ANNUAL OF NAVIGATION 11/2006

ANNUAL OF NAVIGATION 11/2006 TOMASZ PRACZYK Naval Unversty of Gdyna A FEEDFORWARD LINEAR NEURAL NETWORK WITH HEBBA SELFORGANIZATION IN RADAR IMAGE COMPRESSION ABSTRACT The artcle presents the applcaton of the feedforward neural network wth Hebba selforganzaton to radar mages compresson. Influence of number of neurons and sze of segments of a radar mage to ts compressed form s checked. INTRODUCTION The applcaton of radar mages n navgaton s not a new dea. A common method of usng radar mage to fx poston s fndng on a radar mage a pont of known locaton and determnaton the shp poston wth relaton to ths pont usng to ths purpose dstance and bearng. But stuatons happen when a navgator s not able, because of dfferent reasons, to fnd any characterstc pont on a radar mage, whch he could assgn a poston and then on the bass of t determne hs own poston. In such cases we can apply comparatve navgaton methods or algorthms from the artfcal ntellgence doman lke for example neural networks (multlayered perceptron, RBFNN, HRBFNN, GRNN, neurofuzzy network), whch usng knowledge located nto sample radar mages are able, on the bass of a regstered radar mage, fx an approxmated shp s poston. For the sake of huge amount of nformaton, ncluded n a radar mage and dffcultes wth ts processng durng satsfactory perod of tme t s convenent to transform avalable radar mages to a more compact form, preservng the most mportant features of the orgnal. The artcle presents one of the methods that could serve to ths purpose a feedforward lnear neural network wth Hebba selforganzaton that mplements PCA transformaton. There are a lot of mage compresson methods but there s a problem wth estmaton of ther usefulness n radar mages processng and poston approxmaton methods. Presented n [4] and [5] results are based on estmatng the compressng Kohonen neural network usng poston accuracy acheved by the postonng system 89

TOMASZ PRACZYK based on radar mages compressed by ths neural network. Thus, we have the estmaton of the gven soluton wthout knowledge about contrbuton of each part of the system to the fnal result. Just, for that reason, t was necessary to fnd a unversal crteron of estmaton of the radar mage compresson algorthms, wth reference to the poston approxmaton systems. The most mportant queston was to determne what knd of compresson wll help and what can be consdered as an obstacle n the process of fxng the poston by approxmaton system. It was proved that n case when the learnng process of the postonng system wll use orgnal compressed radar mages we wll have a large set of examples of orgnal radar mages taken from the coast area under consderaton then the goal at the compresson phase s to save all relatons between orgnal radar mages n the compressed mages doman. Ths means the stuaton, when smlar radar mages wll possess representatves n the compressed mages doman also smlar to each other. Solutons, whch would dsperse compressed radar mages equvalents from postons close to them, would ncrease the speed of the changeablty of the approxmatng poston functon n the areas where data are smlar to each other but smultaneously are characterzed by the consderably dfferent value of the poston functon. The poston functon can be presented by the followng [3]: f(d) = p (1) where: d s an compressed radar mage and p s a lattude and longtude vector. To ensure approprate accuracy of postonng system these areas would have to be represented by greater number of learnng data extendng smultaneously calculaton tme n the learnng or concluson stage. The evaluaton functon of radar mages s as follows: 1 E = c n * 2 [ ( aj aj ) aj ] < j ( n 1) n c = (3) 2 where: n number of test radar mages wth correspondng features vectors;, j ndexes of consecutve radar mages and ther compressed equvalents; a j normalzed Eucldean dstance between two radar mages; a* j normalzed Eucldean dstance between two compressed mages. (2) 90 ANNUAL OF NAVIGATION

A FEEDFORWARD LINEAR NEURAL NETWORK WITH HEBBA SELFORGANIZATION... RADAR IMAGE COMPRESSION One of the most popular mage compresson methods s PCA (Prncpal Component Analyss). It s the statstcal method determnng lnear transformaton y = Wx, that convert a descrpton of a statonary stochastc process n the form of the vector x R N nto the vector y R K through the matrx W R K N, where K<<N, n the way that the output doman wth reduced dmenson preserves all the most mportant nformaton concernng the process. Durng conducted tests the network mplemented Sanger rule that enables to determne many of egenvalues was used. The network s organzed n the form of many ndependent neurons generatng followng output sgnals [2]: y N () l = W () l x () l j= 0 j j (4) The process of synapses values W determnaton could be presented as follows: W ( ) 2 ( l 1) = W () l + y () l x' () l y () l W () l + η (5) 1 () l = x() l W () l y () l x ' h h (6) = h 1 Durng the researches the soluton wth decreasng value of η was assumed η () l ( 0) η = (7) γ l γ rate was altered n the followng range (0,5, 1). The ntal value of η was fxed accordng to the followng rule: η(0) = 0.5[X T X]. EXPERIMENTAL RESULTS The researches were conducted n order to examne nfluence of the sze of radar mages segments to the compressed form of these mages. Every mage used durng tests, the sze of 100x100 pxels, was subjected to the process of segmentaton (segments of the same sze) and subsequently for a chosen sze of the segment, the number of egenvectors was determned. Amount of egenvectors was fxed n 11/2006 91

