A new finger-knuckle-print ROI extraction method based on probabilistic region growing algorithm
ORIGINAL ARTICLE
A new ?nger-knuckle-print ROI extraction method based on probabilistic region growing algorithm
Tao Kong ?Gongping Yang ?Lu Yang
Received:23May 2013/Accepted:10October 2013/Published online:24October 2013óSpringer-Verlag Berlin Heidelberg 2013
Abstract Finger-knuckle-print pattern is considered to be one of the most promising biometric techniques for per-sonal identi?cation.In this paper,we propose a new region of interest (ROI)extraction method based on the probabi-listic region growing algorithm,which is robust to the ?nger displacement and rotation.Firstly,contrast enhancement is performed for the ?nger-knuckle-print images.And then we detect and correct the skewed images.Finally,ROI is extracted using the new probabilistic region growing algorithm.Experimental results show that the proposed method can achieve better performance com-pared with other existing methods.
Keywords Finger-knuckle-print áROI extraction áSkewed image correction áProbabilistic region growing algorithm
1Introduction
Recently,a new biometric technology based on ?nger-knuckle-print pattern has attracted much attention from the biometrics research communities.Finger-knuckle-print refers to the image pattern of the outer surface around the phalange joint of one’s ?nger,which is formed by slight bend of the ?nger knuckle.Finger-knuckle-print can be a distinctive biometric identi?er as its high uniqueness [1–5].Compared with the traditional biometric characteristics (e.g.faces,?ngerprints,and voices),?nger-knuckle-print pattern exhibits some promising advantages in real
application:(1)it is hard to be abraded since people hold stuffs with the inner side of the hand.(2)Unlike ?nger-print,there is no stigma of criminal investigation associ-ated with the ?nger knuckle surface.So ?nger-knuckle-print has a higher user acceptance rate [6].(3)People rarely leave ?nger-knuckle-print remains on the stuff surface,avoiding the loss of private data.Hence,the ?nger-knuckle-print pattern is considered to be one of the most promising biometric techniques for personal identi?cation in future.
The recognition performance of ?nger-knuckle-print is highly related to the quality of the extracted ROI [7–10].The ROI is the region which is ?lled with abundant texture features [2],and the ROI extraction is an essential step for ?nger-knuckle-print pattern recognition.Some ROI extraction methods for ?nger-knuckle-print have been proposed in recent years.In 2010,Zhang et al.[2]made use of a prede?ned window with a ?xed height and an adjustable width to extract the ?nger-knuckle-print ROI.This method is based on the convex direction coding.But the time complexity of the method is high,and it even cannot meet the real time requirement in some cases.Wang et al.[11]proposed an ROI extraction method based on matrix translation,which de?nes ROI as the region that contains the most texture features.When the ?nger joint part contains more texture features than other parts,the method performs well.But as it did not consider the brightness of the ?nger-knuckle-print image,when the brightness of the joint part is much higher than other parts,the extracted ROI using this method may not be asym-metric with respect to the joint area.In 2010,Kekre and Bharadi [12]proposed a ROI extraction method using Gradient ?eld based parameters for ?tting Co-ordinate system to the ?nger-knuckle-print images.In this method,the direction of gradient ?eld and coherence,which
T.Kong áG.Yang (&)áL.Yang
School of Computer Science and Technology,Shandong University,Jinan 250101,China e-mail:gpyang@https://www.360docs.net/doc/1911614732.html,
Int.J.Mach.Learn.&Cyber.(2014)5:569–578DOI 10.1007/s13042-013-0208-y
determines the strength of the averaged gradient,has been used in the distribution of local gradient vectors.Therefore, the central pixel of?nger-knuckle-print image can be obtained from these vectors.Ehteshami et al.[13]applied the area with maximum intensity to determine the core of ?nger-knuckle-print image.However,these methods have not considered the in?uence of?nger displacement and rotation in the image acquisition process.
By deep analysis of the?nger-knuckle-print image,we propose a robust ROI extraction method based on the probabilistic region growing algorithm.To evaluate the performance of the proposed method,four experiments are conducted on the open database from the Hong Kong Polytechnic University[14].Experimental results demon-strate the proposed method outperforms other existing methods in recognition accuracy and speed.
The rest of this paper is organized as follows.Section2 introduces the proposed ROI extraction method including contrast enhancement,skewed image correction and ROI extraction.Section3describes our experiments in detail, and discusses the experimental results.Finally,conclusion and future work are presented in Sect.4.
