Content Based Image Retrieval Algorithm Based On The Dual-Tree Complex Wavelet Transform: Efficiency Analysis

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1 Content Based Image etrieval Algorithm Based On The Dual-Tree Complex Wavelet Transorm: Eiciency Analysis STELLA VETOVA, IVAN IVANOV 2 Institute o Inormation and Communication Technologies, 2 Telecommunication Technologies Bulgarian Academy o Sciencies, 2 Higher School College o Telecommunications and Post Acad. G. Bonchev Str., Bl. 25A 3-Soia, 2 Acad. St. Mladenov Str., 7-Soia BULGAIA vetova.bas@gmail.com, 2 ivanivanov@hctp.acad.bg Abstract: - The ollowing paper presents a new Content-Based Image etrieval algorithm. In its realization, we applied the Dual-Tree Complex Wavelet Transorm or image eatures extraction and Hausdor distance or similarity distance computing between the eature vector o the query-image and the image eature vectors stored in the image database. To estimate its eiciency, we perormed some experiments in terms o eature extraction time, distance measure time and number o generated wavelet coeicients. The inal result shows that the algorithm produces results which satisy the modern conditions or eiciency o the algorithm including optimum eature extraction rate in shortened data size and short distance measure time necessary or the highest speed o a CBI system. Key-Words: - The Dual-Tree Complex Wavelet Transorm, CBI, eature extraction, eature vector, eiciency, eature extraction time, distance measure time, wavelet coeicients Introduction In the recent decay the amount o digital inormation has been continuously increasing. This process imposes the availability o large storage spaces to store the inormation and large databases to manage it. There are two basic approaches or image retrieval according to the type o the query: Text-Based Image etrieval (TBI) and Content- Based Image etrieval (CBI). The irst approach uses text keywords. The user is given the option to enter a keyword (or some keywords) in a text ield which is (are) used to accomplish the image searching process. This approach is most widespread but it is remarkable or its three drawbacks: irst, it is expensive since it requires the human participation to annotate the images in the database. Second, entering the annotations makes it time-consuming. And third, the retrieved result depends mostly on the human perception which takes part in annotating images. These drawbacks lead to the second and more eicient Content-Based Image etrieval approach. A CBI system implements two basic tasks: irst, image eature extraction where according to the used techniques a set o eatures (eature vectors, image signatures) is generated. This set brings image inormation and represents it in an image database occupying much less storage space. The second task is similarity measurement. It computes the distance between the image query submitted by the user and all the images in the database using their eature vectors. The most similar to the query images are displayed as a result o the searching process. The implemented techniques or image eature extraction use low-level eatures like color, shape, texture and layout. They may be classiied into two groups: spatial and spectral. The irst one relies on computing statistical values and suer rom rotation irresistance, insuiciency o number o eatures and sensibility o image noise. Such methods are [], [2]. In contrast to this, the spectral group o methods eectively measure image energy, generates rotataion resistant image eature vectors which cannot be inluenced by image noise. This methods include Gabor ilters [3], [4], wavelet [5], [6], DCT [7], curvelet [8], DWT [9], contourlet [], [], [2], [3]. This paper presents an algorithm or Content Based Image etrieval using the Dual-Tree Complex Wavelet Transorm. It is arranged as ollows. Section 2 discusses the Dual-Tree Complex Wavelet Transorm as a ilter bank (FB) structure, running process, conditions or shit-invariance and applications. Section 3 is divided into two subsections. Subsection 3. introduces the algorithm or Content Based Image etrieval using the Dual- Tree Complex Wavelet Transorm. Subsection 3.2 ISBN:

2 describes the accomplished test experiments and the experimental results. 2 The Dual-Tree Complex Wavelet Transorm In 998 Nick Kingsbury introduced an eective Complex Wavelet Transorm (CWT) method called the Dual-Tree Complex Wavelet Transorm (DT CWT). It is CWT based on complex valued scaling unction and complex-valued wavelet: Ψ c ( t) = Ψr ( t) + jψi ( t) () where Ψr (t) - real and even part, jψi (t) - imaginary and odd part, Ψ (t c ) - analytic signal; Kingsbury s idea was to develop a transorm which produces analytic signal on the analogy o Fourier transorm and which possesses the ollowing properties:. smooth non-oscillating magnitude; 2. nearly shit-invariant magnitude; 3. signiicantly reduced aliasing eect; 4. directional wavelets in higher dimensions; For the DT CWT realization Kingsbury uses two Discrete Wavelet Transorms (DWTs) perormed on two dierent binary wavelet trees A and B (Fig.) or each. Thus he designs the real and the imaginary part o DT CWT to produce the analytic signal. Figure illustrates graphically the -D DT CWT analysis ilter bank (FB) structure. p l= o(k) 2 (k) 2 o(k) 2 (k) 2 p p p2 p3 l=2 Binary Wavelet Tree A o(k) 2 (k) 2 o(k) 2 (k) 2 p p p2 p3 l=3 o(k) 2 (k) 2 o(k) 2 (k) 2 p p p2 p3 l=4 o(k) 2 (k) 2 o(k) 2 (k) 2 p p p2 p3 The input signal p is decomposed by the lowpass ilters (k) or the real part and (k) or the imaginary one and decimated by 2: generating its lowpass components p and p 2. The highpass ilters (k) and (k) and decimation by 2: produce the highpass components p and p 3 o the signal p. This process continues as ar as required or levels l=, 2, 3, 4. The inal result o the decomposition o p is: p, p, p, p or the real part and p 3, p 3, p 3, p 3 or the imaginary part. The ilters used or DT CWT are chosen to be linear-phase satisying the Perect econstruction (P) condition [4] and are joined so that the inal result o the transorm is approximately analytic: Ψ ( t ) : = Ψ ( t ) + jψ ( t ) (2) where: Ψ (t ), Ψ (t ) - wavelets generated by the two DWTs. In addition, both low-pass ilters (k) and (k) have to be designed to possess a property so as the corresponding wavelets to orm an approximate Hilbert transorm pair: Ψ ( t ) H { Ψ ( t )} (3) where: Ψ ( t ) = 2 ( k ) Φ ( t ) (4) Φ k ( t ) = 2 ( k ) Φ ( t ) (5) k For this goal one o the two lowpass ilters has to be nearly hal-sample shit to the other: { Ψ ( )} ( k ) ( k.5) Ψ ( t ) H t (6) This hal-sample delay leads to nearly shitinvariant wavelet transorm. Besides one-dimensional application, DT CWT may be used or two dimensional tasks through 2-D DT CWT relying on the M-D dual-tree wavelets properties to be approximately analytic and oriented. Thus, it is suitable or edge and surace detection in image processing. The process o iltering is perormed by two dierent groups o ilters providing two 2-D separable DWTs and six subbands: two HL, two LH, and two HH subbands. 2-D DT CWT inds application in image segmentation [5], motion estimation [6], texture analysis and synthesis [7], eature extraction [8]. Binary Wavelet Tree B Fig.. The -D DT CWT analysis ilter bank (FB) structure ISBN:

3 3 Proposed algorithm and experimental results 3. Content-Based Image etrieval Algorithm Using DT CWT In the ollowing section, we propose an algorithm or image eatures extraction using DT CWT or the goals o a CBI system.. The source image (I), shown in Fig.2 is resized to the size o MxN or M=N=256 where M - number o rows, N number o columns through the Matlab unction imresize (A,[mrows,ncols]) which perorms image resize without inormation loss. The obtained result (I') is shown in Fig The result (I') o step (Fig.3) is converted rom a GB color space image (I') into a grayscale color space image (I'') with values o the pixel in the range o [,], as shown in Fig.4 3. The image (I'') is divided into n n '' '' ( n = 8) non-overlapping subimages ( I I 64 ). 4. DT CWT is perormed on each o the '' '' subimages ( I ) obtained in step 3 at level I 64 l = 4 to decompose them and generate their lowpass and bandpass components. Each subimage has components (2 lowpass and 8 bandpass), imaginary and real parts. 5. The extracted wavelet eatures orm the image eature vectors (Table 2) which are stored in a CBI database. 6. The user is given the option to submit a query-image (Q) which is decomposed using the irst ive steps o the algorithm and thus orm a query-image eature vector. 7. To compute the similarity distance between the query-image eature vector and each o the image eature vectors in the CBI database, Hausdor Distance executes according to the ollowing equation: Fig.2. Source image (I) Fig.3. esized image (I') H ( A, B) = max( h( A, B), h( B, A)) (7) where: A = a,..., a }, B = b,..., b } are two { m inite point sets and: { n h( A, B) = max min a b (8) a A b B 8. The inal result is sorted and displayed. Fig.4. Converted grayscale image (I'') Fig. 5 depicts the lowchart o the proposed CBI algorithm in Matlab. ISBN:

4 New Image bl.2 The Image Feature Vectors DB The Image Content Analyser bl. Image Features Extraction DT CWT Image Feature Vectors Queryimage Queryimage Feature Vector The Similarity Measurement Analyzer bl. 3 Hausdor Distance Computation The Graphical User s Interace bl. 4 Query-image Sorted esult Fig.5. Flowchart o the CBI algorithm or image retrieval 3.2 Experimental results For the goal o the proposed algorithm, Wang image test database, containing GB images, was used. The images are classiied into groups: nature, architecture, vehicles, dinosaurs, elephants, lowers, horses, ood and two groups o people each o images. They are distinguished or size 256x384px and 384x256px in PEG ormat. The algorithm is tested via the sotware or mathematical and engineering computation Matlab 28b on personal computer with the ollowing coniguration: Intel () Core (TM) 2 Duo 2,4 GHz, 32-bit Operating System. The goal o the implemented experiments is to estimate the eiciency o the proposed algorithm or levels, 2, 3, 4 ( l =,2,3, 4 ) and to give proo o our choice or transormation level l = 4. With regard to this, we computed eature extraction time and distance measure time Feature extraction time To calculate eature extraction time, we used the ollowing technique, aiming to reduce the inluence o any running processes in the computer system. First, each eature extraction was accomplshed ten times and each extraction time was calculated and marked as t k, k = [ n], n =. Second, we computed the arithmetic average using these ten time measurements using the ormula: n t k ϕ k = avgi = (9) n where: i - treated image. This procedure was applied over all images o the test image database. And third, we deined the arithmetic average on the base o the obtained arithmetic average values o each o the images. The used ormula or this calculation is: avg i ϕ i= avg = () where: - inal arithmetic average value, - number o the images in the test image database ( = ). The obtained result is tabulated in Table. Table Experimental results on eature extraction time using the proposed CBI algorithm Number o Generated Wavelet Coeicients (ms) or t or i= ϕ (ms) or [t-t] or i= Average Feature Extraction Time (ms) or [t-t] or i=[] Average Feature Extraction Time (ms) or i=[-] Figure 6 and 7 graphically illustrate the eiciency o the proposed algorithm according to Table. As they both show, the eature extraction time depends on the transormation level ( l ) and the number o the highpass and lowpass ilters needed or the image wavelet decomposition at this level. Thus, incrementing the transormation level, the eature extraction time increases and or l = the needed time has the lowest values and or l = 4 it has the highest ones or both: Average Feature ϕ Extraction Time (ms) or [t -t ] or i=[], ( avg i ) and Average (ms) or i=[- ], ( avg ). ϕ ISBN:

5 Average (ms) Time (ms) or [t-t] or i=[] Time (ms) or i=[-] Fig.6. Feature extraction time on the base o the proposed CBI algorithm Average (ms) Time (ms) or [t-t] or i=[] Time (ms) or i=[-] Fig.7. Feature extraction time on the base o the proposed CBI algorithm Distance measure time To calculate distance eature time (in our case we used Hausdor distance measure), we applied the same technique as or eature extraction time and treated each image o the test image database as query-image ( q ). However, or this time computation we worked with the ollowing ormulae: or Measure Time (ms) or [t -t ] or q=[], ( avg ): p t r r= avg q = () p where: q treated query-image, t r - extracted time, r = [ p], p = and or Measure Time (ms) or q =[-], ( avg ): avg = L q= q avg L q (2) where: - inal arithmetic average value, L - number o the images in the test image database ( L = ). The obtained result or distance measure time is tabulated in Table 2. Table 2 Experimental results on distance measure time using the proposed CBI algorithm Figure 8 and 9 depict the curve o the Hausdor distance measure time on the base o the result o Table 2. According to it, at level one ( l = ) the time needed or Hausdor distance measure computation exceeds repeatedly the time needed or the same computation at l = 2,3, 4. The reason or this result is the greatest number o generated coeicients at l = (Table ) compared to the other three levels. The number o generated wavelet coeients at l = 4 is the smallest and the time needed or Hausdor distance measure computation is the shortest one respectively. Thus, incrementing the transormation level, the distance measure time between the query-image and each o the eature vectors in the database decreases. Measure Time (ms) Distance Measure Time (ms) or t or q= Hausdor Distance Measure Time Distance Measure Time (ms) or [t-t] or q= Hausdor Distance Measure Time Measure Time (ms) or [t-t] or q= Measure Time (ms) or q=[-] Measure Time (ms) or [t- t] or q=[] Measure Time (ms) or q=[-] Fig.8. Hausdor distance measure time computation on the base o the proposed CBI algorithm ISBN:

6 Measure Time (ms) Hausdor Distance Measure Time Measure Time (ms) or [t-t] or q=[] Measure Time (ms) or q=[-] Fig.9. Hausdor distance measure time computation on the base o the proposed CBI algorithm On the base o the implemented experiments, it is evident that the incrementation o the decomposition levels leads to reduction o the generated wavelet coeicients which increases the search rate by query reducing the Hausdor distance measure time between the query eature vector and the separate eature vectors in the CBI system. In spite o the higher eature extraction time towards the preceding levels, or the algorithm implementation the ourth decomposition level is chosen which produces signiicantly smaller number o generated coeicients than the other levels which takes smaller storage space than the generated coeicients at l =,2, 3, decreases the distance measure time and increases the retrieval time respectively. 4 Conclusion This paper introduces an algorithm or Content-Based Image etrieval using DT CWT. It satisies the high modern requirements or eiciency o the algorithm including optimum eature extraction rate in shortened data size and short distance measure time necessary or the highest speed o a CBI system. eerences: [] B. S. Manjunath et al., Color and Texture Descriptors, IEEE Transactions CSVT, (6):73-75, 2. [2] F. Long, H.. Zhang and D. D. Feng, Fundamentals o Content-based Image etrieval, In Multimedia Inormation etrieval and Management, D. Feng Eds, Springer 23. [3] B. S. Manjunath, W. Y. Ma, Texture Features or Browsing and etrieval o Image Data, IEEE Transactions on Pattern Analysis And Machine Intelligence, vol. 8, No.8, August 996. [4] L. Chen, G. Lu, and D. S. Zhang, Eects o Dierent Gabor Filter Parameters on Image etrieval by Texture, Proceedings o IEEE th International Conerence on Multimedia Modelling, Australia, 24, pp [5] S. Bhagavathy and K. Chhabra, A Waveletbased Image etrieval System, Technical eport-ece278a, Vision esearch Laboratory, University o Caliornia, Santa Barbara, 27. [6] N. Suematsu et al., egion-based Image etrieval using Wavelet Transorm, Proceedings o 5 th International Conerence on Vision Interace, May, 22. [7] Z. Lu, S. Li, and H. Burkhardt, A Content- Based Image etrieval Scheme in PEG Compressed Domain, International ournal o Innovative Computing, Inormation and Control, 2(4):83-839, 26. [8] I.. Sumana et al., Content Based Image etrieval Using Curvelet Transorm, IEEE th Workshop on Multimedia Signal Processing, Australia, 28, pp. -6. [9] N. Kingsbury and. Magarey, Wavelet Transorms In Image Processing, Proceedings First European Conerence on Signal Analysis and Prediction, Prague, 997, pp [] X. Chen,. Ma, Texture Image etrieval Based on Contourlet-2.3 and Generalized Gaussian Density Model, International Conerence on Computer Application and System Modeling, 2, pp. V V9-23. [] X. Chen et al., Contourlet-.3 and Generalized Gaussian Model Texture Image etrieval, International Conerence on Educational and Inormation Technology, 2, pp. V V-462. [2] X. Chen et al., Contourlet-.3 Texture Image etrieval System, Proceedings o the 2 International Conerence on Wavelet Analysis and Pattern ecognition, uly, 2, pp [3] A. Mosleh et al., Texture Image etrieval Using Contourlet Transorm, International Symposium on Signals, Circuits and Systems, 29, pp. -4. [4] I. Selesnick,. Baraniuk, N. Kingsbury, The Dual-Tree Complex Wavelet Transorm, IEEE Signal Processing Magazine, November, 25, pp [5] C. W. Sharey, N. G. Kingsbury, and I. H. ermyn, Unsupervised image segmentation via ISBN:

7 Markov trees and complex wavelets, In Proceedings o IEEE International Conerence on Image Processing, 22, pp [6]. Magarey and N. Kingsbury, Motion Estimation Using a Complex-Valued Wavelet Transorm, IEEE Trans. on Signal Processing, special issue on wavelets and ilter banks, vol. 46, No 4, April 998, pp [7] P.. Hill, D.. Bull, and C. N. Canagarajah, otationally Invariant Texture Features Using The Dual-Tree Complex Wavelet Transorm, in Proceedings o IEEE International Conerence on Image Processing, 22, pp [8] B. Liao, F. Peng, otation-invariant Texture Features Extraction Using Dual-Tree Complex Wavelet Transorm, International Conerence on Inormation, Networking and Automation, 2, pp. V-36 - V-364. ISBN: