Improved Efficiancy of CBIR using Contourlet Transform

Transcription

1 T. Naga Kartheea, M. Koteswara Rao & K.Veeraswaamy ECE Department, QIS college o Engg & technology, Ongole, naga.artheea1@gmail.com, oteshproect@gmail.com, ilarivs@yahoo.com Abstract - Content-based image retrieval (CBIR) is an impotent research area or manipulating large amount o image database and archives. In this paper we explain the eiciency retrieval rate o content based image retrieval system using contourlet transorm. the multiresolution using the Laplacian pyramid (LP).And the directionality can be analyzed by using the Directional Filter ban(dfb).in CBIR system using Contourlet Transorm based eatures directionality and anisotropy are made it powerul. Improved results in terms o retrieval eiciency and less complexity are observed in recent wor.the distance measures VIZ., Manhattan distance and minowasi distance are used in similarity measures in the proposed CBIR system Keywords: Contour lets, Multiresolution, laplacian pyramid Ditrctionalit y,directional Filter Ban. I. INTRODUCTION The unction o a content-based image retrieval system [Niblac et al., 1993, Guibas and Tomasi, 1996] is typically to _nd database images that loo similar to a given query image or drawing. Database and query images are usually summarized by their color, shape, and texture content. Here we use the term images in a very broad sense that includes any type o graphical inormation.content-base image retrieval Image processing typically relies on simple statistical models to characterize images. Natural images tend to have certain common characteristics that mae them loo natural. The aim o statistical modeling is to capture these deining characteristics in a small number o parameters so that they can be used as prior inormation in image processing tass such as compression, denoising, eature extraction, and inverse problems. A simple, accurate and tractable model is an essential element in any successul image processing algorithm. Images have eectively been modeled using the wavelet transorm [1], [2], which oers a multiscale and time requency-localized image representation. Initially, the wavelet transorm was considered to be a good decorrelator or images, and thus wavelet coeicients were assumed to be independent and were simply modeled using marginal statistics [3]. Later it was realized that wavelet coeicients o natural images exhibit strong dependencies both across scales and between neighboring coeicients within a subband, especially around image edges. This gave rise to several successul oint statistical models in the wavelet domain [4], [5], [6], [7], [8], [9], as well as improved image compression schemes [1], [11],[12]. The maor drawbac or wavelets in twodimensions is their limited ability in capturing directional inormation. To overcome this deiciency, researchers have recently considered multiscale and directional representations that can capture the intrinsic geometrical structures such as smooth contours in natural images. Some examples include the steerable pyramid [13], brushlets [14], complex wavelets [15], and the curvelet transorm [16]. In particular, the curvelet transorm, pioneered by Cand`es and Donoho, was shown to be optimal in a certain sense or unctions in the continuous domain with curved singularities. Inspired by curvelets, Do and Vetterli [17], [18] developed the contourlet transorm based on an eicient two-dimensional multiscale and directional ilter ban that can deal eectively with images having smooth contours. Contourlets not only possess the main eatures o wavelets (namely, multiscale and timerequency localization), but also oer a high degree o Directionality and anisotropy. The main dierence between Contourlets and other multiscale directional systems is that the contourlet transorm allows or dierent and lexible number o directions at each scale, while achieving nearly critical sampling. In addition, the contourlet transorm uses iterated ilter bans, which maes it computationally eicient; speciically, it requires O(N) operations or an N-pixel image. 97

