Centroid Based on Branching Contour Matching for 3D Reconstruction using Beta-spline

Transcription

1 Journal of Image Graphcs Vol., No., September 0 Centrod Based on Branchng Contour Matchng for D econstructon usng Beta-splne Norm Abdul Had, Arsmah Iahm, Fatmah Yahya Faculty of Computer Mathematcal Scences, Unverst Teknolog MAA, Shah Alam, Malaysa Emal: {norm, arsmah, fatma}@tmsk.utm.edu.my Jamaludn Md Al School of Mathematcal Scences, Scence Unversty of Malaysa, 800 Mnden, Malaysa Emal: amaluma@cs.my Abstract econstructon of real obect often nvolves anchng contour cases. An effectve technque s requred to determne the correct correspondng sub contour between two connected contours. Ths s to ensure the accuracy of the resulted mage. Ths study has ntroduced a contour matchng method usng the smlarty of the sub contour centrod value. The technque s fast enough equvalence to the requrement of reconstructon technque whch has to be tme space effectve. The matched sub contours then are connected by ntroducng an ntermedate contour called as composte contour. The technque has been appled n the reconstructon of human head Stanford bunny from CT mages. Beta-splne was employed as the ftted surface as ths surface has capablty to gve smoothed accurate result. Index Terms anchng contour, composte contour, centrod, Beta-splne Fgure. Many-to-one anchng case n ear Fgure. One-to-many anchng case n nose Images n Fg. Fg. are from the Computerzed Tomography (CT) scanner. The mage was frst n greylevel form has been processed to extract the boundary of nterest (BOI) as shown n Fg. Fg. 4. I. INTODUCTION Branchng contours s the case where the number of sub contours n the sed contour dfferent wth the anched contours. Most of real obects especally n medcal feld contan the anchng parts, some of the obects contan more than one case of anchng. Therefore, the -dmensonal (D) mage reconstructon technque consumed must have capablty to overcome ths problem to produce an accurate result. Branchng contours always happen at the detal parts of an obect. Human head Stanford bunny for example, parts wth anchng contours are ears nose. In ear part, cross secton of the face has to be connected wth the cross secton of two ears. Same condton s appled n nose part where the lp has to be connected wth two nose holes. The examples of ear nose anchng cases from human face are shown n Fg. Fg.. Manuscrpt receved Feuary, 0; revsed Aprl, 0. Fgure. CT mage Fgure 4. Bnary form of CT mage In Fg., the mage conssts of mult-level of ntensty, I. Therefore, the mage was smplfed to only black whte pxel usng a certan threshold, T as shown n (). for I T I new () 0 for I T T s calculated teratvely untl the desred regon s produced. The BOI s then extracted from the regon. In Fg. 4, the BOI s extracted among the black pxels usng technque as n Def.. Defnton. For each black pxel pont, (, ) t s a potental boundary pont f any of ts four neghbour pxels, ( m, n), m 0,-0,, n0,,, 0 s a whte pxel. From Def., a black pxel pont s set as a potental boundary pont f at least one of ts neghbour whether rght, up, left or down s a whte pxel []. The detals of 0 Engneerng Technology Publshng do: 0.70/og

2 Journal of Image Graphcs Vol., No., September 0 the process can be referred n [-]. For human head cross secton, the example of extracted BOI s n Fg. 5. Fgure 5. Extracted BOI of Fg. 4 The extracted BOI may have more than one contour. Fg. 5 s the example of a contour wth three BOIs whch are the cross sectons of head, two nose holes. Ths contour wll be consdered as anchng case f t has to be connected wth another contour wth dfferent number of sub contours. Branchng contours case can be generally categorzed nto many-to-one (or one-to-many), many-to-many no lnk cases. The examples of these cases are shown n Fg. 6 to Fg. 8. Fgure 6. One-to-many case Fgure 7. Many-to-many case Fgure 8. No-lnk case Fg. 6 s a one-to-many case where the shape of se contour s obvously dssmlar wth both sub contours n the anch. Fg. 7 s a many-to-many case where two sub contours n the se have to be connected wth three sub contours n the anch. In ths case, the correspondence sub contour has to be correctly determned. Same condton appled n Fg. 8 case whch s the example of no-lnk case. In ths fgure, the number of sub