All in Focus Image Generation based on New Focusing Measure Operators

Transcription

1 (JACSA nternational Journal of Advanced Computer Science and Applications, Vol 7, No, 06 All in Focus mage Generation based on New Focusing Measure Operators Hossam Eldeen M Shamardan epartment of nmation Technolog Facult of Computers and inmation Universit of Helwan Egpt Abstract To generate an all in focus image, the Shape-From- Focus (SFF is used The SFF e is finding the optimal focus depth at each piel or area in an image within sequence of images n this paper two new focusing measure operators are suggested to be used SFF The suggested operators are based on modification the state of art tool time-frequenc analsis, the Stocwell Transm ( The first operator depends on iscrete Orthogonal Stocwell Transm (O which represents a pared version of, while the other depends on ielwise O (-O which provides a local spatial frequenc description Both of the operators provides the computational compleit and memor demand efficienc compared to the operator depending on A comparison between the suggested operators to operators based on are permed and showed that the suggested operators permances are as analogous to that of Kewords Focus Measure; All n Focus; Stocwell Transm; O NTROUCTON SFF is an essential process to overcome a specific limitation of imaging sstems which is the different depth of field (OF each part in an image [,, 3] The SFF solves this problem b providing full sharp focused image The SFF depends on measuring the optimal focus b using the focus measure ( operator, the main e, shape estimating The usual SFF methods compute optimal focus and its depth b appling operator on ever area in a frame within a sequence of images and see the optimal focused part along the sequence The full focused image can be constructed from merging the focuses optimal parts [4, 5] The sharp focused area is characteried b its energ high frequenc components, and The operator is used to measure the amount of energ in ever part Man operators have been proposed in the literature both autofocus (AF and SFF applications [5] n [6], the permance of multiple operators were eamined operators can be classified into two broad tpes: space domain and, frequenc domain [7] [8], and others such as compression operators [5] [9] The has been used as a base operator in [0] and compared to other operators The suggested idea is to measure the high frequenc components energ located in a region of interest in the domain The gives good results but it suffers from high computational cost To overcome the problem of high cost, a pared version of, O was provided in [] The O provides efficienc in both computational cost and memor usage Another version of O, piel-wise local spatial frequenc description (- O was given in [] The -O provides a tool studing a specific frequenc at specific piel or area Both of O and -O have low computational cost and robustness to Gaussian noise n this paper two new operators are presented based on O and -O their low computational cost and memor usage This paper is organied as follows n section, the bacground, O and -O are presented The proposed algorithm and operators are described in section 3 Finall, eperimental results and conclusion are presented in sections 4 and 5 respectivel BACKGROUN has been shown as a generaliation of the short-time Fourier transm (FT, and the wavelet transms [3] From [0] the -, H an image h (, of sie N * M st piel (, is given b H st N M,,, Hn, m n0 m0 n m ep( ( ep( i( n m Where H is the Fourier transm of h,, and are -coordinates and -coordinates in space respectivel and, and are indices in the frequenc along -ais and -ais From [4], it has been demonstrated that the redundanc comes from the equal sampling rate both low and high frequenc bands despite the fact of Nquist criterion which states that the sampling rate depends on the frequenc of the sampled data A detailed stud the - computational compleit an image of sie N * N is given in [] t has been shown that has a computational cost of N N log N and a storage requirement of O ( N The O suggested in [] gives lower sampling rates lower frequencies, and higher sample rates higher * ( 30 a g e

