Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 135614 6 pageshttpdxdoiorg1011552013135614
Research ArticleDesign of an Efficient Real-Time Algorithm Using ReducedFeature Dimension for Recognition of Speed Limit Signs
Hanmin Cho1 Seungwha Han2 and Sun-Young Hwang1
1 Department of Electronic Engineering Sogang University Seoul 121-742 Republic of Korea2 Samsung Techwin RampD Center Security Solution Division 701 Sampyeong-dong Bundang-gu Seongnam-siGyeonggi 463-400 Republic of Korea
Correspondence should be addressed to Sun-Young Hwang hwangsogangackr
Received 28 August 2013 Accepted 1 October 2013
Academic Editors P Daponte M Nappi and N Nishchal
Copyright copy 2013 Hanmin Cho et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
We propose a real-time algorithm for recognition of speed limit signs from a moving vehicle Linear Discriminant Analysis (LDA)required for classification is performed by using Discrete Cosine Transform (DCT) coefficients To reduce feature dimension inLDA DCT coefficients are selected by a devised discriminant function derived from information obtained by training Binarizationand thinning are performed on a Region of Interest (ROI) obtained by preprocessing a detected ROI prior to DCT for furtherreduction of computation time in DCT This process is performed on a sequence of image frames to increase the hit rate ofrecognition Experimental results show that arithmetic operations are reduced by about 60 while hit rates reach about 100compared to previous works
1 Introduction
Driver safety is the main concern of the advanced vehiclesystem which became implementable due to the develop-ment of the autonomous driving automatic control andimaging technology An advanced vehicle system gives driverinformation related to safety by sensing the surroundingsautomatically [1] Speed limit signs recognition is regardedto be helpful in safety for drivers using advanced vehiclesystem The system needs to recognize the speed limit signin the distance quickly and accurately in order to givethe driver precaution in time since vehicle is moving fastBut existing algorithms perform recognition by using manyfeatures extracted from captured image requiring a largeamount of arithmetic operations for classification [2]
Several classification algorithms have been proposedwhich include Neural Networks [2 3] Support VectorMachine (SVM) [2] and Linear Discriminant Analysis(LDA) [2 4] Among these SVM has relatively higher recog-nition rate and LDA is used in many classification applica-tions due to its low computational complexity However itscomputational complexity needs to be further reduced to be
used in real-time application It can be achieved by reducingthe number of inputs of LDA
This paper proposes an efficient real-time algorithm forrecognition of speed limit signs by using reduced featuredimension In this research study DCT is employed and partsof Discrete Cosine Transform (DCT) coefficients are used asinputs to LDA instead of features extracted from image DCTcoefficients are selected by a devised discriminant functionTo further reduce DCT computation time binarization andthinning are applied to the detected Region of Interest (ROI)Image of speed limit sign in the distance obtained from cam-era has a low resolution and it gives poor rate of recognitionTo resolve this problem this paper proposes a recognitionsystem using classification results on a sequence of framesIt can enhance hit rate of recognition by accumulating theprobability of single frame recognition
2 Background
In this section LDA is briefly described which is popularlyemployed for classification LDA is a classical statistical
2 The Scientific World Journal
x1
x2
w
(a)
x1
x2
w
(b)
Figure 1 Projection of data x onto an axis in the direction of w
approach for dimensionality reduction [2] It projects high-dimensional data onto a lower dimensional space by maxi-mizing the scatter of data points from different classes andminimizing the scatter of data belonging to the same classsimultaneously thus achieving maximum class discrimina-tion in the dimensionality-reduced space [5] For exampleFigure 1 shows how points in 2-dimensional space can beprojected onto 1-dimensional space
The projection shown in Figure 1(b) shows more efficientseparation of data than that of Figure 1(a)This concept can beexpanded to n-dimensional space Equations to be followedare derived to find the most efficient axis w Let x be datapoints belonging to a certain class Ci and y the projectionpoints of x onto axis w Equation (1) shows the average of y
119894 where119898
119894is mean of x and ni is number of data
119894=
1
119899
119894
sum
119910isin119862119894
119910 =
1
119899
119894
sum
119909isin119862119894
w119905x = w119905m119894 (1)
It is required to find the axis w which maximizes theratio of distance between
1and
2to sum of within-class
scatter This ratio can be represented as (2) where 11990421 11990422are
within-class scatters of projected data in class 1 and class 2respectively
r (w) =1003816
1003816
1003816
1003816
1minus
2
1003816
1003816
1003816
1003816
2
119904
2
1+ 119904
2
2
(2)
Within-class scatter of class i 1199042119894 can be represented as in
the following equation
119904
2
119894= sum
xisin119862119894(w119905x minus w119905m
119894)
2
= sum
xisin119862119894w119905 (x minusm
119894) (x minusm
119894)
119905w = w119905S119894w
(3)
From (3) the denominator of (2) is derived as in thefollowing equation
119904
2
1+ 119904
2
2= w119905 (S
1+S2)w = S
119908 (4)
The numerator in (2) |1minus
2|
2 is shown in the follow-ing equation
1003816
1003816
1003816
1003816
1minus
2
1003816
1003816
1003816
1003816
2= (w119905m
1minus w119905m
2)
2
= w119905 (m1minusm2) (m1minusm2)
119905w = w119905S119861w
(5)
From (4) and (5) r(w) can be written as in the followingequation
r (w) = w119905S119861w
w119905S119908w (6)
Optimal w wlowast can be obtained as in the followingequation which becomes a conventional eigenvalue problem
wlowast = arg maxw
w119905S119861w
w119905S119908w = S
119908
minus1(m1minusm2) (7)
Even though LDA is one of the most popular mathemat-ical models used for classification it is difficult to be directlyused Sw term in (7) becomes singular when the number ofsamples is much smaller than dimension of features as can beobserved in many practical classification applications whichis called small sample size problem [6] Also high dimensionof features makes LDA difficult to be directly applied toclassification due to its computational complexity To solvethe problem a method which applies Principal ComponentAnalysis (PCA) before LDAwas proposed [7 8]The purposeof PCA is to reduce the dimensionality while preserving
The Scientific World Journal 3
Detected ROI
Preprocessing- Conversion into gray-
scale image- Normalization of size
- Cropping- White balancing
Binarization
Thinning
DCT
Classification
Training(off-line)
Classified signs
Class database
Selection criteria
Classification data
Figure 2 Flowchart of the proposed algorithm
the variance information as much as possible Howeverit is suboptimal due to its ignorance of class informationassociated with patterns [9] Direct LDA (DLDA) method[10ndash12] was also proposed It directly processes data in theoriginal high-dimensional vectors The performance of theDLDA algorithm heavily depends on the control scheme thatdetermines the number of features [13]
In this paper a method which can reduce feature dimen-sion effectively without increasing computational complexityis proposed for real-time algorithm for classification of speedlimit signs
3 Proposed Algorithm
As the number of operations in classification process isproportional to the number of data inputs it is desirableto remove less significant inputs for classification [14] Byusing DCT coefficients instead of features extracted from anROI image much less inputs are forwarded to classificationprocess
