterize the objects boundaries. Successful edge

detection filters out most useless information such as noise but preserving the

significant structure in images. The first step before detecting edges is to filter out

noise in the original image by Gaussian smoothing.

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Fig. 14 Discrete approximation to Gaussian function with=1.4

If the image I(x, y) with size M*N and the kernel mask K (k, l) with size m*n,

mathematically, we write the convolution as:

= =

++=m

k

n

l

lkKlykxIyxO1 1

),()1,1(),(

The Gaussian smoothing operator is also a 2D convolution operator similar to

median filter which uses a different kernel that represents the shape of a Gaussian

distribution. 2D Gaussian has the form:

2

22

22

exp2

1),(

yx

yxG

+

=

The 2-D Gaussian distribution with mean (0,0) and =1 is shown in Fig. 13. The

Gaussian filter can be created by the user in terms of mask size and standard deviation

. In practice, a discrete approximation to the Gaussian function should becalculated. Then, the filtering process is a convolution by the filter mask and the

image. Fig. 14 shows a suitable integer Gaussian mask that approximates a

Gaussian distribution with a =1.4.

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Fig. 15 The Sobel mask in x-direction and y-direction.

Fig. 16 Edge detection by Canny operator.

After smoothing the image and eliminating the noise, the second step is to compute

the gradient of the image. Here, the Sobel operator is used for estimating the

gradient in the x-direction and y-direction according to Fig. 15. Then, the magnitude

of edge gradient can be approximated by the following formula:

|||||| yx GGG +=

Finally, Canny method are performed to get more precise edges including non-

maximum suppression thinning the edges and linking edges segments using two

thresholds. Fig. 16 shows some examples of our training vehicle images using

Canny method.

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Fig. 17 The value ofy is nonlinearly increased whenx increases.

4.2.1.2 Distance transform

After getting the binary edge image, a 33 mask is used to detect all boundary points

from a vehicle image. When this mask is used and moved at a non-zero pixelp, if

one pixel in this mask is zero, thenp is a boundary pixel. Assume that VB is a set

of boundary pixels extracted from a vehicle V. Then, the distance transform of a

pixelp in Vis defined as

( ) min ( , )V

Vq B

DT p d p q

= , (12)

where ( , )d p q is the Euclidian distance betweenp and q. Eq.(12) is further modified

to enhance the strength of distance changes as follows

( ) min ( , ) exp( ( , ))V

Vq B

DT p d p q d p q

= , (13)

where 0.1 = . Like Fig. 17, when x increases more, the value ofy will increase

more rapidly thanx. Fig. 18(b) shows the result of the distance transform of Fig. 18

(a). Thus, according to Eq.(13), a set ( )CF V of contour features can be extracted

from a vehicle V. Scanning all pixels of V in a row major order, ( )CF V can be

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then represented as a row vector, i.e.,

0( ) [ ( ),...., ( ),....]V VC iF V DT p DT p= , (14)

where all ip belong to V and i is the scanning index.

(a) (b)

Fig. 18 Result of distance transform. (a) Original Image. (b) Distancetransform of (a).

4.2.2 Wavelet Coefficients

Wavelet transform is a very useful tool to represent images at different resolutions.

It has been successfully applied in many applications like compression, watermarking,

texture analysis, communications, and so on. The wavelet transform uses two kinds

of filers to decompose a signal into different resolutions, i.e., the low-pass filter ( )h k

and the high-pass one ( )g k . Then, given a discrete signalf(n) (assumed at the fine

resolution j=0 and represented as 0 ( )S f n ), with the low-pass filter ( )h k , the

approximation off(n) at lower resolutionj-1 can be calculated as follows:

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1 ( ) ( ) ( 2 )j jk

S f n S f k h k n

=

= . (15)

ng(k)

h(k) 2

2 Wj-1f(n)

Sj-1f(n)

(a)

f(m,n)

h[k] 2 LL

HH

LH

HL

H

L

2

2

2

h[k]

g[k]

g[k]

2g[k]

2h[k]

(b)

Fig. 19 Block diagram of discrete wavelet transform.

(a) 1D Wavelet transform. (b) 2D Wavelet transform.

In addition, information lost between ( )jS f n and 1 ( )jS f n can be obtained using

the high-pass filter ( )g k as follows

1( ) ( ) ( 2 )j j

k

W f n S f k g k n

=

= . (16)

From the view of signal processing,1

( )j

S f n

and1

( )j

W f n

are, respectively, the

components of low frequency and high frequency of ( )jS f n . The above procedure,

which is also known as the sub-band coding, can be repeatedly performed. Fig. 19(a)

shows the diagram of 1D wavelet transform. The 1D wavelet transform can be

easily extended to two dimensions. The simplest way to generate 2D wavelet

transform is to apply two 1D transforms to the rows and columns of a 2D signal f(m,

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n), respectively. Fig. 19(b) shows the block diagram of 2D wavelet

Fig. 20 Wavelet decomposition of three scales

transform. Given f(m, n), convolving its rows with ( )h k and ( )g k , we get two

sub-images whose horizontal resolutions are reduced by a factor 2. Both sub-images

are then filtered columnwise and down-sampled to yield four quarter-size output

subimages.

