Prediction of Sea Ice Edge in the Antarctic Using GVF Snake Model

JOURNAL GEOLOGICAL SOCIETY OF INDIA Vol.78, August 2011, pp.99-108 Prediction of Se Ice Edge in the Antrctic Using GVF Snke Model PRAVIN K. RANA +, MIHIR K. DASH*, A. ROUTRAY* nd P. C. PANDEY* + Royl Institute of Technology, Stockholm, Sweden * Indin Institute of Technology, Khrgpur, Indi Emil: mihir@corl.iikgp.ernet.in Astrct: Antrctic se ice cover plys n importnt role in shping the erth s climte, primrily y insulting the ocen from the tmosphere nd incresing the surfce ledo. The convective processes ccompnied with the se ice formtion result ottom wter formtion. The cold nd dense ottom wter moves towrds the equtor long the ocen sins nd tkes prt in the glol thermohline circultion. Se ice edge is potentil indictor of climte chnge. Additionlly, fishing nd commercil shipping ctivities s well s militry sumrine opertions in the polr ses need relile ice edge informtion. However, s the se ice edge is unstle in time, the temporl vlidity of the estimted ice edge is often shorter thn the time required to trnsfer the informtion to the opertionl user. Hence, n ccurte se ice edge prediction s well s determintion is crucil for fine-scle geophysicl modeling nd for ner-rel-time opertions. In this study, ctive contour modelling (known s Snke model) nd non-rigid motion estimtion techniques hve een used for predicting the se ice edge (SIE) in the Antrctic. For this purpose the SIE hs een detected from se ice concentrtion derived using specil sensor microwve imger (SSM/I) oservtions. The 15% se ice concentrtion pixels re eing tken s the edge pixel etween ice nd wter. The externl force, grdient vector flow (GVF), of SIE for totl the Antrctic region is prmeterised for dily s well s weekly dt set. The SIE is predicted t certin points using sttisticl technique. These predicted points hve een used to constitute SIE using rtificil intelligence technique, the grdient vector flow (GVF). The predicted edge hs een vlidted with tht of SSM/I. It is found tht ll the mjor curvtures hve een cptured y the predicted edge nd it is in good greement with tht of the SSM/I oservtion. Keywords: Se ice modelling, Se ice edge, Snke model, Antrctic. INTRODUCTION Antrctic, the southernmost icy continent, remins prdise to the reserchers for its vst ice sheet, extremely dynmic se ice environment nd ove ll its extreme wether nd climte. Antrctic is often clled pulsting continent ecuse its ice pck (i.e. se ice) grows from n re of 1.8 million km 2 y the end of ustrl summer, to out 20 million km 2 y the end of ustrl winter (Vys et l. 2003). The totl se ice re in the Southern Hemisphere is nerly 10 times greter in the ustrl spring thn in the ustrl fll. On verge the dvncement of ice is most rpid in the utumn from April to June nd continues until lte winter/erly spring. Ice retret is most rpid in the erly summer of the yer with minimum ice extent during Ferury. The chnge in the se ice re is due to (i) the polr loction of the continent which hs n lmost 4 month long winter nd 4 months of continuous summer (ii) the ocenic nd the tmospheric circultion in this region. Extremely dynmic se-ice cover plys n importnt role in the Erth s climte system, primrily y insulting the ocen from the tmosphere nd incresing the surfce ledo. Fresh snow cover on ice hs n ledo of the order 98% (Vowinckell nd Orwing, 1970) compred to 10-15% of tht of open wter (Lm, 1982). Atmospheric het exchnge over se ice is up to two orders of mgnitude less thn tht over Open Ocen. Sesonlly expnding nd contrcting se ice profoundly impedes the exchnge of het, momentum, nd gses etween ocen nd tmosphere. Both the insultion nd the ledo effects provide positive feedck nd influence the locl wether nd climte in long run. Also, the Antrctic se ice zone is hitt for mny species of iot. Regions covered y se ice lso ply n importnt role in specilized humn ctivities in the Antrctic. Antrctic hs no indigenous people, ut severl thousnd people live on Antrctic during prts of the yer, supporting scientific reserch t vrious sttions. Mitri Sttion (70 46'S, 11 45'E), the logistics hu of the Indi s Antrctic Progrm, is resupplied y ships ech yer. Thick se ice delys the re-supply nd costs more money. So, the prediction of se ice edge not only importnt form the 0016-7622/2011-78-2-99/$ 1.00 GEOL. SOC. INDIA