TOMASZ PRACZYK the way that regardless of the segment sze the sze of the compressed mage should be the same 200 unts of nformaton. The followng sze of segments and numbers of egenvectors combnatons were checked (5x10 pxels, 1 egenvector per segment), (10x10, 2), (10x20, 4), (20x25, 10), (20x50, 20), (50x100, 100), (100x100, 200). Durng the experments, 31 orgnal black and whte radar mages comng from the Gdansk Bay area were used (a dstance between consecutve regstratons of radar mages s about 600 m) and 93 dervatves of these mages. Each orgnal mage had addtonally 3 converted from t equvalents whch sums to 4 mage seres each consstng of 31 mages from dfferent postons (prmary seres no. 1 wth the orgnals and seres no. 2, 3 and 4 wth the copes). Images wth the same ndexes n each of the seres corresponded to the same shp poston (poston regstered usng GPS). Addtonal radar mages were constructed by the rotaton of orgnal mages at an angle from the range of < 3, +3 > and then after the rotaton, deformatons to orgnal mages were ntroduced. The rotaton was used n order to take a gyro compass error nto consderaton. A gyro compass s envsaged to use n the postonng system to determne a drecton to arrange radar mages accordng to the N S drecton. The magntude of ntroduced deformatons was dfferent for each of consecutve mages seres. The smallest dfferences occurred between seres no. 1 and no. 2, next between seres no. 1 and no. 3 and the bggest dsparty was between mages seres no.1 and no. 4. 1) Orgnal mage from seres 1 2) Image from seres 2 3) Image from seres 3 4) Image from seres 4 Fg. 1. Hypothetcal radar mages used durng researches 92 ANNUAL OF NAVIGATION

A FEEDFORWARD LINEAR NEURAL NETWORK WITH HEBBA SELFORGANIZATION... 0.3 0.25 E 0.2 E_c1 0.15 E_c2 0.1 0.05 0 0 50 100 150 200 Fg. 2. The evaluaton of radar mages compresson (E_c1 compresson wth the applcaton of the mages from seres no. 1, E_c2 compresson wth the applcaton of the mages from seres no. 2). k s the number of egenvalues k CONCLUSION The coastal postonng system workng on the bass of radar mages usually requres preprocessng of these mages to the more complex form that should however preserve the most mportant features of the orgnal. There are a lot of methods that could serve to ths purpose and one of them s PCA and ts adaptve mplementaton lnear feedforward neural network wth Hebba selforgansaton. Ths method was checked n the context of ts applcaton to features extracton from radar mages presentng nput data to the coastal postonng system. The evaluaton crteron was the error functon (1) that determnes the degree of preservng relatons occurrng n the radar mages doman after the compresson. The most nterestng from the constructed postonng system pont of vew s approprate determnng the sze of a sngle segment of a radar mage as well as the number of egenvectors per segment. Matchng these parameters s crucal for the compresson system performance. The fg. 1 shows that the applcaton of the smallest segments and only frst egenvector per segment s the soluton that the most fathfully preserves all smlartes occurrng between radar mages. Gradual ncrease of the sze of each segment and the number of egenvectors correspondng to a sngle segment causes that results accomplshed by the compresson subsystem are worse and worse. 11/2006 93

TOMASZ PRACZYK REFERENCES [1] Kucharew G., Processng and dgtal mages analyss, Techncal Unversty Szczecn, Szczecn 1999 (n Polsh). [2] Osowsk S., Neural networks n algorthmc depcton, WNT, Warszawa 1996 (n Polsh). [3] Praczyk T., Radar mages compresson for the need of a postonng coastal system and an assessment of ths process, Annual of Navgaton, 2004, no. 8. [4] Praczyk T., Kohonen neural network n radar mages compresson, Scentfc Bulletn, 2003, no. 1, Naval Unversty of Gdyna (n Polsh). [5] Praczyk T., GRNN n radar mages compresson, Scentfc Bulletn, 2003, no. 3, Naval Unversty of Gdyna (n Polsh). [6] Stateczny A., Praczyk T., Artfcal neural networks n radar mage compresson, Iternatonal Radar Symposum IRS 2003, Drezno. [7] Stateczny A., Praczyk T., Artfcal neural networks n shps recognton, Gdańsk Scentfc Socety, 2002 (n Polsh). [8] Tadeusewcz R., Flesńsk M., Image recognton, PWN, Warszawa 1991 (n Polsh). Receved September 2005 Revewed October 2006 94 ANNUAL OF NAVIGATION