Implementation of Gabor Filter on FPGA

Implementation of Gabor filter on the FPGA for

asphalt damage detection

Abstract The aim of this project is to develop a low-cost solution that will enable

identification of holes and road damage

using the FPGA (Field Programmable Gate

Arrays). This solution can be used during

the implementation of driving assistance

systems in order to avoid damage to the

road. Problems that occur in damage

detection on industrial materials are usually

very complex and require integrated

solutions that can be implemented in real

time using the FPGA system. Detailed

description of the system which is based on

image processing, was developed in order to

analyze data recorded with the camera,

which gives a better efficiency and accuracy

compared to conventional detection

methods, is presented in the sequel.

Keywords: FPGA, Gabor filter, damage,

road, image

I. INTRODUCTION

The process of road damage detection is

similar to obstacle detection except the damage

in the form of holes is more common than obstacles. The approach used in solving this

problem is a different visual representation of

the holes in relation to their environment. The basic idea of this system is to alert drivers

when encountering damage on the road, in

order to adjust their speed so they could avoid

holes and notify local road maintenance

services of their existence.

Differences in mean value of gray color on a

small area are not always sufficient to detect

the damage. Instead, it should be relied on the

values of gray in neighboring pixels.

Extracting the damage involves the

identification of areas with a uniform texture

on the image. Region in the picture has a permanent texture if local effect or other local

feature textures are constant, slowly changing

or approximately periodic. [1]

Different approaches for the detection of road (asphalt) damage are based on the separation characteristics in the spatial domain. Basically,

adaptive wavelet has great sensitivity to

sudden changes in the structure caused by

damage.

The main contribution of this paper is:

The rule of combination proposes to integrate information from different

channels. This approach offers a high

level of detection and low probability

of false alarm

The introduction of sensitivity variable improves the performance of the

developed algorithm.

High sensitivity and low convolution mask makes this algorithm computationally cost effective and thus

increases the real-time performance.

Detection of damage with Gabor filters is introduced

Faruk Zaimovi, student,

University of Sarajevo, Faculty of Electrical Engineering [email protected]

Sadid Smajki, student,

University of Sarajevo,

Faculty of Electrical


Univerzitet u Sarajevu,

Elektrotehniki fakultet

Adnan Mehremi, student,



Univerzitet u Sarajevu, Elektrotehniki fakultet





II. GABOR FILTER

Gabor filter is a linear filter that is used for

edge detection in image processing, and was named by Dennis Gabor. Orientation and

frequency Gabor filters are similar frequencies

and orientations for the human visual system to represent the texture and differentiation of

textures. Sinusoidal plane is modulated 2D

Gabor filter whose kernel is a Gaussian

function in the spatial domain. All Gabor filters may arise dilatation and rotation from

one wavelet "parent", thus Gabor filters are

similar to each other. The harmonic function multiplied by a Gaussian function gives the

impulse response of the Gabor filter.

Convolution Fourier transform of the Gaussian

function and the Fourier transform of the harmonic function is the Fourier transform of

the impulse response.

The orthogonal directions are represented by

imaginary and real part of the filter. These two components can be combined into complex

shapes or used separately. In principle, two-

dimensional Gabor function is expressed as

[2]:

(, ) =1

2

[12

(2

2 +

2

2) ]

(20) (1)

Where 0 is the frequency of the Gabor function. Constants and represent the length of the Gaussian envelope along the and -axes. Using (1) as a Gabor wavelet matrix we can get the appropriate bank of

filters using the appropriate dilation and

rotation of function (, ) through a generic function:

(, ) = ( , ) (2)

= ( + ) (3)

= ( + )

> 1; = 1,2, , ; = 1,2, , (4)

and parameters represent scale and orientation indexes respectively. represents the total number of scales and is the total number of orientations. For each orientation , the angle is equal to:

=( 1)

(5)

An important feature of Gabor filter is the

ability to achieve maximum localization or

spatial resolution and spatial frequency domain. One of the disadvantages is the fact

that the filters are not orthogonal but are

complete for displaying visual information. Its feature of extraction, Gabor filter owes to the

ability of adjusting the orientation of filter for

each selected frequency, which depends on the

number of scales.

III. SEPARATION OF FEATURES

The characteristics of the image are obtained by filtering (convolution) the picture with each

of the filters from the bank of filters. Getting

each filter individually is explained in the previous chapter. The total number of filters in

the bank equals (number of scales x number of orientations). Convolution is done

by 3x3 convolution mask. Larger mask produces better results but the execution time

is longer so that a compromise is sought

between the time of execution and the size of

the mask.

IV. DAMAGE DETECTION

One of the advantages of this filter that damage

detection is done directly using vector elements obtained in the manner described in

the previous section. We extract images from that vector element that serve us to get the final image according to the algorithm (6):

Dpq(x, y) = {Rpq(x, y), |Rpq(x, y) pq| K v

0, inae

Where represents a picture obtained by

processing algorithm, represents a picture obtained by convolution filters - scale and -orientation with the picture we want to edit,

is the mean value of images and is the mean of all means of convoluted images. represents a coefficient of sensitivity which

actually determines whether the pixel is

damaged or not.

V. MERGING THE IMAGES

The task of image merging module is to

combine all the pixels that have a high

probability of being damaged into a single

image. The algorithm combines (sums up) all

the images that passed the damage detection

phase. At the end, the obtained image is

divided by the total number of images to obtain

a photo-Z, which represents the mean value of

all Gabor filter mages.