100 PRAVIN K. RANA AND OTHERS climtic study point, ut lso from the point of nvigtion nd the study of Mrine Antrctic iot. Although the stellite system, over the lst four decdes, hve provide us gret del of informtion on the rodscle se ice extent nd its vriility. But difficulties to retrieve n ccurte ice edge from stellite sensor during severe wether condition, need of relile ice edge informtion over the Antrctic for fine-scle geophysicl modelling nd ner-rel-time prediction of se ice edge (SIE) for fishing, for commercil shipping ctivities s well s militry sumrine opertions is very much required. The ice edge is unstle in time, hence the temporl vlidity of the estimted ice edge is often shorter thn the time required to trnsfer the informtion to the opertionl users. For exmple the United Sttes Ntionl Ice Centre provides iweekly informtion out glol se-ice condition (Hrpintner et l. 2004). This pper descries model sed on the rtificil intelligence nd sttisticl nlysis to mp nd predict the Antrctic SIE. This model utilizes the se ice concentrtion informtion over the Southern Ocen otined form the Ntionl Snow nd Ice Dt Center (NSIDC) to predict the SIE. DATA AND METHODOLOGY Our study utilises the se ice concentrtion (SIC) otined from the Ntionl Snow nd Ice Dt Center, USA. These dt sets re generted using the Specil Sensor Microwve/Imger (SSM/I) oservtions using the Bootstrp Algorithm with dily vrying tie-points (Comiso et l. 1997). Dily nd monthly gridded dt re ville on the polr stereogrphic grid with 25km x 25 km resolution pssing plne t 70 ltitude to minimize the error in reduction of re t the polr region. Dily gridded SIC hs een used in our study. 15% SIC hs een considered s the threshold vlue for defining the ice edge (Gloersen et l. 1992). The imge vlues hve een converted into grey scle intensity vlue which contins only two grey level vlues, 255 nd 0. The grey level 255 is ssigned to the lnd pixels nd the pixels hving SIC more thn 15%. The grey level 0 is ssigned to the pixels hving SIC less thn 15%. Output of this processing gives grey level imge dt with lots of noise (Fig.1). Noisy grey level se ice imges for two different periods (i) hving pek se ice extent (1 st Septemer 2006) nd (ii) hving melting of se ice (1 st Ferury 2006) is shown in Fig.1. Noises within ice covered region represent the presence of less concentrtion ice pixel. In order to remove noises s well s the holes inside the foreground imge, the sic concept of reltionship etween pixels nd the imges were studied. The oundries were defined through the connectivity of pixels. The imge filling hs een performed using flood-fill technique y specifying ckground pixel s strting point. The oundries were determined sed on the type of neighourhood pixel specified. The filtered imges for ove periods re shown in Fig.2. Cnny method is used to detect the se ice edge. Figure 3 shows typicl exmples of the Antrctic se ice edges for 1 st Septemer nd 1 st Ferury, 2006. These imges were used to prmeterize the Active Contour Model (ACM). ACM required imges with white ckground s well Fig.1. The grey scle of se ice imge over the Antrctic otined fter processing. The noises nd hole re clerly seen in the imge. () for 1 st Septemer 2006 nd () for 1 st Ferury 2006.

PREDICTION OF SEA ICE EDGE IN THE ANTARCTIC USING GVF SNAKE MODEL 101 Fig.2. Processed imges of the Antrctic with se ice fter the removl of noise nd holes () for 1 st Septemer 2006 nd () for 1 st Ferury 2006. Fig.3. The edge generted using cnny method from the imges given in Fig 2. () for 1 st Septemer 2006 nd () for 1 st Ferury 2006. Fig.4. Se ice edge fter ltering the ckground nd foreground of the imges given in Fig.3 for () Septemer 1 st, 2006 nd () for Ferury 1 st, 2006. These imges serve s the mster to prmeterize the ctive contours.

