analysisof natural imagery [1], [2]. The analysis of textural properties

Transcription

1 272 of integrting multiple texturl fetures into single oundry determintion. The process is designed to simulte ctul perception of texturl discontinuities. Success of the system is demonstrted on pictures with prominent perceived oundries not detectle y methods sed only on differences in verge rightness. Index Terms-Pttern recognition, picture processing, scene segmenttion, texturl edge detection, texture. lest significnt crry- in Fig it EAC dder whose ehvior is determinte. must e greter thn the crry-propgtion dely for single dder cell Ȧn lterntive scheme requiring less control logic to drive the crry lines to the ll 1 stte is illustrted in Figs. 3 nd 4. The group crrypropgte signl P found in mny medium- nd lrge-scle integrtion (MSI nd LSI) dders (Signetics for exmple) is 1 when the ddend inputs to ech it position in the group re propgting inputs. When the group consists of ll it positions, the group crry-propgte signl is 1 only when numer nd its one's complement re dded. In this cse, the output of the OR gte in Fig. 3 is forced to 1 nd the externl crry lines re driven to the ll 1 stte. ACKNOWLEDGMENT The uthor thnks Dr. A. Verdillon for pointing out tht the indeterminism of n EAC dder is netly descried y stte model, where the stle sttes correspond to the ll 0 nd ll 1 crry sttes mentioned in the text. REFERENCES [1] T. C. Brtee, Digitl Computer Fundmentls. New York: McGrw-Hill, [2] H. S. Stone, Ed., Introduction to Computer Architecture. Plo Alto, CA: Science Reserch Assocites, [3] A. Avizienis, "Arithmetic error codes: Cost nd effectiveness studies for ppliction in digitl system design," IEEE Trns. Comput., vol. C-20, Nov [4] J. F. Wkerly, "Low-cost error detection techniques for smll computers," Digitl Systems L., Stnford University, Stnford, CA., Tech. Rep. 51, Dec [5] J. E. Thornton, Design of Computer-The Control Dt Glenview, IL: Scott, Foresmn, nd Co., [6] M. Grhm, Dep. of Elec. Eng. nd Comput. Sci., Univ. of Cliforni, Berkeley, CA, personl communiction. Texturl Boundry Anlysis WILLIAM B. THOMPSON Astrct-A procedure is demonstrted for locting texturl oundries in the digitl imge representtion of nturl scene. The technique involves development of n edge opertor cple Mnuscript received August 1, 1975; revised April 16, This reserch ws sponsored y the Advnced Reserch Projects Agency of the Deprtment of Defense monitored y the Air Force Estern Test Rnge under Contrct F C The uthor ws with the Imge Processing Institute, University of Southern Cliforni, Los Angeles, CA He is currently with the Deprtment of Computer Science, University of Minnesot, Minnepolis, MN Texture is I. INTRODUCTION eing incresingly recognized s n importnt cue for the nlysisof nturl imgery [1], [2]. The nlysis of texturl properties is prticulrly vlule for scene segmenttion systems. In fct, redily perceived texturl oundries my e pprent in scene where no ovious discontinuities in verge rightness exist. A numer of uthors hve developed successful procedures for using imge texture in the scene segmenttion process. Bjcsy incorportes Fourier sed mesures into region merger system [2]. Rosenfeld nd Thurston descrie n edge oriented pproch cple of incorporting In the edge sed system, locl opertor sensitive texturl properties [3]. to some property such s orienttion or corseness is pplied t multiple points in scene. Sptil discontinuities in the output of given opertor re ssumed to correspond to texturl oundries. This pproch hs designed to simulte ctul humn perception demonstrted on pictures with een employed in numer of susequent ppers which investigte different locl opertors nd different criteri for mking oundry determintions [4]-[6]. No cler mechnism hs yet een suggested, however, for integrting the results from multiple opertors. Thus, the pproch must e limited to specific clsses of imgery. This correspondence descries technique for incorporting multiple texturl cues into oundry nlysis system. Furthermore, the procedure which is developed is of texturl discontinuities. The system is prominent perceived oundries which could not e found y conventionl techniques sed on differences in verge rightness. II. SIMILARITY MEASURES A centrl feture of ny scene segmenttion system using texturl properties must e meningful mesure of texturl similrity. Texturl edges my e defined s contiguous imge regions of perceptully differing texture. Region oriented systems must merge or split regions sed on mesures of visul similrity. Unfortuntely, few of the existing systems for scene segmenttion mke use of texturl similrity mesure with ny psychophysicl foundtion. A previous pper descried the construction of texturl distnce function [7]. This