Figure 2 shows the overall flowof the proposed algorithmAfter preprocessing a detected ROI binarization and thin-ning are performed so that DCT computation time can bereduced For further reduction of arithmetic operations inclassification process parts of DCT coefficients are selectedby a devised discriminant function To increase hit rate ofrecognition the proposed algorithm performs classificationfor a sequence of images
31 Preprocessing Since the size of ROI varies with thedistance between vehicle and speed limit sign bicubic inter-polation is employed to normalize the size of ROI intoa predetermined one Normalized ROI is converted intogray image to reduce bit width of each pixel and the areaindicating a speed limit is cropped by separating foregroundfrom background Then white balancing is performed toreduce brightness variance of obtained image To improvethe resultant quality of auto white balancing the proposedalgorithm uses the white area of speed limit sign as areference Figure 3 shows an example Figure 3(a) shows anacquired image and Figures 3(b)ndash3(e) show the results ofpreprocessing for the image of Figure 3(a)
32 Binarization and Thinning Prior to DCT computationbinarization and thinning are performed in the proposedalgorithm DCT computation uses each of pixel values toobtain coefficients which require a large amount of opera-tions for usage in real-time recognition By using 1-bit pixelsobtained by binarization the time for multiplication can besignificantly reduced The threshold of binarization is set to128 middle value of grayscale image since the brightnessvariance has been compensated by applying white balance inadvance Figure 3(f) shows binarized image of preprocessedROI Even though the feature of an image is degraded bybinarization experimental results show that the hit rate ofrecognition has not decreased significantly
For further reduction of DCT computation time thin-ning [15] is applied to generate more 0rsquos in the binarizedimage Thinning also removes noises remaining after bina-rizationThe noise removal will improve classification perfor-mance In thinning process each pixel value is calculated byusing the values of its 8 neighbors For thinning lookup tableis used for binarized image instead of complicated operationsrequired for gray image Figure 3(g) shows the image afterthinning
33 DCT Computation 2D DCT computation can bereplaced by two 1DDCT computations using the row-columndecomposition [16] The time for the first 1D DCT compu-tation can be significantly reduced due to increased numberof 0-valued pixels after binarization and thinning In thesecond 1D DCT computation parts of DCT coefficients aregenerated which are selected using a devised discriminantfunction for reduction of computation time
34 DCT Coefficient Selection Classifierrsquos performanceincreases dependently on the number of features Howevercomputational complexity and memory requirements are
4 The Scientific World Journal
(a) (b)
(c) (d)
(e) (f)
(g)
Figure 3 An example of ROI preprocessing in the proposed algorithm (a) Input ROI (b) normalized ROI (c) gray image (d) croppedimage (e) white balanced image (f) binarized image and (g) image after thinning
proportional to the number of the features both in thelearning and in the classification processes To reduce theseburdens we need to remove less significant features [17] TheselectedDCT coefficients are used as features in the proposedalgorithm and the performance of the classification is notdegraded by using reduced amount of DCT coefficients Asmentioned in the previous section parts of DCT coefficientsare selected by using a devised discriminant functionobtained through intensive analysis on the attributes ofobject class The function is defined through a trainingprocess performed off-line on the classified database Theprocedure to obtain discriminant function is as follows
First mean of DCT coefficients 119863119888(119894 119895) 120583
119888(119894 119895) is cal-
culated for 119873(= 200) images per class c Then intraclassvariance intra varc(119894 119895) is calculated for every D(119894 119895) by (8)and interclass variance for all the classes inter var(119894 119895) isobtained by (9)
intra var119888(119894 119895) =
1
119873
119873
sum
119896=1
119863
119896
119888(119894 119895) minus 120583
119888(119894 119895)
2
(8)
inter var (119894 119895) = 1
119862
119862
sum
119888=1
120583
119888(119894 119895) minus 120583
119888(119894 119895)
2
(9)
Here D(119894 119895) is coefficient of 2D DCT and Dk(119894 119895) isD(119894 119895) of the kth training image From the equations abovediscriminant factor for each DCT coefficient D(119894 119895) can becalculated as in the following equation
Discriminant Factor DF (119894 119895) =inter var (119894 119895)
max119888intra var
119888(119894 119895)
(10)
Classification is more efficient when samples in thesame class are clustered together and samples belongingto different classes are scattered in the feature space Thelarger the discriminant factors are the greater the impacton classification is in the field The devised discriminantfunction selects a number of indices of 2DDCTcoefficients indescending order which have large DF values Those selectedindices are used as reference positions whose correspondingDCT coefficients will be applied in classification process
The Scientific World Journal 5
Table 1 Experimental results of hit rates of recognition
35 Classification of Speed Limit Signs Classification is per-formed using the Linear Discriminant Analysis (LDA) andMahalanobis distances [2] LDA is performed to transformDCT coefficients into the format suitable for matching withthe classes in database and Mahalanobis distance is used asa metric for matching Classification results for a sequence ofimages are used for recognition of speed limit signs Equation(11) expresses the probability of matching with class c afterclassification for N image inputs
119875
119888=
1
119873
119873
sum
119896=1
120596 (119896)119860119888 (119896) (11)
where
119873
sum
119896=1
120596 (119896) = 1
119860
119888 (119896) =
1 when argmin119888(MD119888 (119896))
0 otherwise
(12)
120596(119896)rsquos are the weights determined experimentally They areinversely proportional to the distance between vehicle andobject MDc(k) is Mahalanobis distance between capturedimage k and class c The image is classified as class c whoseprobability Pc is the highest from P
1to PN
4 Experimental Results
Images used for training and classification were capturedon road using a mirrorless camera (MOS sensor 43 inch)mounted with a 20mm lens at 640 times 480 resolution and 30framess in normal daytime Classification is started with an
image of speed limit sign captured about 30meters away ROIdetected from the image consists of 12times12pixelsWeused 200images captured at different distances for training purposeper class Table 1 shows the hit rates of recognition for thespeed limit signs captured 1000 times on the road
The hit rates of recognition are about 100 when clas-sification is performed for 7sim9 consecutive images Table 2compares the number of arithmetic operations with LDAand SVM [2] The numbers in parentheses represent thereduction percentagesThe numbers of arithmetic operationsare reduced by about 60 and 80 when compared withLDA and SVM respectively In the experiments 57DCTcoefficients are selected out of 400 using the proposeddiscriminant function
5 Conclusion
A real-time algorithm for speed limit sign recognition hasbeen proposed with reduced amount of operations usingDCT The number of arithmetic operations was reduced byusing lookup table on binarized image which was obtainedthrough binarization and thinning To reduce feature dimen-sion discriminant function which selects parts of DCTcoefficients was devised Selection of DCT coefficients makesit possible to reduce runtime for recognition