102 PRAVIN K. RANA AND OTHERS s PGM file formt. For this purpose the imge ckground s well s foreground gry level re chnged ccordingly. The resultnt imges with white ckground nd lck foreground for the ove two periods re shown in Fig.4. PARAMETERIZATION OF SEA ICE EDGE USING ACTIVE CONTOUR MODEL Se ice edge is extremely dynmic in nture. Active Contour Model (ACM) or Snke Model is the est tool to simulte se ice edge for prediction. This technique is extensively used in the edge detection prolem nd other computer vision prolem like, shpe recognition, oject trcking nd imge segmenttion. When edge informtion in the imge is insufficient nd corrupted y noise considerle difficulties rise in the ppliction of clssicl edge detection methods for simultion of edge or oundry shpe. As result, clssicl techniques either fil completely or require some kind of post processing step to remove invlid oject oundries in the segmenttion results. ACM promises to provide good solution. Mthemticlly, ctive contour is curve defined s function of rc length, s, is defined s X(s) = [x(s)y(s)], s [0,1] is which moves through the sptil domin of n imge to minimize the following energy functionl: Where α nd β re weighting prmeters tht control the snke s tension nd rigidity, respectively (Kss et l. 1987; Cohen, 1991). The first-term represents the internl energy functionl nd is defined y nd Where, nd denote the first nd second order derivtes of X(s) with respect to s. The externl energy function E ext is derived from imge dt nd tkes smller vlues t oject oundries s well s other feture of interest. Minly there re two different energy functions, (i) edge functionl (E 1 (x,y)) (ii) line functionl ext (E2 (x,y)), which ttrct the ext snke or the contour. Given grey level imge intensity of the imge, I(x, y), viewed s function of continuous position vriles (x, y), typicl externl energy functions designed to led n ctive contour towrd step edge re (1) (2) Where, e is positive weighting prmeter, is twodimensionl Gussin function with stndrd devition is the grdient opertor nd * is the 2D imge convolution opertor (for detiled description of 2 nd 3 plese refer Kss et l. 1987; Xu nd Prince, 1997). Imge with line drwing (lck nd white), eqution 2 nd 3 cn e defined s follows: where l is weighting prmeter. Positive l is used to find lck lines on white ckground, while negtive l is used to find white lines on lck ckground (for detiled description of 4 nd 5 plese refer Xu nd Prince, 1997). For oth edge nd line potentil energies, incresing cn roden its ttrction rnge. However, lrger cn lso cuse shift in the oundry loction, resulting in less ccurte result. INITIALIZING THE CONTOUR For prmeteriztion of se ice edge over Antrctic, initil snke is defined s circle with (166, 158) position in the imge s the origin. Initil snke is tken to e circle, ecuse se ice coverge over Antrctic expnd/contrct lmost rdilly. The edge mp ws otined y convolving the Lplcin with the imge pixels. This edge mp ws single chnnel 8 it imge. This is done ecuse single vlue imge intensity desired to represent the imge energy. Then the Lplcin filter operted on the imge nd the imge is converted into single chnnel grey level imge. The model ws initilised with circle y following eqution x = 158+105*cos(t); y = 166+105*sin(t); Figure 5 gives the initil circle s position on n imge of Antrctic se ice edge. Here we hve shown the ice edge for 1 st Jnury 2002 which is otined s ove. In order to increse the cpture strength of the edges, the edge mp ws lurred so s to diffuse the effect of strong edges onto nery pixels. As soon s ny contour pixel would come within few pixel of the edge, it would strt experiencing the effects of the edge nd the get pulled towrd the edge. A 5x5 Gussin filter ws used to chieve this lurring. Finlly, rmed with lurred edge mp nd the initil (3) (4) (5)