contours n the se n greater than then the number of sub contours n the anch. Thus, a sub contour n the se has no correspondence contour. Each anchng case s solved wthn two consecutve contours called as se anched contours. In connectng these contours, the correspondence sub contour has to be properly recognzed to ensure the correctness of the reconstructed surface avod twsted surface as shown n Fg. 9 Fg. 0. anched contour se contour Fgure 9. ght connectons between se anched contours anched contour se contour Fgure 0. Wrong connectons between se anched contours Fg. 9 s the example of rght connecton between two se sub contours three anched sub contours. However, Fg. 0 shows the twsted surface produces f these contours are mperfectly connected. The effectve technque to dentfy whch sub contour belongs to whch sub contour s usng the smlarty between both of them. Ths smlarty can be determned whether vsually or computatonally wth assocated parameters. However, vsual comparson s not suggested as naked-eyes technque s not relable. Contour matchng s a process to evaluate the smlarty dssmlarty degree between two mages n order to algn or classfy the mage [4]-[5]. It s mostly used n mage recognton classfcaton such as n letter [6]-[7] face recognton, defect [8]-[9] bometrc [4] classfcatons. The smlarty between two mages s sed on the extracted nformaton of the mage whether n geometrc or non-geometrc forms. For geometrc sed classfcaton, the features are such as gradent value of contour ponts [6], the dstance between corner ponts to the mage centrod [4], [0], area, permeter. The nformaton then s structured used to measure the smlarty of the mages. The ntensty of each mage boundary pont can also be one of the mage nformaton, but t s for non-geometrc sed classfcaton. In D reconstructon, contour matchng s the contour algnment process to ensure the correct connecton between se anched contours. Ths process s not the man focus n the reconstructon, thus a fast accurate technque s requred. Moreover, the comparson s done between two contours, not from a datase as for mage recognton. Therefore, ths study has proposed a method to determne the correspondng contour from se to anched contours sed on the contour centrod. The method s dscussed n secton II. Secton III shows the composte contour generaton between se anched contours. The ftted Beta-splne surface s shown n secton IV. Ths paper ends wth concluson n secton V. II. CENTOID BASED CONTOU MATCHING Centrod s the average of all poston of boundary P x, y []. ponts, Centrod Snce the centrod s n x, y form, the value shows the poston of the sub contour n Cartesan coordnate. Thus, the centrod s sutable to be used n detectng the correspondng sub contour from the adacent slce snce the correspondng sub contours commonly have same locaton n the whole contour. The consdered CT mages n ths study are not rotated or scaled whch may change the centrod value. Centrod C for each sub contour S s calculated for both se anched contours labeled as C, C, N N P () 0 Engneerng Technology Publshng 9

3 Journal of Image Graphcs Vol., No., September 0 S S respectvely. Each calculated compared wth all calculated Certan value of centrod centrod C C C C s then error e s evaluated. e shows that sub contour s matched wth sub contour S S wth wth. Detal on error calculaton s dscussed n secton III. The examples of several contours from Stanford bunny are shown n Table I. TABLE I. CENTOID CALCULATION FO STANFOD BUNNY CONTOUS Case Contours Centrod One-to-many Many-to-many ( = ) Many-to-one Many-to-many ( ) Fgure. One-to-two case Fgure. Two-to-two case Fgure. Two-to-one case Fgure 4. Two-to-three case C C C C C C C C C C C C C C C , , , , , , , , , , , , , , ,74.04 Fg. s a one-to-many case where the shape of totally dfferent wth S S S S s S. In Fg., both have respectve correspondng sub contours n the anch. However, the correct connecton has to be determned to avod twsted surface as shown n Fg. 0 before. Fg. Fg. 4 also have smlar contours for example n Fg. S S case, S S S S S S S n Fg. 4. For S S S S S S S S S S S S n Fg., t s a no-lnk n Fg. 4 s the same case as Fg. whch has to be connected wth S S. The decson of whch anchng case the contour belongs to s decded usng the smlarty. The smlarty between the two contours can be