Accurate recognition of speed limit signs in low resolu-tions or in the distance is achievable by applying the proposedalgorithm
Acknowledgment
This research was supported by the MEST (Ministry ofEducation Science and Technology) throughNRF (NationalResearch Foundation) of Korea under Grant no 2012-0002586
References
[1] R Bishop ldquoA survey of intelligent vehicle applications world-widerdquo in Proceeding of the Intelligent Vehicles Symposium pp25ndash30 2000
[2] R Duda P Hart and D Stork Pattern Classification Wiley-Interscience NewYork NY USA 2nd edition 2001
[3] C M Bishop Neural Networks for Pattern Recognition OxfordUniversity Press Oxford UK 1995
[4] K Fukunaga Introduction to Statistical Pattern RecognitionAcademic Press New York NY USA 2nd edition 1990
[5] S Ji and J Ye ldquoGeneralized linear discriminant analysis aunified framework and efficient model selectionrdquo IEEE Trans-actions on Neural Networks vol 19 no 10 pp 1768ndash1782 2008
[6] R Huang Q Liu H Lu and S Ma ldquoSolving the small samplesize problem of LDArdquo in Proceedings of the 16th InternationalConference on Pattern Recognition vol 3 pp 29ndash32 2002
[7] J Li B Zhao and H Zhang ldquoFace recognition based on PCAand LDA combination feature extractionrdquo in Proceedings ofthe 1st International Conference on Information Science andEngineering (ICISE rsquo09) pp 1240ndash1243 December 2009
[8] P N Belhumeur J P Hespanha and D J Kriegman ldquoEigen-faces vs fisherfaces recognition using class specific linear
6 The Scientific World Journal
projectionrdquo IEEE Transactions on Pattern Analysis andMachineIntelligence vol 19 no 7 pp 711ndash720 1997
[9] H Li T Jiang and K Zhang ldquoEfficient and robust featureextraction by maximummargin criterionrdquo in Proceedings of theConference onNeural Information Processing Systems (NIPS rsquo03)pp 97ndash104 2003
[10] L F Chen H Y M Liao M T Ko J C Lin and G J Yu ldquoNewLDA-based face recognition system which can solve the smallsample size problemrdquo Pattern Recognition vol 33 no 10 pp1713ndash1726 2000
[11] H Yu and J Yang ldquoA direct LDA algorithm for high-dimensional data with application to face recognitionrdquo PatternRecognition vol 34 no 10 pp 2067ndash2070 2001
[12] J Yang Y Yu andWKunz ldquoAn efficient LDA algorithm for facerecognitionrdquo in Proceedings of the 6th International Conferenceon Control Automation Robotics and Vision 2000
[13] X Wu J Kittler J Yang K Messer and S Wang ldquoA newdirect LDA (D-LDA) algorithm for feature extraction in facerecognitionrdquo in Proceedings of the 17th International Conferenceon Pattern Recognition (ICPR rsquo04) pp 545ndash548 August 2004
[14] C Bahlmann Y Zhu V Ramesh M Pellkofer and T KoehlerldquoA system for traffic sign detection tracking and recognitionusing color shape and motion informationrdquo in Proceedings ofthe IEEE Intelligent Vehicles Symposium pp 255ndash260 June 2005
[15] T Zhang and C Suen ldquoA fast parallel algorithm for thinningdigital patternsrdquo Communications of the ACM vol 27 no 3 pp236ndash239 1984
[16] D Slawecki and W Li ldquoDCTIDCT processor design for highdata rate image codingrdquo IEEE Transactions on Circuits andSystems for Video Technology vol 2 no 2 pp 135ndash146 1992
[17] E Alpaydin Introduction to Machine Learning MIT PressCambridge Mass USA 2nd edition 2004
Figure 1 Projection of data x onto an axis in the direction of w
approach for dimensionality reduction [2] It projects high-dimensional data onto a lower dimensional space by maxi-mizing the scatter of data points from different classes andminimizing the scatter of data belonging to the same classsimultaneously thus achieving maximum class discrimina-tion in the dimensionality-reduced space [5] For exampleFigure 1 shows how points in 2-dimensional space can beprojected onto 1-dimensional space
The projection shown in Figure 1(b) shows more efficientseparation of data than that of Figure 1(a)This concept can beexpanded to n-dimensional space Equations to be followedare derived to find the most efficient axis w Let x be datapoints belonging to a certain class Ci and y the projectionpoints of x onto axis w Equation (1) shows the average of y
119894 where119898
119894is mean of x and ni is number of data
119894=
1
119899
119894
sum
119910isin119862119894
119910 =
1
119899
119894
sum
119909isin119862119894
w119905x = w119905m119894 (1)
It is required to find the axis w which maximizes theratio of distance between
1and
2to sum of within-class
scatter This ratio can be represented as (2) where 11990421 11990422are
within-class scatters of projected data in class 1 and class 2respectively
r (w) =1003816
1003816
1003816
1003816
1minus
2
1003816
1003816
1003816
1003816
2
119904
2
1+ 119904
2
2
(2)
Within-class scatter of class i 1199042119894 can be represented as in
the following equation
119904
2
119894= sum
xisin119862119894(w119905x minus w119905m
119894)
2
= sum
xisin119862119894w119905 (x minusm
119894) (x minusm
119894)
119905w = w119905S119894w
(3)
From (3) the denominator of (2) is derived as in thefollowing equation
119904
2
1+ 119904
2
2= w119905 (S
1+S2)w = S
119908 (4)
The numerator in (2) |1minus
2|
2 is shown in the follow-ing equation
1003816
1003816
1003816
1003816
1minus
2
1003816
1003816
1003816
1003816
2= (w119905m
1minus w119905m
2)
2
= w119905 (m1minusm2) (m1minusm2)
119905w = w119905S119861w
(5)
From (4) and (5) r(w) can be written as in the followingequation
r (w) = w119905S119861w
w119905S119908w (6)
Optimal w wlowast can be obtained as in the followingequation which becomes a conventional eigenvalue problem
wlowast = arg maxw
w119905S119861w
w119905S119908w = S
119908
minus1(m1minusm2) (7)
Even though LDA is one of the most popular mathemat-ical models used for classification it is difficult to be directlyused Sw term in (7) becomes singular when the number ofsamples is much smaller than dimension of features as can beobserved in many practical classification applications whichis called small sample size problem [6] Also high dimensionof features makes LDA difficult to be directly applied toclassification due to its computational complexity To solvethe problem a method which applies Principal ComponentAnalysis (PCA) before LDAwas proposed [7 8]The purposeof PCA is to reduce the dimensionality while preserving
The Scientific World Journal 3
Detected ROI
Preprocessing- Conversion into gray-
scale image- Normalization of size
- Cropping- White balancing
Binarization
Thinning
DCT
Classification
Training(off-line)
Classified signs
Class database
Selection criteria
Classification data
Figure 2 Flowchart of the proposed algorithm
the variance information as much as possible Howeverit is suboptimal due to its ignorance of class informationassociated with patterns [9] Direct LDA (DLDA) method[10ndash12] was also proposed It directly processes data in theoriginal high-dimensional vectors The performance of theDLDA algorithm heavily depends on the control scheme thatdetermines the number of features [13]
In this paper a method which can reduce feature dimen-sion effectively without increasing computational complexityis proposed for real-time algorithm for classification of speedlimit signs
3 Proposed Algorithm
As the number of operations in classification process isproportional to the number of data inputs it is desirableto remove less significant inputs for classification [14] Byusing DCT coefficients instead of features extracted from anROI image much less inputs are forwarded to classificationprocess