2The proposed method
In this section,a new ROI extraction method is developed for the?nger-knuckle-print image.Firstly,the original image is transformed by the Gaussian?lter and contrast enhancement is performed to eliminate random noise. Secondly,the skewed image detection and correction is carried out.Finally,the probabilistic region growing algorithm is used to extract ROI.The ROI extraction process is shown in Fig.1.
2.1Contrast enhancement
In the acquisition and transmission process,an original image can be affected by a variety of noises(e.g.sensor vibration,background light distribution non-uniform and etc.),resulting in the low quality of the image,which is harmful to the image analysis.Therefore,the image smoothing process is necessary to suppress noise and improve the quality of the image.The Gaussian?lter can be used as the linear smoothing?lter and experi-mental results prove that it can not only effectively suppress the salt and pepper noise,but also protect the edges of the image[2].For image smoothing,the two-dimensional zero-mean discrete Gaussian function,as shown in Eq.(1),is used as a linear?lter to suppress noise.
gei;jT?eàei
2tj2T
2r2e1Twhere r determines the width of the Gaussian.Choosing a value for r,we can obtain a convolution mask with size of m9n.The convolution result of original image f(i,j)and g(i,j)[15]is the output image h(i,j).
hei;jT?fei;jT?gei;jT?
X m
k?àm
X n
l?àn
feitk;jtlTgek;lT;
e2Twhere m and n determine the size of the convolution mask. In this paper,parameters are set as:r=1,m=n=2. The following weight array will be obtained by Eq.(1).
(i,j)-2-1012
-20.0030.0130.0220.0130.003 -10.0130.0600.0980.0600.013 00.0220.0980.1620.0980.022 10.0130.0600.0980.0600.013 20.0030.0130.0220.0130.003
However,we hope that the?lter weights are integer values for the decrease of the time complexity.Therefore, we transform the value in the corner of the array into1,and we obtain the other values according to the same ratio.An example is given in Eq.(3).
g0e0;0T?
ge0;0T
ge2;2T
?55e3TAnd the array becomes the following one:
(i ,j )-2-1012-214741-1420332040733553371420332042
1
4
7
4
1
When performing the convolution,the output pixel values will be normalized by the sum of the weight array to ensure that uniform intensity is not affected.
After smoothing,we remove the random noise of the image.However,there are some other noises with smaller brightness values in the image,which will have negative effects on ROI localization,as shown in Fig 2a.Therefore,contrast enhancement is applied to these images.The enhancement function is de?ned in Eq.(4).
r ei ;j T?h ei ;j Tàc ? 255255àc ;h ei ;j T!c
0;h ei ;j T\c 8
<:
e4T
where c is the prede?ned threshold.Based on analysis of the ?nger-knuckle-print images,we ?nd that the brightness value in the ?nger region is always bigger than 50.So the parameter c is set as 50.Through the contrast enhancement,we highlight the texture features we interested and suppress the noises at the same time,thus making the image more suitable for subsequent processing.
Figure 2shows the comparison of the original enhanced images.By comparison of the images,we can see that the processed image by Gaussian ?lter and contrast enhance-ment is clearer than the original one.At the same time,the noises are effectively suppressed.
2.2Skewed image correction
Due to imperfect placement of ?nger during image capture at different times,there is a certain amount of skewed ?nger-knuckle-images,in which ?ngers show a certain degree of distortion.So it is necessary to carry out detec-tion and correction of the skewed image before ROI extraction,which can reduce the dif?culty of subsequent image processing and increase the robustness of the rec-ognition system [16].The center point of ?nger-knuckle-print is an important reference of each image,which can reduce the loss of image information in skewed image correction.In the following,Sect.2.2.1gives the detection method of tilt angle,and Sect.2.2.2introduces the cor-rection process of the skewed image in detail.2.2.1The detection of tilt angle
It is easy to detect the lower edge of the ?nger using Canny Edge Detection [17].By deep analysis of a large number of images,we draw the conclusion that the lower edge of the ?nger is almost a straight line.So the linear ?tting method is used to synthesize a straight line under the lower edge,and the ?tting equation is de?ned as y =ax ?b .The synthesized line l oc is shown in Fig.3.By the trigono-metric function knowledge,we can know that the angle h between the line l oc and the horizon line l o x can be com-puted by Eq.(5).h ?arctan a :
e5T
2.2.2The correction of skewed image
Based on the detected tilt angle in Sect.2.2.1,we give the correction strategy of the skewed image,which is shown in Table 1.