vsually seen from the shape of the contours or determned usng the ts geometrcal features. In ths study, the smlarty s proposed to be decded by comparng the centrod values from both contours. A sub contour from se can be matched to a sub contour n the anch f the error between two centrods s below a certan threshold. The errors for matchng sub contours n Fg. to Fg. 4 are dsplayed n Table II. TABLE II. EO BETWEEN BASE AND BANCHED SUB CONTOUS CENTOID Fg. Compared Sub contours Error Matched 4 C C C C C C.69 C C.08 C C C C 0 C C C C.859 C C C C C C.845 C C C C.787 C C 7.9 From the calculated error, the sub contours are sad to be matched f the error between both contours s wthn a certan range. esult n Table II shows that the sutable error range for the case s from 0 to.787. Usng ths range, t s suggested that no matched sub contours for Fg., S n Fg. n Fg. 4. Ths s because Fg. S S S n Fg. 4 are the one-to-many case, n Fg. s the no-lnk case. Thus, the calculated error gves the dea whether the sub contour has one-toone case wth correspondng match, or else. Ths error range wll change f more anchng case s consdered. In some case as happened n C C n Fg. 4, the error s.845 whch closed to the maxmum error range.787. Thus, addtonal step s requred to support the dea that C C s unmatched. Another sutable smlarty s usng the area of the sub contour regon. The areas of S S for Fg. 4 are 70 unt 54 unt respectvely. The calculated areas of S S have bg dfferent show dssmlarty between both sub contours. 0 Engneerng Technology Publshng 40

4 Journal of Image Graphcs Vol., No., September 0 Fnally, after matched sub contours have been determned, surface s ftted nto these contours easly snce t s one-to-one case. For many-to-one no-lnk case, other methods are appled before the surface fttng procedure. In no-lnk case as occurs n S n Fg., the sub contour s matched to ts own centrod value. Ths s to ensure ths sub contour has closed surface. Ths case s also called as capped case where the sub contour has to be capped. For many-to-one or one-to-many case, the case s reduced to one-to-one case before the surface s ftted. A new ntermedate contour called as composte contour s nserted between se anched contours dscussed n secton III. III. COMPOSITE CONTOU GENEATION FO BANCHING CONTOUS Composte contour s a new contour nserted between se anched contours. The heght level of ths contour s z composte, where z composte zse zanched () Ths ntermedate contour s used to smplfy the not many-to-one or one-to-many anchng case as shown n Fg. 5. wthout composte contour wth composte contour se one many anch se composte anch one one one one Fgure 5. Smplfcaton of anchng case usng composte contour Fg. 5 shows the way that composte contour has reduced a one-to-many anchng case to two cases of one-to-one. Intally, the data ponts n the composte contour are the ponts of se anched contours. Then, ponts are modfed usng the mdpont e. Let the anched data ponts as resamplng ponts as shortest dstance from. For each P, the se, D s the to the anched at pont P, D s the shortest dstance from to other se sub contours. Then, mdpont e s calculated for D D. esamplng pont, parameter t, where s the curve pont extracted at L s the total contour length calculated as, t t dt L x' y' (6) 0 The stacked form of the se, anch composte contours of Fg. case are shown n Fg. 6. The detals of the composte contour generaton process can be read n ef. []-[]. Fgure 6. Base, anched composte contours After the composte contour s generated, surface s ftted usng one-to-one technque. The surface fttng process usng Beta-splne s dscussed n the next secton. IV. BETA-SPLINE SUFACE FITTING OF CONTOUS Bass equaton of cubc Beta-splne surface s a tensor product where, t, u V, b t b u F (7) 0 0 Wth a set of 44 control ponts matrxv, sc functons b0 b b b b t u t t t t T T t t 6 t 6 b as, ( ) ( ) 6( ) 4( ) ( ) ( ) (8) 4 4 (9) The control ponts are the resamplng ponts extracted as n (4) to (6). The developed anchng technques are appled nto human head Stanford bunny data. The examples of human head Stanford bunny n wreframe form are shown n Fg. 7 Fg. 8. t h (4) h s the requred nterval between the ponts, where Fgure 7. Wreframe of human head Fgure 8. Wreframe of Stanford bunny total contour length, L h (5) requred number of resamplng pont Beta-splne s chosen due to ts capablty to gve an accurate G contnuous although the new contour has been nserted. The reconstructed human head 0 Engneerng Technology Publshng 4