Figure 2 shows the overall flowof the proposed algorithmAfter preprocessing a detected ROI binarization and thin-ning are performed so that DCT computation time can bereduced For further reduction of arithmetic operations inclassification process parts of DCT coefficients are selectedby a devised discriminant function To increase hit rate ofrecognition the proposed algorithm performs classificationfor a sequence of images
31 Preprocessing Since the size of ROI varies with thedistance between vehicle and speed limit sign bicubic inter-polation is employed to normalize the size of ROI intoa predetermined one Normalized ROI is converted intogray image to reduce bit width of each pixel and the areaindicating a speed limit is cropped by separating foregroundfrom background Then white balancing is performed toreduce brightness variance of obtained image To improvethe resultant quality of auto white balancing the proposedalgorithm uses the white area of speed limit sign as areference Figure 3 shows an example Figure 3(a) shows anacquired image and Figures 3(b)ndash3(e) show the results ofpreprocessing for the image of Figure 3(a)
32 Binarization and Thinning Prior to DCT computationbinarization and thinning are performed in the proposedalgorithm DCT computation uses each of pixel values toobtain coefficients which require a large amount of opera-tions for usage in real-time recognition By using 1-bit pixelsobtained by binarization the time for multiplication can besignificantly reduced The threshold of binarization is set to128 middle value of grayscale image since the brightnessvariance has been compensated by applying white balance inadvance Figure 3(f) shows binarized image of preprocessedROI Even though the feature of an image is degraded bybinarization experimental results show that the hit rate ofrecognition has not decreased significantly
For further reduction of DCT computation time thin-ning [15] is applied to generate more 0rsquos in the binarizedimage Thinning also removes noises remaining after bina-rizationThe noise removal will improve classification perfor-mance In thinning process each pixel value is calculated byusing the values of its 8 neighbors For thinning lookup tableis used for binarized image instead of complicated operationsrequired for gray image Figure 3(g) shows the image afterthinning
33 DCT Computation 2D DCT computation can bereplaced by two 1DDCT computations using the row-columndecomposition [16] The time for the first 1D DCT compu-tation can be significantly reduced due to increased numberof 0-valued pixels after binarization and thinning In thesecond 1D DCT computation parts of DCT coefficients aregenerated which are selected using a devised discriminantfunction for reduction of computation time
34 DCT Coefficient Selection Classifierrsquos performanceincreases dependently on the number of features Howevercomputational complexity and memory requirements are
4 The Scientific World Journal
(a) (b)
(c) (d)
(e) (f)
(g)
Figure 3 An example of ROI preprocessing in the proposed algorithm (a) Input ROI (b) normalized ROI (c) gray image (d) croppedimage (e) white balanced image (f) binarized image and (g) image after thinning
proportional to the number of the features both in thelearning and in the classification processes To reduce theseburdens we need to remove less significant features [17] TheselectedDCT coefficients are used as features in the proposedalgorithm and the performance of the classification is notdegraded by using reduced amount of DCT coefficients Asmentioned in the previous section parts of DCT coefficientsare selected by using a devised discriminant functionobtained through intensive analysis on the attributes ofobject class The function is defined through a trainingprocess performed off-line on the classified database Theprocedure to obtain discriminant function is as follows
First mean of DCT coefficients 119863119888(119894 119895) 120583
119888(119894 119895) is cal-
culated for 119873(= 200) images per class c Then intraclassvariance intra varc(119894 119895) is calculated for every D(119894 119895) by (8)and interclass variance for all the classes inter var(119894 119895) isobtained by (9)
intra var119888(119894 119895) =
1
119873
119873
sum
119896=1
119863
119896
119888(119894 119895) minus 120583
119888(119894 119895)
2
(8)
inter var (119894 119895) = 1
119862
119862
sum
119888=1
120583
119888(119894 119895) minus 120583
119888(119894 119895)
2
(9)
Here D(119894 119895) is coefficient of 2D DCT and Dk(119894 119895) isD(119894 119895) of the kth training image From the equations abovediscriminant factor for each DCT coefficient D(119894 119895) can becalculated as in the following equation
Discriminant Factor DF (119894 119895) =inter var (119894 119895)
max119888intra var
119888(119894 119895)
(10)
Classification is more efficient when samples in thesame class are clustered together and samples belongingto different classes are scattered in the feature space Thelarger the discriminant factors are the greater the impacton classification is in the field The devised discriminantfunction selects a number of indices of 2DDCTcoefficients indescending order which have large DF values Those selectedindices are used as reference positions whose correspondingDCT coefficients will be applied in classification process
The Scientific World Journal 5
Table 1 Experimental results of hit rates of recognition
35 Classification of Speed Limit Signs Classification is per-formed using the Linear Discriminant Analysis (LDA) andMahalanobis distances [2] LDA is performed to transformDCT coefficients into the format suitable for matching withthe classes in database and Mahalanobis distance is used asa metric for matching Classification results for a sequence ofimages are used for recognition of speed limit signs Equation(11) expresses the probability of matching with class c afterclassification for N image inputs
119875
119888=
1
119873
119873
sum
119896=1
120596 (119896)119860119888 (119896) (11)
where
119873
sum
119896=1
120596 (119896) = 1
119860
119888 (119896) =
1 when argmin119888(MD119888 (119896))
0 otherwise
(12)
120596(119896)rsquos are the weights determined experimentally They areinversely proportional to the distance between vehicle andobject MDc(k) is Mahalanobis distance between capturedimage k and class c The image is classified as class c whoseprobability Pc is the highest from P
1to PN
4 Experimental Results
Images used for training and classification were capturedon road using a mirrorless camera (MOS sensor 43 inch)mounted with a 20mm lens at 640 times 480 resolution and 30framess in normal daytime Classification is started with an
image of speed limit sign captured about 30meters away ROIdetected from the image consists of 12times12pixelsWeused 200images captured at different distances for training purposeper class Table 1 shows the hit rates of recognition for thespeed limit signs captured 1000 times on the road
The hit rates of recognition are about 100 when clas-sification is performed for 7sim9 consecutive images Table 2compares the number of arithmetic operations with LDAand SVM [2] The numbers in parentheses represent thereduction percentagesThe numbers of arithmetic operationsare reduced by about 60 and 80 when compared withLDA and SVM respectively In the experiments 57DCTcoefficients are selected out of 400 using the proposeddiscriminant function
5 Conclusion
A real-time algorithm for speed limit sign recognition hasbeen proposed with reduced amount of operations usingDCT The number of arithmetic operations was reduced byusing lookup table on binarized image which was obtainedthrough binarization and thinning To reduce feature dimen-sion discriminant function which selects parts of DCTcoefficients was devised Selection of DCT coefficients makesit possible to reduce runtime for recognition
Accurate recognition of speed limit signs in low resolu-tions or in the distance is achievable by applying the proposedalgorithm