The filters ( )h k and ( )g k we use are the D4 family of Daubechess basis, i.e.,

{h(0), h(1), h(2), h(3)}=1 3 3 3 3 3 1 3

{ , , , }4 2 4 2 4 2 4 2

+ + and { g(0), g(1), g(2), g(3)}

= {h(3), -h(2), h(1), -h(0)}. In this paper, a three-scale wavelet transform is used to

process all vehicle images. Then, each wavelet coefficient is quantized to three

levels, i.e., 1, 0, -1, if its value is larger than 0, equal to 0, and less than 0, respectively.

After that, all the quantized coefficients are recorded for further recognition. As

shown in Fig. 20, when recording, each wavelet coefficient is further classified into

different bands, i.e.,LL,LH,HL, andHH. According to this classification, a pixelp

is labeled as 1, 2, 2, and 4 if it locates in the LL, LH, HL, HHbands, respectively.

Let ( )l p denote the labeling vale ofp. Then, given a vehicle V, from its wavelet

coefficients, we can extract a set ( )WF V of WT features. Scanning V in a row-major

order, ( )WF V can be further represented as a row vector, i.e.,

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0 0( ) [ ( ) ( ),...., ( ) ( ),....]W W

W V i V iF V l p Coeff p l p Coeff p= , (17)

where all ip belong to V and i is the scanning index.

4.2.3 Corner Features

Corner is another type of image features like edge. Corner means interesting points

of the object which have stable invariance property even suffers noise, rotation,

compression, and scale or illumination variation. They are often used in image

alignment (homography, fundamental matrix), motion tracking, and image retrieval.

Corner happens in image intensity which has significant change in all directions, yet

edge has no change along the edge direction.

The Harris corner detector is a popular one using the locally averaged moment

matrix M computed from the image gradients:

=

yx yyx

yxx

III

IIIyxwM

,2

2

),(

where w(x, y) means a window function, Ix and Iy means the first derivative of

image inx andy direction respectively. Then, combines the eigenvalues( 1 and 2 )

of M, which describes the intensity structure of local image, to measure of corner

responseR:

21

21

2

*det

)(det

+=

=

=

Mtrace

M

MtracekMR

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where kis empirical constant, k= 0.04~0.06. The maximum value, larger than a

threshold, indicates the corners position. To avoid corners due to image noise, a

Gaussian filter can be used to smooth the image firstly.

(a) (b)

Fig. 21. Corner detection of vehicles (a)Vehicle contains many corners(b)Comparison with background, vehicle contains more corners than background thuscorners features can be adapted as features.

Vehicles contain strong edges and lines with different orientation and scales. The

corners happen in areas of cross lines. In Fig. 21, we present the results of the corner

detector in two vehicle images. Obviously, the area with vehicles often contains

many corners than background.

4.3 Integration and Similarity Measurement

In Sections 4.2.1 and 4.2.2, two features have been illustrated to describe the visual

characteristics of a vehicle template V. We are now able to integrate these two

features together for computing the similarity between ( )IsH X and V. Given V,

based on Eqs. (14) and (17), we can extract two feature vectors ( )CF V and

( )WF V from its contour and wavelet transform, respectively. For convince, we

combine these two features together to form a new feature vector ( )F V , i.e.,

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( ) [ ( ), ( )]C WF V F V F V = . For a vehicle class iC , if there are iN templates in iC ,

we can calculate its meani

and variancei

of ( )F V from all samples V in

iC . Then, given a vehicle hypothesisH, the similarly between Hand iC can be

measured by this equation:

-1( , ) exp(-( - ) ( - ) )i i i i

t

H HS H C F F = , (18)

where tmeans the transpose of a vector. Therefore, given a position X, its vehicle

response can be defined as follows

,( ) max ( ( ), )

ii

I

ss

R X S H X C

= . (19)

When calculating Eq.(19), the parameter i can be further eliminated if the direction

of the hypothesis ( )Is

H X is known in advance. In [18], a good moment-based

method is provided for estimating the orientation of the longest axis of a region. If

( )Is X is denoted the orientation of ( )

I

sH X , Eq.(19) can be then rewritten

( )( ) max ( ( ), )I

s

I

s XsR X S H X C

= . (20)

Fig. 22. The cascade classifier used for vehicle detection

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Fig. 23. Image pyramid structure. Assume the original image size is 320*240,processing the image at each resolution rescaling the original size with 0.8 ratios untilpre-defined resolution is achieved.