We will perform the correction of the skewed image in the plane-coordinate system.When the reference point is the origin of the coordinate system,the relationship between the original point P (x 0,y 0)and the corresponding corrected point Q (x 1,y 1)is shown in Fig.4.In Fig.4,r is the distance from the origin point O to the point P ,a is the angle between the line OP and the X -axis,and h is the detected tilt angle.Before correction,the coordinate
value
Fig.2The comparison of the original and enhanced images.a The original image;b The corresponding enhanced image;c The gray histogram of (a );d The gray histogram of image (b
)
Fig.3The skewed image with the obvious tilt angle
of the point P can be expressed as Eq.(6).After correction,the coordinate value of the corresponding point Q can be expressed as Eq.(7).x 0?r cos a
y 0?r sin a (
e6T
x 1?r cos ea àh T?r cos a cos h tr sin a sin h
y 1?r sin ea àh T?r sin a cos h àr cos a sin h :
(
e7T
The above correction process is based on the origin point O in the coordinate system.In order to make use of the center point of the image to correct the skewed image,we should ?rstly move the origin point of the coordinate system to the center point of the image,which is shown in Fig.5.The origin point of the original coordinate system will be moved to the point (a ,b ).Equation (8)shows the conversion expression.x 2y 210@1A ?10àa 01àb 0010@1A x 1y 110@1A :e8TIf the center point of the image is (a ,b ),after correction it is changed to be (c ,d ).The transformation matrix expression is shown in Eq.(9),and the inverse transformation matrix expression is shown in Eq.(10).
x 1
y 110
B B @1
C C A
?1
0c 01d 0010
B @1
C A cos h
sin h 0àsin h cos h 00
010
B
@1C A 1
0àa 01àb 0
10
B @1
C A x 0y 01
0B B @1
C C A e9T
x 0
y 010
B B @1
C C A
?1
0àa 01àb 00
10
B
@1C A cos h
àsin h 0sin h
cos h 000
1
0B
@1C A 10
c
01d 0010
B
@1C A x 1y 110B B @1
C C A
e10T
It is worth noting that the coordinate values of the
original image are integers,but after the correction of the tilt angle,the values become decimals.Therefore,the correction process of the skewed image includes not only geometric operations,but also interpolation process for the coordinate values of the corrected image.
There are three typical interpolation methods:nearest-neighbor interpolation,bilinear interpolation and bicubic interpolation [18].Among them,nearest-neighbor inter-polation is the simplest method.Through calculating the values of the points around the point (x 0,y 0),it set the point (x 0,y 0)values as the pixel values of the nearest integer coordinates.Bilinear interpolation takes the in?uence of the four neighbor points into consideration.Bicubic inter-polation can get the most clear texture image by using 16adjacent points.But the computation complexity is very high.So in this paper,we use the bilinear interpolation.After contrast enhancement and the skewed image cor-rection,some obtained images are shown in Fig.6.From Fig.6we can see that the lower edge of the ?nger is very close to the horizontal line,which facilitates the extraction of ROI.
2.3The ROI extraction method
In this section,a new ROI extraction algorithm,called the probabilistic region growing algorithm,is described.
Table 1The correction strategy
In the ?nger-knuckle-print image,the ?nger shows bend to some extent,which means that the distance between the joint portion and the image acquisition device is smaller than it between other portions and the device.So the brightness of the joint portion is higher than it of the other parts.In other words,the pixel value of the joint portion in the image is higher than it of the other por-tions.Thus the center point of the joint portion can be determined by ?nding the column and row coordinates with the highest pixel value.The detection method of the center point of the joint portion is given in Sect.2.3.1,and Sect.2.3.2describes the probabilistic region growing algorithm.
2.3.1The detection of the center point
The intensity sum of pixel in p rows or columns is calcu-lated by Eq.(11).
H i
?X h j ?1
X p àp x ei tp ;j T;i ?p t1;p t2;...;l àp L j ?