Acknowledgment
This research was supported by the MEST (Ministry ofEducation Science and Technology) throughNRF (NationalResearch Foundation) of Korea under Grant no 2012-0002586
References
[1] R Bishop ldquoA survey of intelligent vehicle applications world-widerdquo in Proceeding of the Intelligent Vehicles Symposium pp25ndash30 2000
[2] R Duda P Hart and D Stork Pattern Classification Wiley-Interscience NewYork NY USA 2nd edition 2001
[3] C M Bishop Neural Networks for Pattern Recognition OxfordUniversity Press Oxford UK 1995
[4] K Fukunaga Introduction to Statistical Pattern RecognitionAcademic Press New York NY USA 2nd edition 1990
[5] S Ji and J Ye ldquoGeneralized linear discriminant analysis aunified framework and efficient model selectionrdquo IEEE Trans-actions on Neural Networks vol 19 no 10 pp 1768ndash1782 2008
[6] R Huang Q Liu H Lu and S Ma ldquoSolving the small samplesize problem of LDArdquo in Proceedings of the 16th InternationalConference on Pattern Recognition vol 3 pp 29ndash32 2002
[7] J Li B Zhao and H Zhang ldquoFace recognition based on PCAand LDA combination feature extractionrdquo in Proceedings ofthe 1st International Conference on Information Science andEngineering (ICISE rsquo09) pp 1240ndash1243 December 2009
[8] P N Belhumeur J P Hespanha and D J Kriegman ldquoEigen-faces vs fisherfaces recognition using class specific linear
6 The Scientific World Journal
projectionrdquo IEEE Transactions on Pattern Analysis andMachineIntelligence vol 19 no 7 pp 711ndash720 1997
[9] H Li T Jiang and K Zhang ldquoEfficient and robust featureextraction by maximummargin criterionrdquo in Proceedings of theConference onNeural Information Processing Systems (NIPS rsquo03)pp 97ndash104 2003
[10] L F Chen H Y M Liao M T Ko J C Lin and G J Yu ldquoNewLDA-based face recognition system which can solve the smallsample size problemrdquo Pattern Recognition vol 33 no 10 pp1713ndash1726 2000
[11] H Yu and J Yang ldquoA direct LDA algorithm for high-dimensional data with application to face recognitionrdquo PatternRecognition vol 34 no 10 pp 2067ndash2070 2001
[12] J Yang Y Yu andWKunz ldquoAn efficient LDA algorithm for facerecognitionrdquo in Proceedings of the 6th International Conferenceon Control Automation Robotics and Vision 2000
[13] X Wu J Kittler J Yang K Messer and S Wang ldquoA newdirect LDA (D-LDA) algorithm for feature extraction in facerecognitionrdquo in Proceedings of the 17th International Conferenceon Pattern Recognition (ICPR rsquo04) pp 545ndash548 August 2004
[14] C Bahlmann Y Zhu V Ramesh M Pellkofer and T KoehlerldquoA system for traffic sign detection tracking and recognitionusing color shape and motion informationrdquo in Proceedings ofthe IEEE Intelligent Vehicles Symposium pp 255ndash260 June 2005
[15] T Zhang and C Suen ldquoA fast parallel algorithm for thinningdigital patternsrdquo Communications of the ACM vol 27 no 3 pp236ndash239 1984
[16] D Slawecki and W Li ldquoDCTIDCT processor design for highdata rate image codingrdquo IEEE Transactions on Circuits andSystems for Video Technology vol 2 no 2 pp 135ndash146 1992
[17] E Alpaydin Introduction to Machine Learning MIT PressCambridge Mass USA 2nd edition 2004
the variance information as much as possible Howeverit is suboptimal due to its ignorance of class informationassociated with patterns [9] Direct LDA (DLDA) method[10ndash12] was also proposed It directly processes data in theoriginal high-dimensional vectors The performance of theDLDA algorithm heavily depends on the control scheme thatdetermines the number of features [13]
In this paper a method which can reduce feature dimen-sion effectively without increasing computational complexityis proposed for real-time algorithm for classification of speedlimit signs
3 Proposed Algorithm
As the number of operations in classification process isproportional to the number of data inputs it is desirableto remove less significant inputs for classification [14] Byusing DCT coefficients instead of features extracted from anROI image much less inputs are forwarded to classificationprocess
Figure 2 shows the overall flowof the proposed algorithmAfter preprocessing a detected ROI binarization and thin-ning are performed so that DCT computation time can bereduced For further reduction of arithmetic operations inclassification process parts of DCT coefficients are selectedby a devised discriminant function To increase hit rate ofrecognition the proposed algorithm performs classificationfor a sequence of images
31 Preprocessing Since the size of ROI varies with thedistance between vehicle and speed limit sign bicubic inter-polation is employed to normalize the size of ROI intoa predetermined one Normalized ROI is converted intogray image to reduce bit width of each pixel and the areaindicating a speed limit is cropped by separating foregroundfrom background Then white balancing is performed toreduce brightness variance of obtained image To improvethe resultant quality of auto white balancing the proposedalgorithm uses the white area of speed limit sign as areference Figure 3 shows an example Figure 3(a) shows anacquired image and Figures 3(b)ndash3(e) show the results ofpreprocessing for the image of Figure 3(a)
32 Binarization and Thinning Prior to DCT computationbinarization and thinning are performed in the proposedalgorithm DCT computation uses each of pixel values toobtain coefficients which require a large amount of opera-tions for usage in real-time recognition By using 1-bit pixelsobtained by binarization the time for multiplication can besignificantly reduced The threshold of binarization is set to128 middle value of grayscale image since the brightnessvariance has been compensated by applying white balance inadvance Figure 3(f) shows binarized image of preprocessedROI Even though the feature of an image is degraded bybinarization experimental results show that the hit rate ofrecognition has not decreased significantly
For further reduction of DCT computation time thin-ning [15] is applied to generate more 0rsquos in the binarizedimage Thinning also removes noises remaining after bina-rizationThe noise removal will improve classification perfor-mance In thinning process each pixel value is calculated byusing the values of its 8 neighbors For thinning lookup tableis used for binarized image instead of complicated operationsrequired for gray image Figure 3(g) shows the image afterthinning
33 DCT Computation 2D DCT computation can bereplaced by two 1DDCT computations using the row-columndecomposition [16] The time for the first 1D DCT compu-tation can be significantly reduced due to increased numberof 0-valued pixels after binarization and thinning In thesecond 1D DCT computation parts of DCT coefficients aregenerated which are selected using a devised discriminantfunction for reduction of computation time
34 DCT Coefficient Selection Classifierrsquos performanceincreases dependently on the number of features Howevercomputational complexity and memory requirements are
4 The Scientific World Journal
(a) (b)
(c) (d)
(e) (f)
(g)
Figure 3 An example of ROI preprocessing in the proposed algorithm (a) Input ROI (b) normalized ROI (c) gray image (d) croppedimage (e) white balanced image (f) binarized image and (g) image after thinning
proportional to the number of the features both in thelearning and in the classification processes To reduce theseburdens we need to remove less significant features [17] TheselectedDCT coefficients are used as features in the proposedalgorithm and the performance of the classification is notdegraded by using reduced amount of DCT coefficients Asmentioned in the previous section parts of DCT coefficientsare selected by using a devised discriminant functionobtained through intensive analysis on the attributes ofobject class The function is defined through a trainingprocess performed off-line on the classified database Theprocedure to obtain discriminant function is as follows