2 In this paper we explain how to decompose the image using contourlet transorm.in the section 1 we explain multiresolution by using pyramidal decomposition. In this at e4ach level how the image can be reduced.in section 2 we can explain directionality. This directionality can be alalized by using directional ilter bans. This is the main property o the contourlet transorm to which we can [preer this technique. II. CONTOURLETS Do and Vetterli developed Contourlets in [18] [2]. Their primary aim was to construct a sparse eicient decomposition or two-dimensional signals that are piecewise smooth away rom smooth contours. Such signals resemble natural images o ordinary obects and scenes, with the discontinuities as boundaries o obects. These discontinuities, reerred to as edges, are gathered along one-dimensional smooth contours. Twodimensional wavelets, with basis unctions shown in Figure 1(a), lac directionality and are only good at catching zero-dimensional or point discontinuities, resulting in largely ineicient decompositions. For example, as shown in Figure 1(c), it would tae many wavelet coeicients to accurately represent even one simple one-dimensional curve. Contourlets were developed as an improvement over wavelets in terms o this ineiciency. The resulting transorm has the multiresolution and time-requency localization properties o wavelets, but also shows a very high degree o directionality and anisotropy. Precisely, contourlet transorm involves basis unctions that are oriented at any power o two s number o directions with lexible aspect ratios, with some examples shown in Figure 1(b). With such richness in the choice o basis unctions, Contourlets can represent any onedimensional smooth edges with close to optimal eiciency. For instance, Figure 1(d) shows that compared with wavelets, Contourlets can represent a smooth contour with much ewer coeicients we proposed a double ilter ban approach or obtaining sparse expansions or typical images having smooth contours. We called this a pyramidal directional ilter ban (PDFB) [25], where the` Laplacian pyramid [26] is irst used to capture the point discontinuities, then ollowed by a directional ilter ban [27] to lin point discontinuities into linear structures. The overall result is an image expansion using basic elements lie contour segments, and thus named Contourlets Contourlet transorm (CT) can be implemented by using Pyramidal directional decomposition (PDFB). PDFB which is a combination o Laplacian-Pyramid (LP) and Directional Filter ban (DFB). Properties provided by contourlet transorm were given by 1. Multiresolution. The representation should allow images to be successively approximated, rom coarse to ine resolutions. 2) Localization. The basis elements in the representation should be localized in both the spatial and the requency domains. 3) Critical sampling. For some applications (e.g., compression), the representation should orm a basis, or a rame with small redundancy. 4) Directionality. The representation should contain basis elements oriented at a variety o directions, much more than the ew directions that are oered by separable wavelets. 5) Anisotropy. To capture smooth contours in images, the representation should contain basis elements using a variety o elongated shapes with dierent aspect ratios. The Pyramidal directional ilter ban bloc diagram was given in the igure(a).. In order to achieve a multiple resolution with multiple directional eature analysis, a Laplacian pyramid is combined with directional ilter ban In this multiresolution analysis was done by using the laplacian pyramid. Directionality can be implemented by using directional ilter ban Fig 1: Pyramidal Directional Filter Ban. The low graph o Pyramidal directional ilter ban was given below. Image (2,,2).LP Fig 2: Floe Graph O PDFB.DFB 98

3 In the above igure when the image is given to the PDFB,irst the image is decomposed by using Laplacian pyramid and then that image is given to the directional ilter ban or directional decomposition. Here in Laplacian pyramid at every level the image is halved and the sampling rate was doubled.depending upon he given image we can choose the number o level in LP stage and DFB stage. 2.1 MULTIRESOLUTION MULTIRESOLUTION data representation is a powerul idea. It captures data in a hierarchical manner where each level corresponds to a reduced-resolution approximation. One o the early examples o such a scheme is the Laplacian pyramid (LP) proposed by Burt and Adelson [1] or image Coding. The basic idea o the LP is the ollowing. First, derive a coarse approximation o the original signal by low pass iltering and down sampling. Based on this coarse version, predict the original (by up sampling and iltering) and then calculate the dierence as the redaction error. Usually, or reconstruction, the signal is obtained by simply adding bac the dierence to the prediction rom the coarse signal Laplacian decomposition: For the given image we can choose the number o levels or decomposition. At every level the laplacian pyramid gives the one down sampled low pass iltered image and one band pass image which can passed through DFB. For multiscale purpose we use laplacian pyramid. In this Laplacian pyramid, The laplacian Pyramid shown in the below. In LP, the ilters and H are low pass analysis and synthesis ilters is a sampling matrix()the original image is passed through the low pass ilter in which the low requencies are separated.here we are using the Low pass analysis ilter The low pass ilters in the Laplacian pyramid serves two purposes. First, it is used to separate out the low pass content in an image so that it would not spread across multiple directions. Second, it is used to induce a multiple resolution analysis At every level o decomposition LP generates the down sampled version o original image and the dierence between the original and the prediction. In this the scale o the laplacian pyramid doubles at every level. The center requencies o pass band reduced by hal.laplacian pyramid iteratively produces the low pass and high pass sub bands. In LP we use up sampling to reduce the aliasing eect. Pass version o the original and the dierence between the original and the prediction, results in a band pass image. A drawbac o the LP is the implicit over sampling. However, in contrast with the critically sampled wavelet scheme, the LP has the distinguishing eature that each pyramid level generates only one band pass image (even or multidimensional cases) which does not have scrambled requencies. This requency scrambling happens in the wavelet ilter ban when a high pass channel, ater down sampling, is olded bac into the low requency, and thus its spectrum is relected. In the LP, this eect is avoided by only down sampling the low pass channel. In LP decomposition o an image represent original image when it is passed through Low pass analysis ilter and then down sampled represent the low pass iltered version o original image whish is given by lo and the represents the prediction od the low pass iltered version. The prediction error ) which is given by H original image (1) Fig2.Laplacin Pyramid Decomposition (one level). Here the directional decomposition is perormed on ) because here we calculate the directionality on prediction instead o original image because o ) is largely decor related and it requires less number o bits than. ) represents the band pass image.further M decomposition can be perormed on lo by applying equation (1) iteratively to get G M + Low pass image lo Band ass iam ) 99