X l i ?1X p àp
x ei ;j tp T;j ?p t1;p t2;...;h àp 8
>>>>><>>>>>:e11T
where x (i ,j )is the pixel value of the i -th row,j -th column
of the image.h and l are separately the height and width of the image.Considering that the cross point of the row and column with maximum intensity may not just in the center of the ?nger joint,we cannot correctly detect the center point of the ?nger by comparing the intensity sum of pixels in a certain row or column.So we use p rows and p columns to calculate H i and L i respectively.The curves obtained by Eq.(11)with p =5are shown in Fig.7.We can see that pixel values of the center point in the joint portion are relatively higher and there is an obvious peak in the Fig.7c.Therefore,the coordinate (a ,b )of the center point in the joint portion is de?ned in Eq.(12).a ?f i j r i ?max i 2?p t
1;...;l àp
eH i Tg b ?f j j s j ?
max j 2?p t1;...;h àp
eL j Tg :8><>:e12T
2.3.2The ROI extraction algorithm
In order to extract ROI,we need to de?ne a rectangle with ?xed size based on the center point in the joint portion.The key issue is how to determine the position of the ?xed rectangle.We use the proposed probabilistic
region
Fig.6The comparison of the original and corrected images.a The
original images;b tilt angle detection;c the corresponding corrected
images
Fig.7The curves of intensity sum.a The ?nger-knuckle-print image;b The curve of H i ;c The curve of L i
growing algorithm to solve this problem.The algorithm is based on the pixel block.Assuming that the size of the block is K 9K pixels,the whole image is divided into M 9N sub-blocks,and the average pixel value for sub-block B is G B .Firstly we will ?nd a sub-block which must belongs to the ROI,called the selected block.The area,which is ?lled with the selected block,is called the selected area.Then we separately examine the blocks around the selected block to determine which one can be ?t for the growing conditions.If one block is ?t for the growing conditions,it will be seen as the selected block.This pro-cess is called growing.The growing process stops until the size of the selected area reaches the prede?ned value.This paper de?nes the ?rst selected block as the block whose center is the point (a ,b )obtained in Sect.2.3.1.In this paper,the size of the block is 595.
The growing conditions will directly affect the result of ROI extraction.We not only need to extract rich texture feature,but also take the symmetry of ROI into consider-ation.For the selected block S ,its adjacent blocks are the block labeled U ,D ,L ,and R ,in which U is the upper block of S ,D is the lower block of S ,L is the left block of S ,and R is the right block of S.Y U and Y D respectively are the top and bottom boundary of the image,and H is the height of the ROI.The growing process is shown in Fig.8,and the growing algorithm in vertical direction is shown in Table 2.Similarly,X L and X R respectively are the left and right boundary of the image and W is the width of the ROI.The growing algorithm in horizontal direction is shown in Table 3.Some extracted ROI images are shown in Fig.9.
3Experimental results
3.1The experimental database and settings
We use the ?nger-knuckle-print database from the Hong Kong Polytechnic University [14]to evaluate the perfor-mance of the proposed method.The open database was collected from 165volunteers,including 125males and 40females.Among them,143subjects are 20–30years old and the other are 30–50years old.The images were col-lected in two separate sessions.In each session,the subject was asked to provide six images for each of ?ngers
which
Fig.8The growing process.a The growth in vertical direction;b the growth in horizontal direction
Table 2The growing algorithm in vertical direction
Table 3The growing algorithm in horizontal direction
include the index and middle ?ngers of the both hands.In total,the database contains 7,920images from 660differ-ent ?ngers.The original image size is 3849288.Figure 10shows the ?nger-knuckle-print capture device developed by Biometric Research Centre (UGC/CRC)of the Hong Kong Polytechnic University.
The database provides two datasets:one dataset consists of the acquired original images,and the other one consists of the corresponding ROI images.The ROI extraction method is detailed in [2].The size of the ROI image is 1109220pixels.Some typical images are shown in Fig.11.
All the experiments are implemented in Matlab2011a on a PC with a 3.10GHz CPU and 2.0GB memory.To show the performance of the proposed method comprehensively,four experiments are designed to evaluate the proposed method:In experiment 1,we ?rst de?ne the accuracy of the ROI extraction,and then use this measurement to evaluate the proposed method and other existing methods.In experiment 2,we compare the extracted ROI images from the skewed ?nger-knuckle-print images by the proposed method and two other methods.In experiment 3,the rec-ognition performance of three methods are evaluated by the equal error rate (EER)and the receiver operating charac-teristics (ROC).Finally,the average processing times of three methods are measured in Experiment 4.3.2Experiment 1
In order to evaluate the accuracy of the method proposed in this paper,we perform this experiment.Regarding the ROI image from the open database as reference,we de?ne the accuracy of the ROI extraction as the area ratio of two factors:one is the ROI image from the open database;the other is the overlapped portion of the ROI image from
the
Fig.9The extracted ROI images using the proposed
method
Fig.10The ?nger-knuckle-print capture
device
Fig.11Some typical images.a and b the original ?nger-knuckle-print images;c and d the corresponding ROI images
open database and ROI image extracted by other method.We use Eq.(13)to compute the extraction accuracy.p ?