2 (JACSA nternational Journal of Advanced Computer Science and Applications, Vol 7, No, 06 frequencies to solve the redundanc t does so b building a set of N orthogonal unit-length basis vectors, each of which targets a particular region in the time-frequenc domain The regions defined b O are described b a set of parameters: v specifies the center of each frequenc band (voice p, is the width of that band, and specifies the location in time O basis vectors a particular band p and the parameters describing these basis vectors are defined in the following cases according to p where p 0,,log ( N p 0 0,, ( T ( T ( T v,, p, v,, v,, e ( p, v ( p v,, ( i / N p, 0,, ie ( i e * ( p, i ( v / / e sin( i ( v / / where ( N / is the center of the temporal window, and 0,,, N is the inde of time interval The time-frequenc distribution a famil of vectors a signal of length 6 is shown in Fig [5] Calculating O is determined b taing the inner product between the basis vectors mentioned above and the input signal B taing linear combinations of the Fourier comple sinusoids in band-limited subspaces and appling appropriate phase and frequenc shifts, the -O of M * N image [, ] is defined in [] as follows: s, Where h p p m ep(iπ ( p H(m v,n v n p * ( p p m n (3 p p v and p p v are representing the horiontal and vertical voice frequencies, and p p is representing the number of points in the partition, and H ( m, n is the Fourier transm image h [, ] The -O due to using orthonormal set of basic functions as described above, has computational compleit of N N log N and storage requirements of N which was proved in [6] t is obvious O has less computational compleit required than the - Fig Time-Frequenc distribution O components in positive direction The -O suggested in [] aims to find the voice frequenc distribution a piel or region within the image B choosing a set of (, coordinates representing a single piel or area, all the values of s, ] all horiontal [ and vertical voices v can be determined position ( (, ue to the variable sie and limits of ever O components at each band, the -O is constructed b obtaining all components of O at each band ( p, p b: S[ / N * p, / N * p From (4, the -O corresponding response is occuping part of the O response space Hence t onl requires sie of, considering the negative side, log ( N *log ( N ( * The -O response is referred to as the local domain (or spectrum Since -O selects onl some components from the whole components set O, a reduction will consequentl go further the computational compleit and memor demands Consequentl, the computational compleit calculating - O single piel is of order O (( * Log( N^ Considering the O calculations, it is obvious that -O is less demanding computational compleit than O ROOSE ALGORTHM The algorithm suggests a stac of L frames L with the same sie, and same scene pictures an object at different focusing depths The frames are divided into windows W(,, each of sie M * N located at position (, in ever frame The Suggested algorithm is described as follows: ivide ever frame L into windows Each window W(,, is located at position (, in frame Appl the or window W,, using mulas in (5 or (6 along all the L frames 3 Find Z b using (7 optimal 4 Repeat steps from to 3 and merge all windows to get the generated full focused image ] (4 3 a g e

3 The mulas calculating v v( pm v v( pn v v( pm v v( pn is given as follows: ( Z (,, v (JACSA nternational Journal of Advanced Computer Science and Applications, Vol 7, No, 06 where (,, v M N 0 0 abs s, ( v (0,0 (5 And v v( p M v v( p N (, (, 0 0 ( ( 0 0 v v p M v v p N where ( 0,0, v abs 0,0 For determining Z Optimal Z optimal s ( v, (0,0 argma( ( Z, L (7 The suggested and in the algorithm are based on O and -O respectivel and both of them measure the energ in high frequencies components (frequenc > 0 (C A mula used the suggested operators are given in (5 and (6 The operators are used to find the optimal focused window b measuring the highest response resulted b the operator B merging the optimal focused window a full focused image of the scene can be reconstructed The idea measuring the energ is the of the energ the components within an area reflects the sharpness and hence the focusing For, the piel (, 0 0 is selected at the center of the targeted window and used to represent the window V EXERMENTAL RESULTS To evaluate the permance of the proposed algorithm and its robustness, three eperiments three sequences of images were conducted each of 56 gra levels The first eperiment contains sequence of 60 images of cone The sie this sequence is 360*360 A simulation software was used to generate the images focused at different parts of the image Fig a through d, the proposed algorithm has been used to construct all in focus image through and operators on this sequence The resulting images are shown in Fig e, f The second eperiment contains a sequence of 30 natural images, each of sie 99*5 The sequence and the generated all in focus image are shown in Fig 3 The third eperiment contains also 30 natural images of sie 5 * 5 Results are shown in Fig 4 (6 Fig ictures from (a to (d are defocus cone images at different focusing level, e SFF b using, (f SFF b using The first sequence of images was adopted and used net evaluating tests To evaluate the robustness of the algorithm against noise, three different measures were adopted to measure the all in focus image quantitativel The first measure is the rmse (root mean square error which is defined as follows rmse (8 MN M N (, (, Where (, the original is image, and (, is the all in focus image from the sequence of images To test the permance of the algorithm, the algorithm was applied to the sequence with added Gaussian noise of variance ranging from 0 to 0 and the window sie is ranging from 4 to 64 Fig 5 shows the results of this test Fig 3 ictures from (a to (d are defocus cone images at different focusing level, (e SFF b using, (f SFF b using 3 a g e