4 l 1, l2( i,, l3( i,... ln,where n represents the number o levels. For reconstruction o image by simply adding bac the dierences to the prediction rom the coarse image.lp with orthogonal ilters provide with tite rame bounds equals to 119[] 2.2 DIRECTIONALITY The main property o contourlet transorm is directionality. This Directionality can be analyzed using directional ilter ban(dfb). By its nature, the DFB is designed to capture the high requency components (representing directionality) o images. Thereore, low requency components are handed poorly by the DFB. DFbSeveral implementations o DFBs are available in the literature[21]. III. PRAPOSED ALOGORITHM The basic steps involved in the proposed CBIR system includes database processing and resizing, creation and normalization o eature database, and then compare the query image with the database and inally that image can be retrieved. Proposed algorithm will be given in the steps wise. Step1:By using Contourlet Transorm we can decompose each image in the Contourlet Domain.. Step 2: Compute the standard deviation (SD) o the CT decomposed image on each directional sub band. Standard deviation is given as M N 1 2 ( W ) 2 Where M N i1 1 W =Co-eicient o th CT decomposed sub band. = Mean value o th sub band. Fig 3. DFB requency partitioning The DFB can be implemented by using a -level binary tree decomposition that leads 2 directional sub bands with edge shaped requency partitioning. The based building blocs o DFB are quinicx ilter ban and shearing operators. Quinicx ilter ban with an ilters is used to to divide 2=d spectrum into two directions i.e., horizontal and vertical. Resampling metrics which is used to reassembled the pixels. due to these operations the directional inormation was preserved. From the igure it is niticed that the band pass image which is passed through the low pass and high pass ilters.then decomposed into horizontal and vertical directional inormation. In this the properties o CT are i.e directionality and anisotropy was done in Directional Filter Ban. The applications o directionality in image Enhancement, Denoising, Edge detection Segmentation The properties o directionality are exact reconstruction, reduced redundancy, high computational complexity and they are able to decompose a multidimensional signal into directional sub bands, that are non redundant. In quincx ilter ban Here we are using a simpliied []2 M N =size o the CT decomposed sub band. The resulting Sd vector is = 1, 2, 3, n (3) Step 3; Normalize the standard deviation vector to the range [,1] or every image in the database. CT Where (4), are the mean and the standard deviation o.the normalized standard deviation vector to create the eature database. Step 4: CT is used Apply query image and calculate the eature vector as given in step 2 to 3. Step 5: calculate the similarity measure Minowsi s distance which is given by the ormula 1