function cn numericlly quntify the perceived degree of dissimilrity etween two imge regions. A prominent feture of the distnce function is tht it hs een developed to ccurtely simulte humn perception of texturl differences. This is importnt in system designed to descrie scene in mnner comprle to wht humn oserver would "see" in tht scene. Texturl similrity is usully estimted y compring specific imge sttistics in the two regions of interest. For exmple, one of the mny numericl chrcteriztions of texture [2], [8] could e evluted in oth regions. An solute vlue difference of the two mesures might e used s n indiction of similrity (the smller the vlue, the greter the similrity). Experience hs shown, however, tht none of the commonly used sttistics, tken lone, is dequtely correlted with perceptul response. The distnce function model is le to integrte lrge numer of simple, sttisticl mesures into vlue which more closely corresponds with ctul perception. Specificlly, it ws shown tht in certin pplictions, prticulr liner comintion of simple difference mesures ws quite successful in simulting the perception of texturl differences. As n exmple, let i(n) e the ith texturl property of region n. Then, we cn define the difference etween regions I nd m sed on property i s di(i,m) = Ii (I )-i (m) I. Ech di represents n elementry difference function. A single estimte of region dissimilrity my e found y exmining collection of elementry mesures. In prticulr, it is usully possile for n pproprite set of mesures to find set of coefficients {ci I such tht the vlue

2 273 CORRESPONDENCE Fig. 1. Templte for texturl edge opertor. D(1,m) = cidi(l,m) + + c,d,(i,m) ccurtely reflects the perceived difference etween the textures in region I nd the textures in region m. With such function on pirs of imge regions, it is now possile to quntittively specify "significnt difference" in perceived textures. It is importnt to recognize the-utility of this pproch. The distnce function model is pplicle to most of the existing systems incorporting texture s cue to segmenttion. More generlly, systems dependent on differences in verge rightness my e expnded to include texturl considertions with little chnge in the sic computtionl frmework. Texture my then e used, long with rightness, color, nd ny desired semntic processing, in determining oject oundries. The utility of texturl oundry detection will e demonstrted in n edge oriented system. III. TEXTURAL EDGE OPERATOR Mny uthors hve developed edge finding systems which serch for mjor discontinuities in the rightness function of n imge [9]. This is normlly done y computing n estimte of the derivtive or grdient of the imge nd then finding peks in the derivtive function. Mny opertors hve een suggested for this purpose. A common nd often successful function is clled the modified Roerts cross opertor [10], [9] nd is defined s R(i, j) = Ip(i, j) - p(i+1, j+1)i + Ip(i+', j) - p(i, j+1). Thus, the Roerts "grdient" is found y summing rightness differences in two orthogonl directions. Mny more sophisticted opertors re possile [11]. In prticulr, n opertor which returns edge orienttion my e quite useful. A procedure ws developed to serch for edges defined y texturl properties in mnner similr to the Roerts opertor. At specified intervls in the scene to e processed, four imge regions rrnged in squre pttern were considered (see Fig. 1). The sum of the estimted perceived texturl differences etween regions nd d nd etween regions nd c ws found. As with conventionl grdient opertions, it ws postulted tht lrger vlues of this sum corresponded to texturl edges running pproximtely through the intersection of the four regions. In ddition, n edge direction ws clculted. Let D(i,j) e the computed dissimilrity etween two regions i nd j (D(i,j) > 0 for ny two imge regions). Then we cn define texturl oundry opertor t the point in the scene shown in Fig. 1 s T = D(,d) + D(,c). To determine the orienttion of the edge, oserve tht ng = 4rctn(D(,d)/D(,c)), where ng = 0 _ n edge with negtive slope t 450 to the x xis. To see why two ngles re possile, notice tht D(,d) = D(,c) my correspond to either verticl or horizontl edge. This is direct consequence of the multiple degrees of freedom possile nd the lck of direction implicit in the dissimilrity mesure. The miguity is stright forwrdly resolved y considering D(,c), D(,d), D(,), nd D(c,d). In the current system, n edge mp is first produced y pplying the texturl oundry opertor t selected points in n imge. A second edge mp is produced y smering ech point in the first mp long the direction of edge orienttion. This is done to emphsize colliner edges. Finlly, inry edge points re isolted y locting "yidge points" in the edge mp. A ridge point is defined s n imge point sufficiently greter thn its neighors long some direction.