4 (JACSA nternational Journal of Advanced Computer Science and Applications, Vol 7, No, 06 Fig 6 Comparison between (UQ versus window sie and operators permance Fig 4 ictures from (a to (d are defocus cone images at different focusing level, e SFF b using, (f SFF b using To compare between and permance, a test was applied showing the rmse permance of the two operators against the window sie and different noise variances The results are shown in Fig 6 t is obvious that the is advantageous than the since it considers all the piels rather than a single central one The net measures are the UQ (universal image qualit inde and SSM (structural similarit inde measure [0] and are defined as following: Fig 7 Comparison between (SSM versus window sie and operators permance UQ SSM 4 c c c c (9 (0 Where and represent mean of the original and all in focus image constructed from the sequence of images respectivel The results are shown in Fig 7,8 t is clear that both UQ and SSM gives similar permance both and Fig 5 rmse against window sie different variance levels of gaussian noise Another eperiment was conducted to compare between and permances generating the cone image give in Fig, assuming window is of sie 4 The results showed that provides permance little bit better than The achievable rmse the is 05 while the O achieved 07 Of course the provides better permance (38% however, the resultant permance is ver minor (less than out of 56 gra level Compared to the computational compleit, the is of order 4 4 N N log N while the is of order N N log N V CONCLUSON AN FUTURE WORK n this paper, two new operators are suggested to reconstruct all-in-focus image The two operators are built on etensions of Stocwell Transm, a space-frequenc transmation tool Stocwell Transm has been proved to suffer from ecessive abundant computations and high memor requirements and to reduce the computational compleit that is the reason the and are adopted as bases the suggested operators Results have shown to 33 a g e

5 (JACSA nternational Journal of Advanced Computer Science and Applications, Vol 7, No, 06 be as good as The two suggested methods are of almost similar permance and with less computational compleit and memor demands The future research can etend the usage of those tools to get automatic focusing and to enhance the robustness REFERENCES [] Z Li, A Fischer and G Li, "Volumetric retinal fluorescence microscopic imaging with etended depth of field," in SE 973, Three-imensional and Multidimensional Microscop: mage Acquisition and rocessing XX, San Francisco, 06 [] E Anderes, B Yu, V Jovanovic, C Morone, M Gara, A Braverman and E Clothiau, "Maimum lielihood estimation of cloud height from multi-angle satellite imager," The Annals of Applied Statistics, pp 90-9, 5 October 009 [3] Y Song, Y Xie, V Malarchu, J Xiao, Jung, K Choi, Z Liu, H ar, C Lu, R Kim, R Li, K Croier, Y Huang and J Rogers, "igital cameras with designs inspired b the arthropod ee," Nature, vol 497, no 7447, p 95 99, Ma 03 [4] A Anish and T J Jebaseeli, "A surve on multi-focus image fusion methods," nternational Journal of Advanced Research in Computer Engineering & Technologol, no 8, p 39 34, October 0 [5] S ertu, uig and M A Garcia, "Analsis of focus measure operators shape-from-focus," attern Recognitionol 46, no 5, p 45 43, Ma 03 [6] A S Mali and T S Choi, "Consideration of illumination effects and optimiation of window sie accurate calculation of depth map 3 shape recover," attern Recognitionol 40, no, pp 54-70, 007 [7] T M Mahmood, S O Shim and T S Choi, "Shape from focus using principal component analsis in discrete wavelet transm," Optical Engineeringol 48, no 5, p 05703, 8 Ma 009 [8] J Baina and J ublet, "Automatic focus and iris control video cameras," in mage rocessing and its Applications, 995, Fifth nternational Conference on, Edinburgh, 995 [9] H Mir, Xu and V Bee, "An etensive empirical evaluation of focus measures digital photograph," in SE 903, igital hotograph X, 9030, 04 [0] T M Mahmood and T S Choi, "Focus measure based on the energ of high-frequenc components in the S transm," in epth Map and 3 maging Applications: Algorithms and Technologiesol 35, G Global, 0, pp [] R G Stocwell, "A basis efficient representation of the S- transm," igital Signal rocessing, p , Januar 007 [] S rabc, R G Stocwell and J R Mitchell, "mage Teture Characteriation Using the iscrete Orthonormal S-Transm," Journal of igital magingol, no 6, pp , ecember 009 [3] Y Wang and J Orchard, "On the use of the Stocwell transm image compression," in mage rocessing: Algorithms and Sstems V,74504, 009 [4] Y Wang, Efficient stocwell transm with applications to image processing (h thesis, Waterloo, Ontario: The Universit of Waterloo, 0 [5] Y Wang and J Orchard, "Fast iscrete Orthonormal Stocwell Transm," SAM Journal on Scientific Computingol 3, no 5, p , November 009 [6] M K N B and K, "almprint Authentication S stem Based on Local and Global Feature Fusion Using O," Journal of Applied Mathematicsol 04, p, 6 ecember a g e