4.4 Verification Procedure

This section describes the method constructing a cascade classifier that improves

detection performance and reduces the computation time. We follow the idea from

Viola and Jones [19] to construct a simple cascade classifier. The classifiers are

connected in cascade to create a pipeline structure. In general, a classifier with low

threshold causes higher detection rates and higher false positive rates. Once many

features can be utilized, a progressive classifier should be designed.

As shown in Fig. 22, corner features formed a simple classifier which is used to

eliminate the almost impossible candidates though some false candidates survive.

The threshold of the corner classifier can be adjusted such that the detection rate is

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close to 100%. In the second step, edge maps and Wavelet coefficients are combined

to form more complex classifiers to achieve low false positive rates. Thus, we

prevent to verify most candidates with all features and save a large number of

computation times. The negative candidates in any classifier are rejected and the

survivals get into the subsequent classifiers. Subsequent classifiers eliminate

additional negatives but require additional edges and wavelet features. Finally a real

vehicle is determined through the cascade classifier.

In real implementation, we borrow a well-known pyramid technique from face

detection methodologies [19]-[21] to speed up the calculation of Eq.(20). This

technique constructs a pyramid structure (see Fig. 23) of image by gradually resizing

the input image. For a vehicle pixel X at the full resolution, its corresponding

vehicle hypothesis ( )IsH X will be generated at the pyramid level s. Then, ( )R X

can be found by searching the optimal value of( )

( ( ), )Is

I

s XS H X C

across each

pyramid level. Two thresholds are used to remove spurious responses and to declare

whether a vehicle is detected at the position X. Let R be the average value of

( )R X for all the centersXof the training vehicle samples. For a vehicle pixelX, if

its response ( )R X is larger than 0.8 R , it is considered a vehicle candidate. In

addition to R , another threshold C (threshold of corners) is used to remove false

detections of vehicles. IfXcontains a real vehicle, the number of corners around X

should be larger thanC

. The parameters R and-1

i (the weight used in

Eq.(18)) can also be learned using the AdaBoost algorithm [22] for increasing the

accuracy of vehicle verification.

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(a) (b)

Fig. 24 Red points represent the possible vehicle candidates with stronger responses.These points should be clustered by nearest-neighbor algorithm. (a) Original image(b) The white area denotes the region of possible vehicle pixels.

From experimental results, we can find that the above verification scheme performs

well enough in detecting all reveal vehicles. Finally, due to noise or shadows, there

would be many vehicle candidates which are overlapped together. These candidates

should be eliminated if they are inside other stronger candidates. Once an image

conations many vehicles and they parks very closely to each other, location of a

vehicle position is starting when the verification procedure is completed. A real

vehicle position may contain more than one vehicle pixel that has the stronger

respones. As shown in Fig. 24, these candidates are performed nearest-neighbor

algorithm for locating the best position of vehicles or separating the two vehicles that

are very close to each other.

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CHAPTER 5

EXPERIMENTAL RESULTS

5.1 Data Set

To ensure our proposed method works well under large varieties of the data, training

examples were collected in different days, different weather conditions, and different

viewing angles. Especially, vehicle training examples are collected in different

orientations and various colors where vehicle parks on road, high way, and parking lot,

etc. The images used in our vehicle detection system were collected in the campus

of National Central University and Zong-shan high way during different seasons.

Highway images were captured in the summer of 2002 and the others were captured

from the summer of 2003 until the spring of 2004.

5.2 Performance Analysis of Pixels Classification

The dimension of training vehicles is clipped into the size of 3636. To tackle the

variations of vehicle orientation, eight classes of vehicles with different orientations

were collected in training samples. In order to analyze the robustness and

effectiveness of the proposed method, several experiments under different conditions

were demonstrated in this paper. The first experiment was conducted to evaluate the

performance of our vehicle-color detection method. Fig. 25 shows the result of

detecting vehicle colors using Eq.(11). (a) is the original image and (b) the result

obtained from (a). To evaluate and measure the performances of our proposed

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method to detect vehicle colors, the precision and false-alarm rates are defined.