First mean of DCT coefficients 119863119888(119894 119895) 120583
119888(119894 119895) is cal-
culated for 119873(= 200) images per class c Then intraclassvariance intra varc(119894 119895) is calculated for every D(119894 119895) by (8)and interclass variance for all the classes inter var(119894 119895) isobtained by (9)
intra var119888(119894 119895) =
1
119873
119873
sum
119896=1
119863
119896
119888(119894 119895) minus 120583
119888(119894 119895)
2
(8)
inter var (119894 119895) = 1
119862
119862
sum
119888=1
120583
119888(119894 119895) minus 120583
119888(119894 119895)
2
(9)
Here D(119894 119895) is coefficient of 2D DCT and Dk(119894 119895) isD(119894 119895) of the kth training image From the equations abovediscriminant factor for each DCT coefficient D(119894 119895) can becalculated as in the following equation
Discriminant Factor DF (119894 119895) =inter var (119894 119895)
max119888intra var
119888(119894 119895)
(10)
Classification is more efficient when samples in thesame class are clustered together and samples belongingto different classes are scattered in the feature space Thelarger the discriminant factors are the greater the impacton classification is in the field The devised discriminantfunction selects a number of indices of 2DDCTcoefficients indescending order which have large DF values Those selectedindices are used as reference positions whose correspondingDCT coefficients will be applied in classification process
The Scientific World Journal 5
Table 1 Experimental results of hit rates of recognition
35 Classification of Speed Limit Signs Classification is per-formed using the Linear Discriminant Analysis (LDA) andMahalanobis distances [2] LDA is performed to transformDCT coefficients into the format suitable for matching withthe classes in database and Mahalanobis distance is used asa metric for matching Classification results for a sequence ofimages are used for recognition of speed limit signs Equation(11) expresses the probability of matching with class c afterclassification for N image inputs
119875
119888=
1
119873
119873
sum
119896=1
120596 (119896)119860119888 (119896) (11)
where
119873
sum
119896=1
120596 (119896) = 1
119860
119888 (119896) =
1 when argmin119888(MD119888 (119896))
0 otherwise
(12)
120596(119896)rsquos are the weights determined experimentally They areinversely proportional to the distance between vehicle andobject MDc(k) is Mahalanobis distance between capturedimage k and class c The image is classified as class c whoseprobability Pc is the highest from P
1to PN
4 Experimental Results
Images used for training and classification were capturedon road using a mirrorless camera (MOS sensor 43 inch)mounted with a 20mm lens at 640 times 480 resolution and 30framess in normal daytime Classification is started with an
image of speed limit sign captured about 30meters away ROIdetected from the image consists of 12times12pixelsWeused 200images captured at different distances for training purposeper class Table 1 shows the hit rates of recognition for thespeed limit signs captured 1000 times on the road
The hit rates of recognition are about 100 when clas-sification is performed for 7sim9 consecutive images Table 2compares the number of arithmetic operations with LDAand SVM [2] The numbers in parentheses represent thereduction percentagesThe numbers of arithmetic operationsare reduced by about 60 and 80 when compared withLDA and SVM respectively In the experiments 57DCTcoefficients are selected out of 400 using the proposeddiscriminant function
5 Conclusion
A real-time algorithm for speed limit sign recognition hasbeen proposed with reduced amount of operations usingDCT The number of arithmetic operations was reduced byusing lookup table on binarized image which was obtainedthrough binarization and thinning To reduce feature dimen-sion discriminant function which selects parts of DCTcoefficients was devised Selection of DCT coefficients makesit possible to reduce runtime for recognition
Accurate recognition of speed limit signs in low resolu-tions or in the distance is achievable by applying the proposedalgorithm
Acknowledgment
This research was supported by the MEST (Ministry ofEducation Science and Technology) throughNRF (NationalResearch Foundation) of Korea under Grant no 2012-0002586
References
[1] R Bishop ldquoA survey of intelligent vehicle applications world-widerdquo in Proceeding of the Intelligent Vehicles Symposium pp25ndash30 2000
[2] R Duda P Hart and D Stork Pattern Classification Wiley-Interscience NewYork NY USA 2nd edition 2001
[3] C M Bishop Neural Networks for Pattern Recognition OxfordUniversity Press Oxford UK 1995
[4] K Fukunaga Introduction to Statistical Pattern RecognitionAcademic Press New York NY USA 2nd edition 1990
[5] S Ji and J Ye ldquoGeneralized linear discriminant analysis aunified framework and efficient model selectionrdquo IEEE Trans-actions on Neural Networks vol 19 no 10 pp 1768ndash1782 2008
[6] R Huang Q Liu H Lu and S Ma ldquoSolving the small samplesize problem of LDArdquo in Proceedings of the 16th InternationalConference on Pattern Recognition vol 3 pp 29ndash32 2002
[7] J Li B Zhao and H Zhang ldquoFace recognition based on PCAand LDA combination feature extractionrdquo in Proceedings ofthe 1st International Conference on Information Science andEngineering (ICISE rsquo09) pp 1240ndash1243 December 2009
[8] P N Belhumeur J P Hespanha and D J Kriegman ldquoEigen-faces vs fisherfaces recognition using class specific linear
6 The Scientific World Journal
projectionrdquo IEEE Transactions on Pattern Analysis andMachineIntelligence vol 19 no 7 pp 711ndash720 1997
[9] H Li T Jiang and K Zhang ldquoEfficient and robust featureextraction by maximummargin criterionrdquo in Proceedings of theConference onNeural Information Processing Systems (NIPS rsquo03)pp 97ndash104 2003
[10] L F Chen H Y M Liao M T Ko J C Lin and G J Yu ldquoNewLDA-based face recognition system which can solve the smallsample size problemrdquo Pattern Recognition vol 33 no 10 pp1713ndash1726 2000
[11] H Yu and J Yang ldquoA direct LDA algorithm for high-dimensional data with application to face recognitionrdquo PatternRecognition vol 34 no 10 pp 2067ndash2070 2001
[12] J Yang Y Yu andWKunz ldquoAn efficient LDA algorithm for facerecognitionrdquo in Proceedings of the 6th International Conferenceon Control Automation Robotics and Vision 2000
[13] X Wu J Kittler J Yang K Messer and S Wang ldquoA newdirect LDA (D-LDA) algorithm for feature extraction in facerecognitionrdquo in Proceedings of the 17th International Conferenceon Pattern Recognition (ICPR rsquo04) pp 545ndash548 August 2004
[14] C Bahlmann Y Zhu V Ramesh M Pellkofer and T KoehlerldquoA system for traffic sign detection tracking and recognitionusing color shape and motion informationrdquo in Proceedings ofthe IEEE Intelligent Vehicles Symposium pp 255ndash260 June 2005
[15] T Zhang and C Suen ldquoA fast parallel algorithm for thinningdigital patternsrdquo Communications of the ACM vol 27 no 3 pp236ndash239 1984
[16] D Slawecki and W Li ldquoDCTIDCT processor design for highdata rate image codingrdquo IEEE Transactions on Circuits andSystems for Video Technology vol 2 no 2 pp 135ndash146 1992
[17] E Alpaydin Introduction to Machine Learning MIT PressCambridge Mass USA 2nd edition 2004
Figure 3 An example of ROI preprocessing in the proposed algorithm (a) Input ROI (b) normalized ROI (c) gray image (d) croppedimage (e) white balanced image (f) binarized image and (g) image after thinning