-much of the code to process the edge mps ws dpted with little modifiction from system originlly designed to operte only on intensity i'nformtion [12]. Fig. 2. Texturl mosic 1. IV. RESULTS While most nlysis systems designed to operte on nturl imgery will use texture s only one of set of multiple cues to determine imge orgniztion, some wy is needed to evlute the utility of the texturl oundry opertor on its own. As result, this opertor ws pplied to pictures in which the edges could e descried s "purely texturl." These test imges were creted s mosics of texturl ptterns tken from pic- tures of nturl scenes. Ech component of the mosic ws individully normlized such tht ll components hd pproximtely the sme distriution of intensity levels. Thus, it ws impossile to distinguish ptterns sed on verge rightness or contrst criteri. The normliztion technique used ws histogrm mpping procedure with clipped Gussin trget distriution. Figs. 2 nd 3 show representtive mosic pttern. Note tht to humn oserver, there re severl quite prominent edges. Thus, it is cler tht humn perception cn identify oundries on criteri other thn differences in verge rightness. Fig. 4 is nother mosic pttern. Fig. 5 indictes the different texturl regions present in Fig. 4. In Fig. 4, very prominent oundry exists etween ptterns nd. The oundry etween nd d is reltively noticele while the edge etween nd d is hrdly detectle. Region c my e viewed t one level s uniform texturl region. On nother level, however, the region my e thought of s eing composed of mny smller regions corresponding to the predominntly light nd predominntly drk res in the pttern. The texturl edge opertor ws pplied to these nd severl other mosic ptterns using severl different sizes for the sic locks in the opertor (i.e., the locks in Fig. 1). The originl mosics were 256 y 256 picture elements in size. Fig. 6 is n edge mp for Fig. 4 using sic lock size of 16 y 16 picture elements. An effective jo hs een done of identifying the visully prominent oundries in the mosic.

3 Fig. 3. Edge mp for Fig. 2 using 8 y 8 regions. Fig. 4. Texturl mosic 2.. c d Fig. 5. Identifiction of regions in mosic 2. Testing dt indicted tht humns cn differentite etween the texturl ptterns in Figs. 2 nd 4 over regions s smll s 6 to 8 pixels on side [13]. Fig. 7 is n edge mp for Fig. 4 using n 8 y 8 sic lock size nd the perceived oundries hve een well locted. Fig. 7 is n edge mp for the mosic in Fig. 4 using the sme 8 y 8 lock size. Agin, the oundries re well identified. The opertor completely degenertes in region c, however. A look t the originl picture will show tht mny of the elementry light nd drk res re of comprle size to the 8 y 8 sic locks. Thus, t this resolution, the microedges re dominnt effect. This is nother exmple of the importnce of relizing tht per-

4 CORRESPONDENCE _ -. i &,,,,,. i_ 6,, L L, r..; & L_ A. L_ L _ IE Fig. 6. Edge mp for Fig. 4 using 16 y 16 regions. -., * _n - S - L.., #, _ fi, 3 ''.. F: _SJ, ^ g - L _ L S Fig. 7. Edge mp for Fig. 4 using 8 y 8 regions. 275 ceived edges hve "size" ssocited with them tht is function of the size of the ojects eing serched for. Comprle results were otined on the other mosic test ptterns. REFERENCES (1] R. M. Pickett, "Visul nlysis of texture in the detection nd recognition of ojects," in Picture Processing nd Psychopictorics, B. C. Lipkin nd A. Rosenfeld, Eds. New York: Acdemic Press, 1970, pp [2] R. Bjcsy, "Computer identifiction of textured visul scenes," Stnford Univ., Plo Alto, CA, Tech. Rep. AIM-180, Oct [3] A. Rosenfeld nd M. Thurston, "Edge nd curve detection for visul scene nlysis," IEEE Trns. Comput., vol. C-20, pp , My [4] A. Rosenfeld, M. Thurston, nd Y. H. Lee, "Edge nd curve detection: further experiments," IEEE Trns. Comput., vol. C-21, pp ; July [5] A. Rosernfeld, "A note on utomtic detection of texture grdients," IEEE Trns. Comput., vol. C-24, pp , Oct [6] S. W. Zucker, A. Rosenfeld, nd L. S. Dvis, "Picture segmenttion y texture discrimintion," IEEE Trns. Comput., vol. C-24, pp , Dec [7] A. L. Zorist nd W. B. Thompson, "Building distnce function for gestlt grouping," IEEE Trns. Comput., vol. C-24, pp , July [8] R. M. Hrlick, K. Shnmugn, nd I. Dinstein, "Texturl fetures for imge clssifiction," IEEE Trns. Syst., Mn, Cyern., vol. SMC-3, pp , Nov [9] R. O. Dud nd P. E. Hrt, Pttern Clssifiction nd Scene Anlysis. New York: Wiley, `$ [10] L. G. Roerts, "Mchine perception of three-dimensionl solids," in Opticl nd Electro-Opticl Informtion Processing, J. T. Tippett, et l., Ed. Cmridge, MA: MIT Press, 1965, pp [11] L. S. Dvis, "A survey of edge detection techniques," Comput. Grph. nd Imge Processing, vol. 4, pp , Sept