5 n d 1 Where p q r is a parameter, r 1 r (5) n is the number o dimensions (attributes) and p and q are, respectively, the th attributes (components) or data obects p and q. Where d is the Minowsi s distance between the eature vector o the query image and every image in the database, q i are the normalized standard deviation vectors o query image and data respectively. Step 6: base image Retrieve all relevant images to the query image based on maximum Minowsi s distance. A query image may be any one o the database images. this query is then proposed to compute the eature vector as in equation (3) and (4).The distance where q is the query image and i is an image rom database)is computed. The distances are the sorted in increasing order and the closest sets o images are then retrieved. The top n preerence o the proposed method. The retrieval eiciency is measured by counting the number o matches. Spatial and spectral eatures o the images can be explored or images retrieved in CBIR systems. Due to the local nature,it is diicult to detect edge and texture orientations using spatial methods[26].spatial methods based on multiscale directions. They are also ineicient to capture edge and smooth contours in natural images. The contourlet transorm (Ct) is a directional transorm capable o capturing contours and the details in images. The contourlet expansion is composed o basis unctions oriented at variety o directions in multiple scales with lexible aspect ratios. With this rich set o basis unctions the Contourlets can eiciently capture smooth contours (edge and texture orientations)that are the dominant eature in image in the database. IV. EXPERIMENTAL RESULTS: Retrieval perormance in terms o average retrieval rate and retrieval time o the proposed CBIR system is tested by conducting as experiment on gale ace database. Fig 4: Sample images rom gale ace data base o dierent obects. SD vector is then normalized to the range [,1] as given in equation(4). 4.1Feature Extraction Edge and texture orientations are captured by using CT decomposition with a 4-level(,2,3,4) LP decomposition. At each level the number o directional sub-bands are 3,4,8 and 16 respectively. Pva ilters [25] are used or LP decomposition and directional sub band decomposition.these parameters results in a 32- directional eature vector 9n=32.Standard deviation (SD) Vector is used as image eature, which is computed on each directional sub band o the CT decomposed image and normalized [26] to range [,1]. The normalized eature vector is used or the creation o the eature database.. Fig: Sample image rom gale ace database (image no.11) A sample image rom ace database (sample image is used in the database) and the corresponding CT decomposition with 4- level LP decomposition i.e. (, 2, 3,4) are shown in the igure 11

6 Fig :CT decomposed image (using 4-=level & pva ilters Some o the retrieved results when all the 1 images (N=1) in one o the image database are retrieved are shown in the igure. Fig 5: Retrieved images with (image no 11.) top let image query image Average retrieval Rate: The average retrieval rate or the query image is measured by counting the number o images rom the some category which are ound in the top N matches. Comparative retrieval perormance o the proposed CBIR system on the database using CT eatures is shown in table Number o Top Matches M<method CT using Manhattan Distance CT using Minowasi Distance Table1:Retrievai rate in Gale Face database (1,3,5,8,1 are the top n retrieved images) In this wor, retrieval perormance o the proposed method is computed using Manhattan distance and minowashi distance as similarity measures Manhattan distance taes the sum o the absolute dierences but in our approach we can tae the minowasi distance in CBIR system in improved retrieval perormance.the superiority o proposed method is ado observed in all cases i.e., when N is considered as 1,2 3,5,7,1(N is the no o retrieved images ). When all the images in a class are retrieves (N=1) proposed method with minowasi distance is able to produce an improved average retrieval rate o 29.25(i.e., rom 38 to 67.25%). V. CONCLUSIONS: The eature vector that represents the image in data base can eect the perormance o the CBIR system. Important characteristics o contourlet transorm viz., directionality and anisotropy are explored in this wor. The contourlet transorm decompose the image into sub bands and calculate the normalized standard deviation or that sub bands whish are used as the eatures in the eature vector representing image. Superiority o this wor is observed in terms o retrieval rate. The perormance o retrieval system can be urther improved by considering the energy o each sub band in CT decomposed image. The eature vector can be varied i the data base consists o o images with dierent rotations. REFERENCES: [1] M. Vetterli and J. Kovaˇcevi c, Wavelets and Subband Coding. Prentice- Hall, [2] S. Mallat, A Wavelet Tour o Signal Processing, 2nd ed. Academic Press, [3] A theory or multiresolution signal decomposition: the wavelet representation, IEEE Trans. Patt. Recog. and Mach. Intell., vol. 11,no. 7, pp , July [4] E. P. Simoncelli, Modeling the oint statistics o images in the wavelet domain, in Proc. SPIE 44- th Annual Meeting, 1999, pp [5] K. Mihc a, I. Kozintev, K. Ramchandran, and P. Moulin, Low complexity image denoising based on statistical modeling o wavelet coeicients, IEEE Signal Proc. Letters, pp. 3 33, Dec [6] S. G. Chang, B. Yu, and M. Vetterli, Spatially adaptive image wavelet thresholding with context modeling or image denoising, IEEE Trans.Image Proc., vol. 9, no. 9, pp , Sep. 2. [7] M. Crouse, R. D. Nowa, and R. G. Baraniu, Wavelet-based signal processing using hidden 12

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