proportional to the number of the features both in thelearning and in the classification processes To reduce theseburdens we need to remove less significant features [17] TheselectedDCT coefficients are used as features in the proposedalgorithm and the performance of the classification is notdegraded by using reduced amount of DCT coefficients Asmentioned in the previous section parts of DCT coefficientsare selected by using a devised discriminant functionobtained through intensive analysis on the attributes ofobject class The function is defined through a trainingprocess performed off-line on the classified database Theprocedure to obtain discriminant function is as follows
First mean of DCT coefficients 119863119888(119894 119895) 120583
119888(119894 119895) is cal-
culated for 119873(= 200) images per class c Then intraclassvariance intra varc(119894 119895) is calculated for every D(119894 119895) by (8)and interclass variance for all the classes inter var(119894 119895) isobtained by (9)
intra var119888(119894 119895) =
1
119873
119873
sum
119896=1
119863
119896
119888(119894 119895) minus 120583
119888(119894 119895)
2
(8)
inter var (119894 119895) = 1
119862
119862
sum
119888=1
120583
119888(119894 119895) minus 120583
119888(119894 119895)
2
(9)
Here D(119894 119895) is coefficient of 2D DCT and Dk(119894 119895) isD(119894 119895) of the kth training image From the equations abovediscriminant factor for each DCT coefficient D(119894 119895) can becalculated as in the following equation
Discriminant Factor DF (119894 119895) =inter var (119894 119895)
max119888intra var
119888(119894 119895)
(10)
Classification is more efficient when samples in thesame class are clustered together and samples belongingto different classes are scattered in the feature space Thelarger the discriminant factors are the greater the impacton classification is in the field The devised discriminantfunction selects a number of indices of 2DDCTcoefficients indescending order which have large DF values Those selectedindices are used as reference positions whose correspondingDCT coefficients will be applied in classification process
The Scientific World Journal 5
Table 1 Experimental results of hit rates of recognition
35 Classification of Speed Limit Signs Classification is per-formed using the Linear Discriminant Analysis (LDA) andMahalanobis distances [2] LDA is performed to transformDCT coefficients into the format suitable for matching withthe classes in database and Mahalanobis distance is used asa metric for matching Classification results for a sequence ofimages are used for recognition of speed limit signs Equation(11) expresses the probability of matching with class c afterclassification for N image inputs
119875
119888=
1
119873
119873
sum
119896=1
120596 (119896)119860119888 (119896) (11)
where
119873
sum
119896=1
120596 (119896) = 1
119860
119888 (119896) =
1 when argmin119888(MD119888 (119896))
0 otherwise
(12)
120596(119896)rsquos are the weights determined experimentally They areinversely proportional to the distance between vehicle andobject MDc(k) is Mahalanobis distance between capturedimage k and class c The image is classified as class c whoseprobability Pc is the highest from P
1to PN
4 Experimental Results
Images used for training and classification were capturedon road using a mirrorless camera (MOS sensor 43 inch)mounted with a 20mm lens at 640 times 480 resolution and 30framess in normal daytime Classification is started with an
image of speed limit sign captured about 30meters away ROIdetected from the image consists of 12times12pixelsWeused 200images captured at different distances for training purposeper class Table 1 shows the hit rates of recognition for thespeed limit signs captured 1000 times on the road
The hit rates of recognition are about 100 when clas-sification is performed for 7sim9 consecutive images Table 2compares the number of arithmetic operations with LDAand SVM [2] The numbers in parentheses represent thereduction percentagesThe numbers of arithmetic operationsare reduced by about 60 and 80 when compared withLDA and SVM respectively In the experiments 57DCTcoefficients are selected out of 400 using the proposeddiscriminant function
5 Conclusion
A real-time algorithm for speed limit sign recognition hasbeen proposed with reduced amount of operations usingDCT The number of arithmetic operations was reduced byusing lookup table on binarized image which was obtainedthrough binarization and thinning To reduce feature dimen-sion discriminant function which selects parts of DCTcoefficients was devised Selection of DCT coefficients makesit possible to reduce runtime for recognition
Accurate recognition of speed limit signs in low resolu-tions or in the distance is achievable by applying the proposedalgorithm
Acknowledgment
This research was supported by the MEST (Ministry ofEducation Science and Technology) throughNRF (NationalResearch Foundation) of Korea under Grant no 2012-0002586
References
[1] R Bishop ldquoA survey of intelligent vehicle applications world-widerdquo in Proceeding of the Intelligent Vehicles Symposium pp25ndash30 2000
[2] R Duda P Hart and D Stork Pattern Classification Wiley-Interscience NewYork NY USA 2nd edition 2001
[3] C M Bishop Neural Networks for Pattern Recognition OxfordUniversity Press Oxford UK 1995
[4] K Fukunaga Introduction to Statistical Pattern RecognitionAcademic Press New York NY USA 2nd edition 1990
[5] S Ji and J Ye ldquoGeneralized linear discriminant analysis aunified framework and efficient model selectionrdquo IEEE Trans-actions on Neural Networks vol 19 no 10 pp 1768ndash1782 2008
[6] R Huang Q Liu H Lu and S Ma ldquoSolving the small samplesize problem of LDArdquo in Proceedings of the 16th InternationalConference on Pattern Recognition vol 3 pp 29ndash32 2002
[7] J Li B Zhao and H Zhang ldquoFace recognition based on PCAand LDA combination feature extractionrdquo in Proceedings ofthe 1st International Conference on Information Science andEngineering (ICISE rsquo09) pp 1240ndash1243 December 2009
[8] P N Belhumeur J P Hespanha and D J Kriegman ldquoEigen-faces vs fisherfaces recognition using class specific linear
6 The Scientific World Journal
projectionrdquo IEEE Transactions on Pattern Analysis andMachineIntelligence vol 19 no 7 pp 711ndash720 1997
[9] H Li T Jiang and K Zhang ldquoEfficient and robust featureextraction by maximummargin criterionrdquo in Proceedings of theConference onNeural Information Processing Systems (NIPS rsquo03)pp 97ndash104 2003
[10] L F Chen H Y M Liao M T Ko J C Lin and G J Yu ldquoNewLDA-based face recognition system which can solve the smallsample size problemrdquo Pattern Recognition vol 33 no 10 pp1713ndash1726 2000
[11] H Yu and J Yang ldquoA direct LDA algorithm for high-dimensional data with application to face recognitionrdquo PatternRecognition vol 34 no 10 pp 2067ndash2070 2001
[12] J Yang Y Yu andWKunz ldquoAn efficient LDA algorithm for facerecognitionrdquo in Proceedings of the 6th International Conferenceon Control Automation Robotics and Vision 2000
[13] X Wu J Kittler J Yang K Messer and S Wang ldquoA newdirect LDA (D-LDA) algorithm for feature extraction in facerecognitionrdquo in Proceedings of the 17th International Conferenceon Pattern Recognition (ICPR rsquo04) pp 545ndash548 August 2004
[14] C Bahlmann Y Zhu V Ramesh M Pellkofer and T KoehlerldquoA system for traffic sign detection tracking and recognitionusing color shape and motion informationrdquo in Proceedings ofthe IEEE Intelligent Vehicles Symposium pp 255ndash260 June 2005
[15] T Zhang and C Suen ldquoA fast parallel algorithm for thinningdigital patternsrdquo Communications of the ACM vol 27 no 3 pp236ndash239 1984
[16] D Slawecki and W Li ldquoDCTIDCT processor design for highdata rate image codingrdquo IEEE Transactions on Circuits andSystems for Video Technology vol 2 no 2 pp 135ndash146 1992
