Spectral Analysis of MCDF Operations in Image Processing

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1 Spectrl Anlysis of MCDF Opertions in Imge Processing ZHIQIANG MA 1,2 WANWU GUO 3 1 School of Computer Science, Northest Norml University Chngchun, Jilin, Chin 2 Deprtment of Computer Science, JilinUniversity Chngchun, Jilin, Chin 3 School of Computer nd Informtion Science, Edith Cown University 2 Brdford Street, Mount Lwley, Western Austrli 6050, Austrli Astrct Modified conjugte directionl filtering (MCDF) is new method proposed for digitl dt nd imge processing. This method is le to not only integrte directionl-filtered results in conjugte directions into one imge tht shows the mximum liner fetures in these conjugte directions, ut lso to further mnipulte the outcomes using numer of predefined MCDF opertions for different purposes. Although numer of cses hve een used to test the usefulness of severl proposed MCDF opertions, nd the results re visully etter thn some conventionl methods, however, no spectrl nlysis on its effectiveness over conventionl methods hs een conducted. In this pper, we pply MCDF(dd3) opertion to the processing of chest X-ry imge, long with trditionl directionl filtering. For ech of these processed imges, spectrl nlysis using 2D FFT is then mde in order to verify tht the MCDF(dd3) opertion indeed performs etter thn conventionl directionl filtering in imge processing in terms of informtion integrtion nd retention of low-frequency components. Key-Words: - Modified conjugte directionl filtering (MCDF), Digitl dt nd imge processing, Spectrl nlysis, MCDF opertion 1 Introduction Directionl filtering is used to enhnce liner fetures in specific direction [1][2][3]. In some cses, identifying conjugte liner informtion on n imge is prticulrly concerned. Directionl filtering cn e mde in two specific conjugte directions to enhnce these conjugte fetures. Normlly the filtered results from the two conjugte directions re shown on two seprte imges. This is inconvenient for reveling the reltionships etween liner fetures in these two conjugte directions. The liner enhncement using directionl filtering is chieved y constrining or removing the texturl fetures or low-frequency components from the originl imge to outline the structurl fetures or high-frequency components contined in the originl imge. Thus, directionlly filtered imge often lcks contrst depth ecuse most ckground informtion is removed. These two weknesses of using the conventionl directionl filtering re overcome y MDCF method [4], which firstly comines two (or more) directionl-filtered results in conjugte directions into one imge tht exhiits the mximum liner fetures in these two conjugte directions, nd secondly retins the ckground informtion y superimposing the directionlly filtered dt onto the originl dt. MCDF lso enles further mnipultion during the integrtion y using numer of predefined MCDF opertions for different purposes [5]. Although numer of tests hve shown the usefulness of severl proposed MCDF opertions, nd the results re visully etter thn some conventionl methods [4][5], however, no quntified nlyticl comprisons on its effectiveness over conventionl methods in liner enhncement hve een done. In this pper, we process chest X-ry imge using oth MCDF(dd3) opertion nd conventionl directionl filtering to mke comprisons etween the two methods. Ech of the processed imges is then nlysed using 2D FFT spectrl nlysis in order to verify the improvements rought y MCDF(dd3) opertion over the conventionl directionl filtering. To mke the nlyticl results cceptle s widely s possile, the FFT nlysis

MCDF = F 0 [W 0 *f 0 ] + F 2 [W 1 *F 1 (f 1 ), W 2 *F 1 (f 2 )], (1) where W 0, W 1 nd W 2 re selective constnts; F 0, F 1 nd F 2 re pre-defined functions.

2 is crried out using FFT functions provided y Mtl [6][7]. 2 Concepts of MCDF Opertions Assuming f 0 to e the originl dt file, f 1 nd f 2 to e the directionl-filtered dt files in the two conjugte directions, the generl opertion of the MCDF cn e expressed s MCDF = F 0 [W 0 *f 0 ] + F 2 [W 1 *F 1 (f 1 ), W 2 *F 1 (f 2 )], (1) where W 0, W 1 nd W 2 re selective constnts; F 0, F 1 nd F 2 re pre-defined functions. Correspondingly, some MCDF opertions re defined s [4]: MCDF(dd1) = W 0 *f 0 + W 1 *f 1 + W 2 *f 2 ; (2) MCDF(dd2) = W 0 *f 0 + s(w 1 *f 1 + W 2 *f 2 ); (3) MCDF(dd3) = W 0 *f 0 + W 1 *s(f 1 ) + W 2 *s(f 2 ); (4) MCDF(mx1) = F 0 (W 0 *f 0 ) + mx(w 1 *f 1, W 2 *f 2 ); (5) MCDF(mx2) = F 0 (W 0 *f 0 ) + mx[w 1 *s(f 1 ), W 2 *s(f 2 )]; (6) MCDF(origin) = origin[mcdf(mx2)]; (7) MCDF(mpl) = F 0 (W 0 *f 0 ) + sqrt(w 1 *f 1 * f 1 + W 2 *f 2 * f 2 ); (8) MCDF(norm1) = norm1[mcdf(*)]; (9) MCDF(norm2) = norm2[mcdf(*)]. (10) Oviously, MCDF(dd3) is result of choosing F 0 = 1, F 1 = s, F 2 = 1 nd using ddition opertion from formul (1). 3 Spectrl Anlysis of Chest X-ry Imge Figure 1 is the originl chest X-ry imge [8]. There re fetures rrnged in two pirs of conjugte directions: the north-south direction nd the est-west direction, nd the northest-southwest direction nd northwest-southest directions. This distriution is reflected in the 2D spectrum of the originl imge (Fig. 1). It should e noticed tht xes in frequency domin re opposite to those in sptil domin, i.e., verticl nd horizontl xes in 2D spectrum imge correspond to horizontl nd verticl directions in the originl imge. Highfrequency components (in white) re clustered in the centre nd lso distriuted in the est-west (verticl), north-south (horizontl), northestsouthwest (NW-SE), nd northwest-southest (NE- SW) directions. Figure 1 Originl chest X-ry imge (), nd its 2D spectrum (). To enhnce the north-south trending fetures in this imge, conventionl Soel horizontl opertor is pplied to this imge nd the result is shown in Figure 2. Result of using Soel verticl opertor is illustrted in Figure 2c. In oth imges, directionl filtering in the NS nd EW directions hs enhnced the liner fetures long their conjugted directions, ut imges look very drk ecuse the lowfrequency components in the originl imge hve een removed or depressed. The 2D spectrum of Figure 2 shows tht Soel horizontl opertor hs indeed enhnced the north-south components in the