PREDICTION OF SEA ICE EDGE IN THE ANTARCTIC USING GVF SNAKE MODEL 103 GVF SNAKE METHOD Fig.5. A typicl Lplcin filtered single chnnel grey level imge of the se ice edge over the Antrctic with the Initil circulr snke. contour configurtion is invoked which is emedded in the progrm. CHOICE OF,, AND The tension prmeter of the contour is defined t 0.2. It mens tht n verge seprtion of 10 pixels etween two control points should cuse ech to expert n elstic pull of 2 pixel on the other. Now, the ending effect is sutler. A movement of few pixels cn ffect the ending energy gretly. Hence, lower vlue of, the rigidity prmeter is defined s 0. Furthermore, the imge force needs to perform like little stronger force thn the elstic force. It could e surmise s if few points in the contour egin to drift wy from n edge they should not e le to dislodge those points which hve lredy found good strong edge. The presence of ny stry noise pixel my trp one point t flse minimum nd ffect the movement of snke. To void this sitution imge force should e slightly greter thn elstic force. A difference of imge intensity y grey level 255 etween neighouring pixel; is considered s trnsition from pure lck (intensity vlue 0) to pure white (intensity vlue 255), which is the strongest edge possile. But even difference in grey level y 100 represents good visile edge. So we might sy tht n intensity grdient of 128 should exert out the sme level of force s elstic force t 10 pixels prt, which is denoted y. This suggests vlue of 1/64 for. The mjor drw ck of ACM is ssigning vlues to the constnts. After some tril nd error, the vlues = 0.05, = 0, nd = 1 were decided upon. The model strts from the initil contour (circle in this cse) provided to it s input. The grdient vector flow (GVF) snke (Xu nd Prince, 1997) egins with the clcultion of field of forces, clled the GVF forces. The field forces were clculted etween different points on the initil contour nd the finl ice edge in steps. These forces re derived from the diffusion opertions crried out in the imges considering the grey vlues nd tendency to extend very fr wy from the oject. This extends the cpture rnge so tht snkes cn find ojects tht re quite fr wy from the snke s initil position. The typicl exmple of these forces over the entire imge domin for the Antrctic se ice edge is shown in Fig.6. These diffusive forces re normlized (Xu nd Prince, 1997) to give the position of the contour t the end of ech itertion. The output of the (n-1) th itertion is considered s the initil condition for the n th itertion. Figure 7 shows the position of the contours t different itertions. It cn e inferred from the Fig.7 tht the contour intervls re not the sme t ech intervl, ecuse the normlised GVF force (mgnitude nd direction) chnges with itertions. Sine the diffusion property cretes force, the ctive contours cn e pull into concve regions (see Fig.7). The GVF forces ct on oth side of the edge nd try to converse to the oundry (see Fig. 8). The forces inside/outside the contour represent the diffusive forces coming from inside/outside to the contour oundry. Mthemticl expressions for these forces re descried ove. It is oserved tht the GVF field hs much lrger cpture rnge thn trditionl potentil forces. A second oservtion is tht the GVF vectors within the oundry concvity i.e. t the top of the Antrctic se ice edge hve downwrd component. Finlly, it cn e seen in tht the GVF field ehves in n nlogous fshion when viewed from the inside of the oject (see Fig. 8). In prticulr, the GVF vectors re pointing outwrd into Antrctic se ice edge, which represent concvities from this perspective. The performnce of the GVF ctive contour model is studied on 53 weekly (corresponding to one yer) se ice concentrtion imges with the sme initil conditions nd the forcing prmeters (the snke prmeters re chosen s: á = 0.2, â = 0.0, ë =0.3, nd ã =0.4). It is found tht in ll the cses the model fitted to the given edge very nicely. This gives confidence tht using discrete pixel informtion continuous edge cn e simulted using GVF pproch. This potentility hs een explored to predict the se ice edge in the Antrctic.

104 PRAVIN K. RANA AND OTHERS Fig.6. GVF externl forces for typicl Antrctic se ice edge imge (the ice edge shown in Fig.5). Fig.7. A view of snke deformtion during run of snke model, fter 230 itertions.