[17] E Alpaydin Introduction to Machine Learning MIT PressCambridge Mass USA 2nd edition 2004
35 Classification of Speed Limit Signs Classification is per-formed using the Linear Discriminant Analysis (LDA) andMahalanobis distances [2] LDA is performed to transformDCT coefficients into the format suitable for matching withthe classes in database and Mahalanobis distance is used asa metric for matching Classification results for a sequence ofimages are used for recognition of speed limit signs Equation(11) expresses the probability of matching with class c afterclassification for N image inputs
119875
119888=
1
119873
119873
sum
119896=1
120596 (119896)119860119888 (119896) (11)
where
119873
sum
119896=1
120596 (119896) = 1
119860
119888 (119896) =
1 when argmin119888(MD119888 (119896))
0 otherwise
(12)
120596(119896)rsquos are the weights determined experimentally They areinversely proportional to the distance between vehicle andobject MDc(k) is Mahalanobis distance between capturedimage k and class c The image is classified as class c whoseprobability Pc is the highest from P
1to PN
4 Experimental Results
Images used for training and classification were capturedon road using a mirrorless camera (MOS sensor 43 inch)mounted with a 20mm lens at 640 times 480 resolution and 30framess in normal daytime Classification is started with an
image of speed limit sign captured about 30meters away ROIdetected from the image consists of 12times12pixelsWeused 200images captured at different distances for training purposeper class Table 1 shows the hit rates of recognition for thespeed limit signs captured 1000 times on the road
The hit rates of recognition are about 100 when clas-sification is performed for 7sim9 consecutive images Table 2compares the number of arithmetic operations with LDAand SVM [2] The numbers in parentheses represent thereduction percentagesThe numbers of arithmetic operationsare reduced by about 60 and 80 when compared withLDA and SVM respectively In the experiments 57DCTcoefficients are selected out of 400 using the proposeddiscriminant function
5 Conclusion
A real-time algorithm for speed limit sign recognition hasbeen proposed with reduced amount of operations usingDCT The number of arithmetic operations was reduced byusing lookup table on binarized image which was obtainedthrough binarization and thinning To reduce feature dimen-sion discriminant function which selects parts of DCTcoefficients was devised Selection of DCT coefficients makesit possible to reduce runtime for recognition
Accurate recognition of speed limit signs in low resolu-tions or in the distance is achievable by applying the proposedalgorithm
Acknowledgment
This research was supported by the MEST (Ministry ofEducation Science and Technology) throughNRF (NationalResearch Foundation) of Korea under Grant no 2012-0002586
References
[1] R Bishop ldquoA survey of intelligent vehicle applications world-widerdquo in Proceeding of the Intelligent Vehicles Symposium pp25ndash30 2000
[2] R Duda P Hart and D Stork Pattern Classification Wiley-Interscience NewYork NY USA 2nd edition 2001
[3] C M Bishop Neural Networks for Pattern Recognition OxfordUniversity Press Oxford UK 1995
[4] K Fukunaga Introduction to Statistical Pattern RecognitionAcademic Press New York NY USA 2nd edition 1990
[5] S Ji and J Ye ldquoGeneralized linear discriminant analysis aunified framework and efficient model selectionrdquo IEEE Trans-actions on Neural Networks vol 19 no 10 pp 1768ndash1782 2008
[6] R Huang Q Liu H Lu and S Ma ldquoSolving the small samplesize problem of LDArdquo in Proceedings of the 16th InternationalConference on Pattern Recognition vol 3 pp 29ndash32 2002
[7] J Li B Zhao and H Zhang ldquoFace recognition based on PCAand LDA combination feature extractionrdquo in Proceedings ofthe 1st International Conference on Information Science andEngineering (ICISE rsquo09) pp 1240ndash1243 December 2009
[8] P N Belhumeur J P Hespanha and D J Kriegman ldquoEigen-faces vs fisherfaces recognition using class specific linear
6 The Scientific World Journal
projectionrdquo IEEE Transactions on Pattern Analysis andMachineIntelligence vol 19 no 7 pp 711ndash720 1997
[9] H Li T Jiang and K Zhang ldquoEfficient and robust featureextraction by maximummargin criterionrdquo in Proceedings of theConference onNeural Information Processing Systems (NIPS rsquo03)pp 97ndash104 2003
[10] L F Chen H Y M Liao M T Ko J C Lin and G J Yu ldquoNewLDA-based face recognition system which can solve the smallsample size problemrdquo Pattern Recognition vol 33 no 10 pp1713ndash1726 2000
[11] H Yu and J Yang ldquoA direct LDA algorithm for high-dimensional data with application to face recognitionrdquo PatternRecognition vol 34 no 10 pp 2067ndash2070 2001
[12] J Yang Y Yu andWKunz ldquoAn efficient LDA algorithm for facerecognitionrdquo in Proceedings of the 6th International Conferenceon Control Automation Robotics and Vision 2000
[13] X Wu J Kittler J Yang K Messer and S Wang ldquoA newdirect LDA (D-LDA) algorithm for feature extraction in facerecognitionrdquo in Proceedings of the 17th International Conferenceon Pattern Recognition (ICPR rsquo04) pp 545ndash548 August 2004
[14] C Bahlmann Y Zhu V Ramesh M Pellkofer and T KoehlerldquoA system for traffic sign detection tracking and recognitionusing color shape and motion informationrdquo in Proceedings ofthe IEEE Intelligent Vehicles Symposium pp 255ndash260 June 2005
[15] T Zhang and C Suen ldquoA fast parallel algorithm for thinningdigital patternsrdquo Communications of the ACM vol 27 no 3 pp236ndash239 1984
[16] D Slawecki and W Li ldquoDCTIDCT processor design for highdata rate image codingrdquo IEEE Transactions on Circuits andSystems for Video Technology vol 2 no 2 pp 135ndash146 1992
[17] E Alpaydin Introduction to Machine Learning MIT PressCambridge Mass USA 2nd edition 2004
projectionrdquo IEEE Transactions on Pattern Analysis andMachineIntelligence vol 19 no 7 pp 711ndash720 1997
[9] H Li T Jiang and K Zhang ldquoEfficient and robust featureextraction by maximummargin criterionrdquo in Proceedings of theConference onNeural Information Processing Systems (NIPS rsquo03)pp 97ndash104 2003
[10] L F Chen H Y M Liao M T Ko J C Lin and G J Yu ldquoNewLDA-based face recognition system which can solve the smallsample size problemrdquo Pattern Recognition vol 33 no 10 pp1713ndash1726 2000
[11] H Yu and J Yang ldquoA direct LDA algorithm for high-dimensional data with application to face recognitionrdquo PatternRecognition vol 34 no 10 pp 2067ndash2070 2001
[12] J Yang Y Yu andWKunz ldquoAn efficient LDA algorithm for facerecognitionrdquo in Proceedings of the 6th International Conferenceon Control Automation Robotics and Vision 2000
[13] X Wu J Kittler J Yang K Messer and S Wang ldquoA newdirect LDA (D-LDA) algorithm for feature extraction in facerecognitionrdquo in Proceedings of the 17th International Conferenceon Pattern Recognition (ICPR rsquo04) pp 545ndash548 August 2004
[14] C Bahlmann Y Zhu V Ramesh M Pellkofer and T KoehlerldquoA system for traffic sign detection tracking and recognitionusing color shape and motion informationrdquo in Proceedings ofthe IEEE Intelligent Vehicles Symposium pp 255ndash260 June 2005
[15] T Zhang and C Suen ldquoA fast parallel algorithm for thinningdigital patternsrdquo Communications of the ACM vol 27 no 3 pp236ndash239 1984
[16] D Slawecki and W Li ldquoDCTIDCT processor design for highdata rate image codingrdquo IEEE Transactions on Circuits andSystems for Video Technology vol 2 no 2 pp 135ndash146 1992
[17] E Alpaydin Introduction to Machine Learning MIT PressCambridge Mass USA 2nd edition 2004
![Fuel Efficient Motor Oil Technical Article[1]](https://static.documents.pub/doc/80x56/577d22531a28ab4e1e971360/fuel-efficient-motor-oil-technical-article1.jpg)