S 0^S 1
S 0
?100%:e13T
where S 0represents the area of the ROI image from the open database,S 1represents ROI area extracted by other method,and S 0^S 1is the overlapped area between S 0and S 1.The extracted ROI images and the ROI images from the open database are shown in Fig.12and the accuracy is
shown in Table 4.From Table 4,we can see that the average accuracy of our method is 94.80%,and the smallest accuracy value is 87.06%,which show that the proposed method has high extraction accuracy.
We also examine the samples whose accuracy values are lower than 85%,which is shown in Table 4.However,the average accuracy of the method in [13]is 86.88%,which is much lower than our method.This experiment also veri?ed the effectiveness of the proposed method.3.3Experiment 2
One advantage of our method is that it is robust to the rotation of the ?nger-knuckle-print image.In this experi-ment,we arti?cially rotate the ?nger-knuckle-print images by a random angle and compare the extracted ROI images by different extraction methods.We rotate the original ?nger-knuckle-print images from -5°to 10°randomly,and the rotated images are shown in Fig 13a.The corre-sponding ROI images extracted by [2,13]and our method are illustrated in Fig.13b–d respectively.We can see,when the image is rotated,the effectiveness of [2]and [13]are not as good as it of our method.However,no matter how many degrees the image is rotated,our method can detect the title angle and correct it
effectively.
Fig.12The comparison of ROI images extracted by different methods.a The ROI images in the open database;b the ROI images extracted by the method in [13];c the ROI images extracted by the proposed method
Table 4The accuracies of the different ROI extraction methods Accuracy
Average value (%)Minimum value (%)Percentage of accuracy lower than 85%(%)The method in [13]86.8862.3022.81The proposed method
94.80
87.06
Fig.13The ROI images
extracted from skewed images by different methods.a The skewed ?nger-knuckle-print images;b ROIs extracted by [2];c ROIs extracted by [13];d ROIs extracted by our method
Table 5The performance of ?nger-knuckle-print identi?cation by different ROI extraction methods (%)Methods
Left index Left middle Right index Right middle The method in [2]11.039.0810.789.78The method in [13]9.458.988.127.54Our method
7.24
6.54
6.89
6.65
3.4Experiment 3
In this section,we compare our method with the two existing ROI extraction methods in the veri?cation mode.As described in Sect.3.1,the open database contains ?n-ger-knuckle-print images from four types of ?nger:the left index ?ngers,the left middle ?ngers,the right index ?ngers and the right middle ?ngers.For each type of ?nger,there are 165classes and each class contains 12images.We take images collected at the ?rst session as the gallery set and take images collected at the second session as the test set.To obtain statistical results,each test image is matched with all images in the gallery set.If the two matching
templates are from the same class,the matching is called the intraclass matching;otherwise,we call the matching as the interclass matching.Therefore,for each type of ?nger-knuckle-print,there are 5,940intraclass matchings and 974,160interclass matchings.The performance of the system is evaluated by the EER widely used as bench-marking in biometric systems.In ?nger-knuckle-print identi?cation,we perform size normalization to the ROI of ?nger-knuckle-print images,so the size of the region used for feature extraction is 1109220pixels.Besides,the speeded up robust features technique proposed in [19]is used for feature extraction.The matching score between different feature vectors is computed using nearest-neigh-bour-ratio method [20].
The experimental results of different approaches are summarized in Table 5,and the corresponding ROC are illustrated in Fig.14.
It can be ascertained from Table 5and Fig.14that the proposed method achieves the best performance among all the approaches considered in this work.Speci?cally,the advantage of our method is mainly the result of the
skewed
Fig.14ROC curves by different ROI localization methods
Table 6The processing times of the different ROI extraction methods Methods The method in [2]The method in [13]The proposed method Time (ms)
208
160
103
image correction and the probability growing process.As the method in[2]is based on the convex direction coding, it will lose effectiveness when the textures are not obvious. Although the method in[13]can effectively get the central pixel of the?nger ROI image,it does not work properly for skewed images.
3.5Experiment4
In this section,we compare the processing times of the proposed method and the methods proposed in[2]and[13]. The average processing times of different methods are measured and shown in Table6.From Table6,the average ROI extraction time of the proposed method is103ms,and the proposed method is faster than methods proposed in[2] and[13].In a word,the proposed method can be used in real-time applications.