PREDICTION OF SEA ICE EDGE IN THE ANTARCTIC USING GVF SNAKE MODEL 105 Fig.8. A close-up GVF externl forces within the oundry concvity. PREDICTION OF SEA ICE EDGE To predict se ice edge over Antrctic, weekly se ice edges hve een computed from the concentrtion imges for the yer 2004. The imge is found to e of the form 332 pixel x 316 pixel coordinte system strting from (0, 0) t its left upper corner of the imge. In this coordinte system, the imge is treted s grid of discrete elements, ordered from top to ottom nd left to right. For pixel coordintes, the first component i (the row) increse downwrd, while the second component j (the column) increses to the right. Assuming the expnsion nd contrction of se ice edge is rdil, ech edge pixels re trnsferred to rdil co-ordinte system with the origin of the centre of the co-ordinte system t the pixel loction (166, 158). All the edge pixels hve een trnsformed the rdil co-ordinte system using the following reltion: where, i new-pixel nd j new-pixel re the new trnsformed imge edge pixel in pixel coordinte system of imge. The verged rdius of edge pixels t ech 1 ± 0.2 intervl is clculted for ll 53 weeks. If no ice edge is found then n undefined vlue (-9999.0) is ssigned to the corresponding ngle. In certin cses more thn one solution re found for prticulr ngle. In this cse the edge informtion is verged nd put s single solution. Using the weekly dt sets descried ove time series of ngulr distriution of rdius is generted. Then time series of rdil vrition of the edge corresponding to ech ngle is fitted to four degree polynomil nd mtrix with coefficients of the polynomil is generted. The eqution for the mtrix is given elow (9) i new-pixel = 166 i pixel (6) j new-pixel = j pixel 158 (7) In the trnsformed co-ordinte system the rdil distnce of ech edge pixel (r) nd the ngle covered (θ) with reference to the 158 th row in the nti-clock wise is clculted. The reltion used for the computtion of the ngulr coordinte is given s follows: with, (10) (11) (8) where, r θ is the rdius of the ech pixel loctions, nd = 1,2,3,4, 360, ech vlue of corresponds to n ngles,

106 PRAVIN K. RANA AND OTHERS t is the time nd A, B, C, D, E re known polynomil coefficients. Eight smple curves with 4 degree polynomil fit re shown in Fig.9. By using coefficient mtrix of polynomil eqution, the rdil distnce of the se ice edge r t few ngulr positions re predicted for the time step t=55, 56. The rdil components re converted ck to the pixel vlues using the reltion given elow: (12) These pixel vlues otined re with respect to the coordinte system with origin t (166,158). Agin the ove informtion is converted to the originl imge co-ordinte system hving origin t (0,0) loction. The trnsformtion equtions re given elow: (13) Now, we hve few predicted edge pixel position informtion in the imge domin tht cn e given s input to simulte the se ice edge. The informtion re put into GVF snke model nd the se ice edge is simulted using the prmeters descried ove. After 250 itertions, snke simultes the predicted Antrctic SIE imge. Figures 10 nd 11 show typicl GVF Snke model derived SIE imge for 1 st week nd 2 nd week of Jnury, 2005 respectively. The corresponding SSM/I Antrctic se ice edge imge is 130.00 120.00 120.00 110.00 100.00 110.00 90.00 100.00 80.00 90.00 70.00 10.00 20.00 30.00 40.00 50.00 60.00 0.00 20.00 40.00 60.00 () θ = 1 () θ = 93 120.00 130.00 110.00 120.00 100.00 110.00 90.00 100.00 80.00 90.00 70.00 80.00 0.00 20.00 40.00 60.00 0.00 20.00 40.00 60.00 (c) θ = 185 (d) θ = 241 Fig.9. Typicl exmple of 4 th order polynomil curve fitting for 53 weeks, 2004 edge informtion dt for different ngles.

PREDICTION OF SEA ICE EDGE IN THE ANTARCTIC USING GVF SNAKE MODEL 107 Fig.10. () Predicted imge of 4 th of Jnury 2005 y points otin y polynomil eqution nd edge simulted y point using GVF snke. () SSM/I imge of the Antrctic se ice edge of 4 th Jnury 2005 used for vlidtion of prediction result. Fig.11. () Predicted imge of 11 th of Jnury 2005 y points otin y polynomil eqution nd edge simulted y point using GVF snke. () SSM/I imge of the Antrctic se ice edge of 11 th Jnury 2005 used for vlidtion of prediction result. lso shown in these figures. This is to note tht the imge domin remins sme s tht of the polr stereogrphic projection imge provided y NSIDC. VALIDATION AND ERROR ANALYSIS The predicted imge vlidted y using Antrctic se ice edge of sme dy which is otin y SSM/I sensor. Though we trined the GVF for the 1 st Jnury 2006 nd used the model prmeters find out the SIE for 4 th nd 11 th Jnury 2005 form few predicted position of the edges. Becuse the model is sensitive to the initil contour provided to it nd the converging points (predicted points) provided to it. The rod fetures of the predicted edge mtch well (up to 90%) with tht oserved edge. But there is lrge devition round Antrctic peninsul. This my e due to the use of verging technique to decide the ice edge when multiple edges re present t prticulr ngle. Though, less ut similr error hs een noticed in the Ross ice shelf region. The rdil RMS error computed for oth predicted imge 4 th Jnury s well s 11 th Jnury of 2005 nd found to e of the order of 11% for oth the cses. When multiple edges re encountered long prticulr rdil direction this technique dds error to the prediction model. CONCLUSIONS From the present study it is found tht the GVF snke is roust technique to prmeterize ny deformle edge like the se ice extent. Following conclusions re drwn from the prmeteriztion of se ice edge. The GVF field hs much lrger cpture rnge thn trditionl potentil forces. GVF vectors fits smoothly to the oundry concvity nd the GVF vectors re pointing outwrd into Antrctic SIE, which represent concvities.