Z =1

p q Di

pq

i=1

(7)

VI. RESULTS

The implementation of the algorithm is done

by using the FPGA. First, it was needed to

determine the number of the scales and

orientations. Number of scales in general

represents the number of intensity levels of

gray color in the image to be sampled while

the number of orientations can be linked to the

number of orientations that we apparently can

see in the picture. It is determined individually

and in combination with images that get

filtered. By repeatedly changing the number of

scales and orientations, we can get excellent

parameters for a particular image, but the aim

of this paper is to implement Gabor filter on

FPGA and show the example that is taken in

this paper, which is the detection of asphalt

holes (damage), as its application.

Another important part is to determine whether

its needed to use the real part of the received

image or the amplitude part. In this paper we

have used the real part, just to give an example

of application, in an analogous way as this was

done for the real part, it can be done for an

amplitude part as well.

We wanted to show, through filtering more

images, how the filtering affects different

damages, and also that the threshold and the

coefficient K, which is explained earlier have a

major impact on detection. We also showed

that increasing scale and orientation number,

increases and the quality of filtering which

results in precisely obtained damage surface.

We have taken an example of 1x1 (x scale

orientation) and 2x2 (scale and orientation),

and difference can be obtained in terms of

filtration visually and through PSNR and MSE

values set out in table (1 and 2 ..) for the

sample images we worked on.

Image 1. Obtained by using 4 filters




Image 5. Obtained by using 1 filter




Also, it is very important to note that the value

of detection can be changed for different

values of the parameters that are defined in the

formula for calculating the response of the

filter, due to the limitation by paper size and

time we are constrained to one parameter.

Whereas time of filtering depends on the

number of scales and orientations, compromise

is sought between the execution time and the

precision of detection. Also in this example

can be seen that the algorithm detects even the

smallest details in the picture.

This represents a matrix of pixels from the

image that we take so we can perform

convolution with (, ) Gabor filter, with the designations that have been used in the model.

(1_2 1_1 12_2 2_1 23_2 3_1 3

) (8)

Here is the MATLAB code for calculating

Gabor filters matrix, and the values of the

parameters that were used in our work.

Through this example we can illustrate

how Gabor filter works in general. u=2;

v=2;

m=3;

n=3;

fmax = 0.125;

gama = 0.8;

eta =0.8;

for i = 1:u

fu = fmax/((sqrt(2))^(i-1));

alpha = fu/gama;

beta = fu/eta;

for j = 1:v

tetav = ((j-1)/8)*pi;

gFilter = zeros(m,n);

for x = 1:m

for y = 1:n

xprime = (x-

((m+1)/2))*cos(tetav)+(y-

((n+1)/2))*sin(tetav);

yprime = -(x-

((m+1)/2))*sin(tetav)+(y-

((n+1)/2))*cos(tetav);

gFilter(x,y) =

(fu^2/(pi*gama*eta))*exp(-

((alpha^2)*(xprime^2)+(beta^2)*(ypri

me^2)))*exp(1i*2*pi*fu*xprime);

end

end

gFilter

end

end

Formula for MSE (9) and PSNR calculation:

= ( (( )

2))

255 255

= 10 10 (1

) (10)

Table 1. MSE and PSNR values while using 4

filters

Slika 1 Slika 2 Slika 3 Slika 4

MSE 0.2954 0.3586 0.3453 0.3080

PSNR 5.2965 4.4537 4.6174 5.1151

Table 1. MSE and PSNR values while using 1

filter

Slika 1 Slika 2 Slika 3 Slika 4

MSE 0.3102 0.3727 0.3614 0.3225

PSNR 5.0833 4.2868 4.4198 4.9149

VII. FUTURE WORK PROPOSAL

For future work on this or a similar model, we

suggest using a large number of scales and

orientations eg. 39x39 and perform testing on a

bigger size (, ) Gabor filter than the one that was used in this paper. Also, the model can be

adapted to detect other material damages such

as canvas, and it depends on the number of

scales and orientations and the coefficient K,

which strongly affects the accuracy of

detection. The detection can also be done on

the video, because video is made up of a series

of images, where each image is separately

analyzed as a single image. Furthermore, it can

try to perform the analysis for different areas

of image and to try to find the optimal value of

K that will support these models, both

mathematically and practically.

VIII. CONCLUSION

This paper describes the process of setting

Gabor filter to identify asphalt damage which

is implemented on the FPGA. Throughout the

proceedings the conclusions have been drawn

which can be used in setting the parameters for

the other type of error and damage or to adjust

Gabor filter to detect any features on any other

picture. It can be concluded that the use of a

large number of filters, increases the accuracy

of damage detection, and therefore increases

the complexity and execution time. Based on

all of the above, it is clear that the possibilities

of Gabor filter application are numerous.

References:

[1] Ajay Kumar, Grantham Pang, Defect detection in textured materials using Gabor filters, Industrial

Automation Research Laboratory, The University of

Hong Kong, 2000

[2] Ajay Kumar, Grantham K. H. Pang,, Defect Detection in Textured Materials Using Gabor Filters,

IEEE transactions on Industry aplications, vol. 38, no. 2,

March/April 2002.

Documents

Implementation of Gabor Filter on FPGA