4Conclusion and future work
ROI extraction is a key step for?nger-knuckle-print pattern recognition.In this paper,we present a new ROI extraction method based on the probabilistic region growing algorithm.In order to demonstrate the accuracy and ef?ciency of the proposed method,four experiments are performed on the open?nger-knuckle-print database. From the experimental results,we can see that the proposed method can not only extract the ROI accurately in real time but also avoid the effects of noises and ?nger displacement and rotation.In the future,we plan to further improve the speed and accuracy of our method.
Acknowledgments The work is supported by National Natural Science Foundation of China under Grant No.61070097,61173069, and Program for New Century Excellent Talents in University of Ministry of Education of China under Grant No.NCET-11-0315.In addition,the authors would particularly like to thank the anonymous reviewers for their helpful suggestions.
References
1.Morales A,Travieso C,Ferrer M,Alonso J(2011)Improved
?nger-knuckle-print authentication based on orientation enhancement.Electron Lett47(6):380–381
2.Zhang L,Zhang L,Zhang D,Zhu H(2010)Online?nger-
knuckle-print veri?cation for personal authentication.Pattern Recogn43(7):2560–2571
3.Zhang L,Zhang L,Zhang D,Zhu H(2011)Ensemble of local and
global information for?nger-knuckle-print recognition.Pattern Recogn44(9):1990–1998
4.Zhang L,Zhang L,Zhang D(2009)Finger-knuckle-print:a new
biometric identi?er.In:Proceedings of the IEEE International Conference on Image Processing,pp1981–1984
5.Zhang L,Zhang L,Zhang D(2009)Finger-knuckle-print veri?-
cation based on band-limited phase-only correlation.In:Pro-ceedings of the13th International Conference on Computer Analysis of Images and Patterns,pp141–148
6.Kumar A,Ravikanth C(2009)Personal authentication using
?nger knuckle surface.IEEE Trans Inf Forensics Security 4(1):98–110
7.Li Q,Qiu Z,Sun D,Wu J(2004)Personal identi?cation using
knuckle print.In:Proceedings of the5th Chinese conference on Advances in Biometric Person Authentication,pp680–689
8.Meraoumia A,Chitroub S,Bouridane A(2011)Palmprint and
?nger-knuckle-print for ef?cient person recognition based on Log-Gabor?lter response.Analog Integr Circ Signal Process 69(1):17–27
9.Yang J,Shi Y(2012)Finger-vein ROI localization and vein ridge
enhancement.Pattern Recogn Lett33(12):1569–1579
10.Xiong M,Yang W,Sun C(2011)Finger-knuckle-print recogni-
tion using LGBP.In:Advances in Neural Networks–ISNN2011.
Springer,Berlin,Heidellberg,pp270–277
11.Wang CY,Song SL,Sun FR,Mei LM(2006)A novel biometrics
technology-?nger-back articular skin texture recognition.Acta Automatica Sinica32(3):360–367
12.Kekre HB,Bharadi VA(2010)Finger-knuckle-print region of
interest segmentation using gradient?eld orientation&coher-ence.In:The3rd International Conference on Emerging Trends in Engineering and Technology,pp130–133
13.Ehteshami NSM,Tabandeh M,Fatemizadeh E(2012)A new ROI
extraction method for FKP images using global intensity.In: 20126th International Symposium on Telecommunications, pp1147–1150
14.PolyU FKP Database,https://www.360docs.net/doc/1911614732.html,.hk/*bio
metrics/FKP.htm
15.Jain R,Kasturi R,Schunck BG(1995)Machine vision.McGraw-
Hill,USA
16.Arampatzis A,Monte GD,Karamanidis K(2008)Effect of joint
rotation correction when measuring elongation of the gastrocne-mius medialis tendon and aponeurosis.J Electromyogr Kinesiol 18(3):503–508
17.Bao P,Zhang L,Wu X(2005)Canny edge detection enhance-
ment by scale multiplication.IEEE Trans Pattern Anal Mach Intell27(9):1485–1490
18.Battiato S,Gallo G,Stanco F(2003)Smart interpolation by
anisotropic diffusion.In:Proceedings of12th International Conference on Image Analysis and Processing,pp572–577 19.Bay H,Ess A,Tuytelaars T,Van Gool L(2008)Speeded-up
robust features(SURF).Comput Vis Image Underst110(3): 346–359
20.Badrinath G S,Nigam A,Gupta P(2011)An ef?cient?nger-
knuckle-print based recognition system fusing sift and surf matching scores.In:Proceedings of the13th International Con-ference on Information and Communications Security, pp374–387