5 276 [12] E. L. Hll, G. Vrsi, W. B. Thompson, nd R. Guldin, "Computer mesurement of prticle sizes in electron microscope imges," IEEE Trns. Syst., Mn, CNvern., vol. SMC-6, pp , Fe [13] W. B. Thompson, "The role of texture in computerized scene nlysis," University of Southern Cliforni, Los Angeles, Tech. Rep. USCIPI-550, Dec Shift Register Binry Rte Multipliers W. H. NINKE AND G. R. RITCHIE Astrct-Novel implementtions of inry rte multiplier (BRM) circuit re descried. These BRM's, which use the input dt word to lod ptterns into shift registers, re cple of working t higher speed thn conventionl circuit, nd should e more suitle for silicon integrtion. Long input dt words cn e ccommodted with long shift register or y interconnecting severl short registers. Index Terms-Binry rte multipliers (BRM's), code conversion, logic design, shift registers, vector genertion. INPUT REGISTER Fig. 1. Conventionl BRM circuit. INTRODUCTION In mny res of digitl signl processing, there is need for device which will generte inry code words, or vectors, contining specified numer of l's nd hving these l's more or less uniformly distriuted over the time intervl of the code word. Such device my e used, for exmple, s prt of vector genertor for CRT disply or in converting differentil pulse code modultion encoding of signl to delt modultion pproximtion. Circuits to ccomplish this genertion re known s inry rte multipliers (BRM's) [1], [2]. The conventionl BRM implementtion involves using the input dt word to gte the output of inry counter. This correspondence descries BRM implementtion which involves using the input dt word to lod pttern of l's nd O's into prllel input shift register. Elimintion of the inry counter mens tht high-speed opertion cn e more esily chieved, nd sustitution of the shift register elimintes the need for holding register for the input dt word nd leds to possile dvntges in integrted circuit implementtion. In the next section the sic shift register BRM technique is descried. In the third section, modifiction of the sic circuit is discussed which gretly reduces the numer of shift register stges required, t the expense of more complicted clocking rrngements. THE BASIC SHIFT REGISTER BRM An exmple of conventionl 4-it BRM circuit is shown in Fig. 1. The counter is driven y clock 1 t rte 16f. The input dt word K is loded y clock 2 t rte f. Ko is the lest significnt it nd K3 the most significnt it of the input word. The counter wveforms shown in Fig. 2 re gted y the flip-flops holding K in such mnner tht ech 16-it inry output vector contins numer of l's equl to the vlue of the input inry numer, nd these l's re more or less evenly distriuted over the entire 16-it period of this BRM. For exmple, for the input dt word 1001, the output vector is Output Timeslot The shift register BRM equivlent of the circuit of Fig. 1 is shown in Fig. 3. At the eginning of ech cycle, with the occurrence of clock 2, the input dt word K is trnslted y the shift register input led rrngement into sptil distriution of l's nd O's corresponding to the time distriution produced y the circuit of Fig. 1. Then on ech pulse of clock 1 the register shifts once to the right, converting the sptil inry pttern into time pttern identicl to tht produced y conventionl BRM. Mnuscript received Novemer 21, 1975; revised April 13, The uthors re with Bell Lortories, Holmdel, NJ CLOCK 1'l 1llf L CLOCK 2 A J PU JL B_ C_ 4 12 D Fig BRM wveforms. This shift register BRM hs inherent dvntges over the conventionl BRM circuit. "Ripple-through" dely prolems, which re usully ssocited with ripple-crry counters, or the complexities of synchronous counters [31 re not present in the shift register BRM. Both the loding of the shift register nd the shift itself re prllel opertions. Thus, the circuit of Fig. 3 is cple of working t very high speeds, pproching the mximum clock frequency of the shift register. For smll input words nd single chnnel opertion, equl or less circuitry is required compred to conventionl circuit. For exmple, with n input word of 4 its, 15 shift register stges, nd some gting re required which compres fvorly to 4-it holding register, 4-it counter, nd some gting for the conventionl BRM. The use of shift register rises the poissiility of integrting the circuit using dynmic trnsfer cells for oth the shift register nd the gtes, thus reducing oth the silicon re nd the power consumption required in conventionl implementtion. REDUCING THE SHIFT REGISTER SIZE BY INTERCONNECTING BASIC UNITS Although the circuit of Fig. 3 my e extended in strightforwrd mnner to ccommodte longer dt words with very little scrifice in speed, such direct extension would require tht the length of the shift register e douled ech time it is dded to the input word. For dt 0