5 Journal of Image Graphcs Vol., No., September 0 Stanford bunny usng Beta-splne surface are shown n Fg. 9 Fg. 0. anch. However, the calculaton of error range n determnng the matched sub contours should be mproved to ensure the effectveness of the technque. ACKNOWLEDGMENT Ths s study s supported by Mnstry of Hgher Educaton, Unverst Teknolog MAA, Malaysa. Fgure 9. econstructed human head usng Beta-splne Fgure 0. econstructed Stanford bunny usng Beta-splne The use of composte contour also makes the reconstructon obects separated nto several parts accordng to the number of composte contours. In Stanford bunny for example, t s dvded nto four man parts: body, ck, head, ears as shown n Fg. to Fg. 4. Fgure. Body Fgure. Back Fgure. Head Fgure 4. Ears Composte contour generaton process as shown n Fg. 5 has produce the body, head, ck parts. These parts are not connected to each other. Thus, the number of resamplng ponts for each part can be dfferent assocated wth the part sze. Body part for example s larger than ck part. Therefore, the number of resamplng ponts of body should be larger than the ck. Ths method also can reduce the storage tme usage snce the number of resamplng pont can be reduced. V. CONCLUSION A fast accurate technque for contour matchng process of anchng contour case s proposed. The technque s the comparson of centrod value of sub contours n se anched contours respectvely. Besdes the comparson of centrod, other geometrc features can also be used such as area, permeter, elongaton. The error result shows the relablty of ths method n determnng the matched contours of se EFEENCES [] M. Sarfraz A. Masood, "Capturng outlnes of planar mages usng Bézer cubcs," Computers & Graphcs, vol., pp , 007. [] N. A. Had, A. Iahm, F. Yahya, J. M. Al, "Beta-splne Surface Fttng to Mult-slce Images," Journal of World Appled Scence Technology, pp. 6-, 0. [] N. A. Had, A. Iahm, F. Yahya, J. M. Al, "-Dmensonal Beta-splne wreframe of human face contours," n Proc. IEEE 8th Internatonal Colloquum on Sgnal Processng ts Applcatons, 0, pp [4] H. L, Z. Guo, S. Ma, N. Luo, "A New Touchless Palmprnt Locaton Method Based on Contour Centrod," n Proc. Internatonal Conference on H-Based Bometrcs, 0, pp. -5. [5] I. Y. Lao, P. Zheng, B. Belaton, "Skull regstraton usng rgd super-curves," n Proc. Sxth Internatonal Conference on Computer Graphcs, Imagng Vsualzaton, 009, pp [6] Y. Pourasad, H. Hassb, M. Banaeyan, "Persan characters recognton sed on spatal matchng," World Appled Scences Journal, vol., pp. 9-4, 0. [7] H. Aboasha, Z. Xu, I. El-Fegh, "An nvestgaton on effcent feature extracton approaches for Arabc letter recognton," n Proc. Queen s Damond Jublee Computng Engneerng Annual esearchers Conference, 0, pp [8] S. A. Halm, N. A. Had, A. Iahm, Y. Manurung, "The geometrcal feature of weld defect n assessng dgtal radographc mage," n Proc. IEEE Internatonal Conference on Imagng Systems Technques, 0, pp [9] L. Y. Fang, H. L, J. P. Ba, "Defect contour matchng sed on smlarty measure for D reconstructon," Advanced Materals esearch, vol. 08, pp , 0. [0] F. P. M. Olvera J. M.. S. Tavares, "Matchng contours n mages through the use of curvature, dstance to centrod glol optmzaton wth order-preservng constrant," FEUP- Artgo em evsta Centífca Internaconal, 009, pp. 9-0,. [] Q. Zhou J. K. Aggarwal. (00). Trackng classfyng movng obects from vdeo. [Onlne]. Avalable: d%0classfyng%0movng%0obects%0from%0vdeo.pdf [] J. H. yu, H. S. Km, K. H. Lee, "Contour-sed algorthms for generatng D CAD models from medcal mages," Internatonal Journal of Advanced Manufacturng Technology, vol. 4, pp. -9, 004. [] N. A. Had, A. Iahm, F. Yahya, J. M. Al, "Composte contour generaton for Beta-splne surface reconstructon," presented at the 0th Natonal Symposum on Mathematcal Scences, Malaysa, 0. Norm A. Had s a lecturer n Mathematcs department of Unverst Teknolog MAA, Malaysa. The author s a member of Malaysan Mathematcal Scences Socety, Geometrc Surface Desgn research group. The research nterest s n curve surface fttng process especally n medcal mages. 0 Engneerng Technology Publshng 4