Precision is the ratio of the number of correctly detected vehicle pixels to the number

of exactly existing vehicle pixels. False alarm rate is the ratio of the number of

background pixels but misclassified as vehicles to the number of all background

pixels. These two measures are defined as:

Precision = Cvehicle / Nvehicle and

Rate of False-Alarm = Fvehicle / Nbackground-pixels,

whereNvehicle is the total number of vehicle pixels, Cvehicle the number of correctly

detected vehicle pixels, Nbackground-pixels the number of all background pixels, and

Fvehicle the number of background pixels but misclassified as vehicle ones. When

calculating these two measures, the ground truth of vehicle pixels was manually

obtained. In Fig. 25 (a) and (b), the precision rate and false-alarm rate of vehicle

pixel detection were 86.1% and 6.3%, respectively. The lower false-alarm rate

implied that most of background pixels were filtered out and didnt need to be further

verified. Thus, many redundant searches can be avoided in advance and the

verification process can be significantly speeded up to find desired vehicles. It is

noticed that none of vehicle candidates was missed at this stage of vehicle hypothesis

generation. Fig. 26 shows another result of vehicle color detection. The precision

rate and false-alarm rate of vehicle pixel detection are 89.9% and 2.1%, respectively.

All of possible vehicle candidates were also correctly extracted.

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(a) (b)

Fig. 25. Result of vehicle color detection. (a) Original image. (b) Detection result

of vehicle color.

(a) (b)

Fig. 26. Result of vehicle color detection. (a) Original image. (b) Detection result ofvehicle color.

5.3 Detection Result in Various Environments

Some detection examples are given in this section. All testing images are collected

outdoor under different lighting and weather conditions even vehicles contain various

sizes, shapes and orientation. Although these vehicles have different colors, all of

them were correctly detected and located. Fig. 27 shows result of vehicle detection

in the parking lot. The proposed method is suitable for constructing a parking space

display system. This system can provide drivers real-time and accurate information

of free parking space.

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Fig. 27. Result of vehicle detection in a parking lot

Fig. 28. Result of vehicle detection in a parking lot with different orientation.

Fig. 28 shows another result of vehicle detection when vehicles pose with another

orientation. Fig. 29 shows result of vehicle detection when vehicles driven on road.

Fig. 30 shows two results of vehicle detection when vehicles were driven on highways.

This technique can also be used for counting numbers of vehicle in duration to

estimate the traffic flow. Fig. 31 shows another result of vehicle detection on road.

It is noticed that although vehicles were occluded by a tree, they still were correctly

detected. The average processing time is 0.54 ~ 0.72 seconds per image depending

on vehicle numbers. The average accuracy rate of vehicle detection using the

proposed algorithm is 94.5% and the false alarm rate is 3.2%.

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Fig. 29. Result of vehicle detection on road.

Fig. 30. Result of detecting vehicles from highway. Although these vehicles werewith different colors, all of them were correctly detected.

Fig. 31. Result of vehicle detection in road with occlusion.

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CHAPTER 6

DISCUSSIONS AND CONCLUSIONS

6.1 Discussions

In this section, a brief discussion will be addressed about the proposed color model.

Although the experimental results demonstrate satisfactory results of color

classification, some false alarms still exist. They may be resulted from the following

two reasons.

1. The fraction of the proposed color model is calculated and generated by K-Ltransform. In fact, the eigenvector of each eigenvalue is floating points

represented as the coefficient of R, G, and B components. For convenience

sake, we take them to be nearly an integer. The accuracy will be more or less

lost in this part to a certain extent.

2. The training set is made up of two groups (i.e., vehicle and non-vehicle). The performance of the Bayesian classifier is heavily influenced by the collected

training set. Some erroneous judgments are due to the lack of representative

non-vehicle training set. The choosing of good non-vehicle examples will

efficiently decrease the false classification.

6.2 Conclusions

In this thesis, a novel vehicle detection method is presented to detect various vehicles

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from static images. Firstly, a novel color projection method is presented. All

pixels of the input image are projected onto a 2D feature space such that vehicle

pixels form a compact cluster and can thus be easily identified from background ones.

Many redundant vehicle candidates are eliminated in advance using the Bayesian

classifier.

Then, three features including corners, edge maps, and wavelet coefficients are

employed to form a cascade and multi-channel classifier. The correctness of each

vehicle hypothesis can be effectively calculated even with different sizes and

orientations. Since the classifier can well record different changes of vehicle

appearances, real vehicles can be accurately detected from static images. The

contributions of this thesis can be summarized as follows:

(a)A novel color model is proposed to identify vehicle colors pixels from background ones. This identification procedure eliminates most impossible

candidates before the performing of vehicle verification. Different from

other methods [6]-[7] which need an exhaustive search to find possible

vehicles candidates, the proposed method detects vehicles more quickly and

efficiently.

(b) A cascade and multi-channel classifier is proposed to verify each vehicle

hypothesis. According to this classier, an effective scan is performed to

verify all vehicle candidates from static images even though they have

different sizes and orientations.

The proposed method is robust in dealing with various outdoor images containing

different weather and lighting conditions. Experimental results demonstrate the

superiority of our proposed method in vehicle detection.

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