108 PRAVIN K. RANA AND OTHERS The GVF is insensitive to the initiliztion of the snke. The GVF field ehves in n nlogous fshion when viewed from the inside of the oject. Another oservtion is tht the GVF snke hs superior convergence properties. The finl snke configurtion closely pproximtes the true oundry, rriving t su pixel interpoltion through iliner interpoltion of the GVF force field. The vlidtion of the predicted se ice edge shows good mtch with tht of the oserved SSM/I se ice edge. The rod fetures of the predicted edge mtch well (up to 90%) with tht oserved edge. But lrge devition round Antrctic peninsul is noticed. This my e due to the use of verging technique to decide the ice edge when multiple edges re present t prticulr ngle. Though, less ut similr error hs een noticed in the Ross ice shelf region. The rdil RMS error computed for oth the predicted imges re found to e of the order of 11%. When multiple edges re encountered long prticulr rdil direction this technique dds error to the prediction model. Though we hve used time series of one yer for the prediction purpose, longer time series could e used for etter prediction. Also, etter contour trcking methods like locking mtching method, opticl flow method re under process for etter prediction of the se ice edge long longitude. Acknowledgements: The dt used in the study re downloded from NSIDC nd NCEP/NCAR. Some of the softwre used re ville from http://www.icl.ece. jhu.edu/sttic/gvf. Finncil ssistnce is provided y Ntionl Centre for Antrctic nd Ocen Reserch, Go, Indi. References CHENYANG, Xu nd PRINCE, J.L. (1997) Grdient Vector Flow: A New Externl Force for Snkes, Proc. IEEE Conf. on Comp. Vis. Ptt. Recog. (CVPR), Los Almitos: Comp. Soc. Press, pp.66-71, June 1997. COHEN, L.D. (1991) Note on ctive contour models nd lloons. CVGIP: Imge Understnding, v.53, pp.211 218. COMISO, J.C., CAVALIERI, D., PARKINSON, C. nd GLOERSEN, P. (1997) Pssive microwve lgorithms for se ice concentrtions. Remote Sensing of the Environment, v.60, pp.357-384. GLOERSON, P., CAMPBE, W.J., CAVALIER, D.J., COMISO, J.C., PARKINSON C.L. nd ZWALLY H.J. (1992) Arctic nd Antrctic Se Ice:178-1987. NASA-SP_511, 290p. KASS, M., WITKIN, A. nd TERZOPOULOS, D. (1987) Snkes: The Active contour models. Internt. Jour. Computer Vision, v.1, pp.321-331. LAMB, H.H. (1982) The climte environment of the Arctic Ocen. In: L. Ry (Ed.), The Arctic Ocen. John Wiley nd Sons, New York, pp.135-161 VOWINCKELL, E. nd ORWING, S. (1970) The climte in the north polr sin, climte of the polr regions. World Survey of Climtology, Elsevier, Amsterdm, v.14, pp.129-252. VYAS, N.K., DASH, M.K., BHANDARI, S.M., KHARE, N., MITRA, A. nd PANDEY, P.C. (2003) On the seculr trend in se ice extent over the Antrctic region sed on OCEANSAT 1 MSMR Oservtions. Internt. Jour. Remote Sensing, v.24, pp.2277-2287.