cost of depressing the est-west components (Fig. 2). In contrst, Soel verticl opertor removes the north-south components to oost the est-west fetures (Fig. 2d).

Its corresponding 2D spectrum is shown in Figure 3. Result of using Soel northwestern opertor nd its spectrum re illustrted in Figures 3c & 3d.

In ddition to the wekness reveled in Figures 2 & 3 with the conventionl directionl filtering, the other concern with this trditionl method is tht the results from the four

Figure 4 shows the imge fter pplying MCDF(dd3) with W 0 = 1 nd W NS = W EW = W NE = W NW = 1 to the originl imge.

3 cost of depressing the est-west components (Fig. 2). In contrst, Soel verticl opertor removes the north-south components to oost the est-west fetures (Fig. 2d). A conventionl Soel northestern opertor is pplied to the originl imge to enhnce the northwest-southest trending fetures in the imge, nd the result is shown in Figure 3. Its corresponding 2D spectrum is shown in Figure 3. Result of using Soel northwestern opertor nd its spectrum re illustrted in Figures 3c & 3d. Similr conclusions s Figure 2 cn e drwn from these results. In ddition to the wekness reveled in Figures 2 & 3 with the conventionl directionl filtering, the other concern with this trditionl method is tht the results from the four directions hve to e displyed in four individul imges. c d Figure 2 Soel horizontl imge () nd its spectrum (), nd Soel verticl imge (c) nd its spectrum (d). Figure 4 shows the imge fter pplying MCDF(dd3) with W 0 = 1 nd W NS = W EW = W NE = W NW = 1 to the originl imge. This MCDF(dd3) opertion enhnces fetures in two pirs of conjugte directions, i.e., the EW nd NS directions, nd NW nd NE directions.. Unlike Soel imges, MCDF(dds) imge not only contins ll fetures enhnced in these four directions, ut lso keeps the ckground informtion. The 2D spectrum of this imge confirms oth the dt integrtion y the existence of the components long these four directions nd enhncement of high-frequency components y the expnsion of the white re in the spectrum.

4 c d Figure 3 Soel northest imge () nd its spectrum (), nd Soel northwest imge (c) nd its spectrum (d). Figure 4 MCDF(dd3) imge () nd its spectrum ().

5 4 Conclusion Our FFT spectrl nlysis on oth conventionl directionl filtering nd MCDF opertion pplied to the chest X-ry imge proves tht the MCDF(dd3) opertion rings enhnced informtion integrtion nd retins ckground informtion wheres the higher-frequency components re enhnced, which re the weknesses of using the conventionl methods in imge processing. Although the result of using MCDF(dd3) is presented here only, tests on other MCDF opertions lso revel the similr results. Therefore, the MCDF method is effective nd worth for further development. References [1] B. Jhne, Digitl Imge Processing: Concepts, Algorithms nd Scientific Applictions, Springer-Verlg, Berlin, [2] J.G. Prokis, nd D.G. Mnolkis, Digitl Signl Processing: Principles, Algorithms nd Applictions, Prentice-Hll, New York, [3] J.A. Richrds, Remote Sensing Digitl Imge Anlysis, Springer-Verlg, Berlin, [4] W. Guo, nd A. Wtson, Modifiction of Conjugte Directionl Filtering: from CDF to MCDF, Proceedings of IASTED Conference on Signl Processing, Pttern Recognition, nd Applictions, Crete, Greece, pp , [5] A. Wtson, nd W. Guo, Appliction of Modified Conjugted Directionl Filtering in Imge Processing, Proceedings of IASTED Conference on Signl Processing, Pttern Recognition, nd Applictions, Crete, Greece, pp , [6] D. Hnselmn, nd B.R. Littlefield, Mstering MATLAB 6, Prentice Hll, [7] C.L. Phillips, J.M. Prr, nd E.A. Riskin, Signls, Systems, nd Trnsforms, Prentice Hll, [8] R.C. Gonzlez, nd R.E. Woods, Digitl Imge Processing, Prentice Hll, 2002.

Before We Begin. Introduction to Spatial Domain Filtering. Introduction to Digital Image Processing. Overview (1): Administrative Details (1):

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