Chinese Academy of Surveying and Mapping, Beijing , China - - (zhangjx, b

Size: px
Start display at page:

Download "Chinese Academy of Surveying and Mapping, Beijing , China - - (zhangjx, b"

Transcription

1 SEMI-AUTOMATIC EXTRACTION OF RIBBON ROADS FORM HIGH RESOLUTION REMOTELY SENSED IMAGERY BY COOPERATION BETWEEN ANGULAR TEXTURE SIGNATURE AND TEMPLATE MATCHING X. G. Lin,,, J. X. Zhng, Z. J. Liu, J. Shen Chinese Acdemy of Surveying nd Mpping, Beijing 00039, Chin - linxingguo@gmil.com, - (zhngjx, zjliu)@csm.cn School of Resources nd Environment, Wuhn University, Wuhn , Chin Commission III, WG III/5 KEY WORDS: Rod extrction; Semi-utomtic; Angulr texture signture; Templte mtching ABSTRACT: Rod trcking is promising technique to increse the efficiency of rod mpping. In this pper n improved rod trcker, sed on coopertion etween ngulr texture signture nd templte mtching, is presented. Our trcker uses prol to model the rod trjectory nd to predict the position of next rod centreline point. It employs ngulr texture signture to get the exct moving direction of current rod centreline point, nd moves forwrd one predefined step long the direction to rech new position, nd then uses curvture chnge to verify the new dded rod point whether right enough. We lso uild compctness of ngulr texture signture polygon to check whether the ngulr texture signture is suitle to e used to go on trcking. When ngulr texture signture fils, lest squres templte mtching is then employed insted. Coopertion etween ngulr texture signture nd templte mtching cn relily extrct continuous nd homogenous rion rods on high resolution remotely sensed imgery.. INTRODUCTION Extrction of rod from digitl eril/stellite imgery is not only sceniclly chllenging ut lso of mjor importnce for sptil dt cquisition nd updte of geodtses. Trditionl mnul plotting is time consuming nd expensive, so utomtic cquisition nd updte of rod dt is gretly needed. In (Bjcsy nd Tvkoli, 976; Wng nd Newkirkr, 988; Trinder nd Wng, 997; Long nd Zho, 005; Hverkmp, 00; Hinz nd Bumgrter, 003; Zhng nd Couluigner, 006; Brzohr nd Cooper, 996; Grdner nd Roerts, 00; Btz nd Schpe, 004), vrious fully utomtic pproches re proposed. But the rod chrcteristics vry considerly with ground resolution, rod type, density of surrounding ojects, nd light conditions nd so on, dding tht the limits of stte of the rt on computer vision nd photogrmetry, the desired fully utomtion could not e chieved y now, however, semiutomtic pproch tht retins the humn opertor in the loop where computer re used to ssist humn performing is considered to e good compromise etween the fst computing speed of computer nd the efficient interprettion skills of n opertor. And quite lot of promising pproches for semi-utomtic rod extrction hve een proposed in the lst two decdes. Qum (978) trcked rod y rod surfce model nd profile model; Nevti nd Bu (980) proposed edge-sed technique; Mckeown nd Denlinger (988) comined edge-sed nd profile correltion sed pproch; Vosselmn nd de Knecht (995), Bumgrtner (00) nd Zhou (006) used lest squre profile mtching; Prk nd Kim (00), Hu, Zhng nd Zhng (000) employed templte mtching; Grun nd Li (995), Merlet nd Zerui (996) connected rod seeds y dynmic progrmming; Grun nd Li (997) used snkes to optimize the pth of rod seed points; Vndn nd ChndrKnth nd Rmchndrn (00) employs minimum cost to follow pth; Bltsvis (004) revised rod mp sed on existing geodt nd knowledge. But stndrd cliché of rod extrction is tht every lgorithm hs its limits, so we elieve tht numer of techniques developed for different clsses of rod will led to mny-rnched solution for rod extrction tht will e effective for wide rnge of rod types. Improved ngulr texture signture is proposed nd coopertion etween ngulr texture signture nd templte mtching is employed to semi-utomticlly extrct rod network in this pper. Rod chrcteristics nd the principles of the proposed lgorithm re descried in Sect.. In Sect. 3 we introduce the process of our trcker. Section 4 compres our trcker with clssic lgorithms. Section 5 evlutes the trcker y cse study. Section 6 summrizes the results of our study nd mkes conclusion.. Rod chrcteristics. METHOD Rod chrcteristics cn e clssified in five groups: geometricl, photometric, topologicl, functionl nd contextul chrcteristics (Vosselmn nd de Knecht, 995; Grun nd Li, 997; Zhou, 006) on high-resolution imgery. Detils of these chrcteristics re: ) Geometry ) Rods re elongted rions rther thn liner fetures; ) A rod segment hs mximum curvture; Corresponding uthor 539

2 The Interntionl Archives of the Photogrmmetry, Remote Sensing nd Sptil Informtion Sciences. Vol. XXXVII. Prt B3. Beijing 008 c) A rod segment hs constnt width. ) Rdiometry d) The rod surfce usully is smooth nd homogeneous; e) The rod hs good contrst with its djcent res. 3) Topology f) The rod will continue nd do not stop without reson; g) The rods intersect nd form network. 4) Function h) The rods connect humn settlements. 5) Context i) Overpsses, higher rods, djcent uildings nd tress my cst shdow; j) Rods my e occluded y vehicles nd other ostcles. The opertor use the ove chrcters nd prior knowledge to detect nd identify rod segment, nd the proposed trcker works sed on ), ), c), d), e) properties. Principles of ngulr texture signture A texture mesure is descried in (Hverkmp, 00) nd defined nd extended y us s follows. At ech pixel p of grey imge, ngulr texture signture (ATS) T ( α, w, h, p) is defined s the men, stndrd devition, vrince or entropy for rectngulr set of pixels of width w nd height h round the potentil rod pixel p whose principl xis lies t n ngle of α from the potentil rod direction. This mesure is computed for set of ngles α 0,,α n t pixel p.at the point p, the ATS is defined s the set of vlues {T ( α, w, 0, w, h, p), T ( α, w, h, p),,t ( α n h, p. The grph nd vlues of n ATS for single point p re shown in Fig.. The locl limits on this grph correspond to the most likely directions of the rod t point p (e.g. directions 3, 0, 0, 9). At ech pixel p, the numer k nd loction of the strong locl limits re computed from the ATS. For exmple, the signture shown in Fig. () hs 4 limits tht re significnt. We refer to the numer k of limit s the degree of the pixel. The texture mesures tht re used in rod detection re: the degree of the pixel nd the direction of the limit. In our pproch, on the ssumption tht the rods hve the ove ), ), c), d), e) properties, rectngulr templte is extended from nd rotted 80 deg from the perpendiculr of the potentil rod direction out ech rod pixel. At discrete intervls out the pixel, the ATS is clculted; nd the direction of the limit is regrded s the rod direction. If the ATS tkes the vrince or entropy s mesure, the direction of locl minimum is tken; while if the ATS tkes the men s mesure, the direction of locl minimum is tkes for right rods nd the direction of locl mximum is tken for drker rod s shown in Fig.. Once the rod direction is given, move on one step long the direction nd iterte the ove process until the trcker fils or reches to nother trcked rod trjectory or reches to the oundry of the imge..3 Rod trjectory model Rod trjectory cn e modelled y B-splines ( Trinder nd Li, 997), stright line (Hverkmp, 00), Klmn filter (Vosselmn nd de Knecht, 995), extended Klmn filter (Zhou, 006), prticle filter (Zhou, 006), nd prol (Mckeown nd Denlinger, 988). )} x y plne cn hve ritrry The prol in the orienttion, hving n eqution of the form: Ax + Bxy + Cy + Dx + Ey + F = 0 () where x nd re coordintes of point on the prol, y A, B, C, D, E, F Angulr Stndrd devition Angulr Men re prmeters Fig. Angulr texture signture () The effect of rotting templtes in 36 discrete ngles (the rectngles whose indexes re odd is invisile for convenience) () The stndrd devitions of 36 templtes (c) The mens of 36 templtes Direction Index Direction Index 4 c

3 The Interntionl Archives of the Photogrmmetry, Remote Sensing nd Sptil Informtion Sciences. Vol. XXXVII. Prt B3. Beijing 008 We don t use this eqution since the prmetric form is more convenient for our purpose. We represent the rod pth prmetriclly s two seprte functions x(l) nd y(l) where l is the totl length in steps tht we hve trversed long the rod s pth. We use multiple regression with l nd l s the independent vriles to fit prols to x(l) nd y(l), getting pproximte functions: X ( l) = l Y ( l) = l X (l) Y(l) x coordintes nd y coordintes, + l + c + l + c where nd re the rod centreline points the prmeters., c, c,,, To get the most possile potentil direction of the rod, we resort to compute X ( l +) nd Y( l +), tht is the most possile loction of the next rod centreline point. Given tht the rod segment hs mximum curvture, then the chnge of the curvture of two djcent rod points must e less thn predefined threshold T. The curvture K t some point on the prol cn e computed s follows: K c c = (3) 3/ [4( c + c) l + 4( c + c ) l + + ], c, c,,, where re the sme s in Eq. (). () re ATS for some interesting pixels with the ATS polygons shown in red. If the rod hs good contrst with its surrounding ojects, the polygon looks like n ellipse or -Shpe. The compctness of ATS is defined s the compctness of the ATS polygon using Eq. (4). We must note tht the ATS polygon in our trcker is just hlf of the ove illustrted polygon ecuse we just rotte the rectngulr templte 80 deg, nd our ATS polygon is form y plotting the ATS vlues round the pixel under considertion with corresponding direction nd link the lst point nd the first point to the current pixel. The compctness tells us whether the ATS polygon looks like circle. A circle-like ATS polygon usully mens tht the trcker is no longer fit to e used to follow rod centerline point, nd it needs mnul plotting. ATS compctness π A = P where A nd P re the re nd perimeter of the ATS polygon, respectively. Note tht P doesn t include the distnce etween the first point nd the current pixel nd the distnce etween the lst point nd the current pixel..5 Lest squre templte mtching Our lest squres templte mtching is s the sme s Prk nd Kim one (00). 3. THE PROCESS OF OUR TRACKER Semi-utomtic rod extrction here is undertken s follows. 3. Pre-process the input imge If the originl imge doesn t hve good contrst etween rod nd other fetures, it needs stretching. Then the imge is convolved with Gussin filter to smooth the imge nd reduce the high-frequency noise. (4) where σ = G x + y exp( σ = (5) pixels. ) 3. The opertor detects rod segment Fig. The wind rose chrt of Angulr Texture Signture () The men ATS of drker rod () The men ATS of righter rod.4 Compctness of ATS When we tke closer look t the ATS rotting full 360 deg of ech pixel, we cn find some interesting links etween the shpe of the ATS polygon nd corresponding pixel types. To form the ATS polygon, insted of plotting the ATS vlues for ech direction long horizontl line, we plot the ATS vlues round the pixel under considertion with corresponding direction nd link the lst point to the first point. The resulting polygon is clled the ATS polygon. Fig. shows the clculted A humn opertor hs to identify short prt of rod xis; this rod prt serves s initiliztion for n utomtic trcker. The trcker need strting point on the rod centreline nd second point to define the direction of the rod nd third point to define the width w of the rod. Then the rod trcker move forwrd t lest 5 steps long the initil direction, then the rod trjectory model cn e uilt y Eq. (). Predict the next rod position nd get the most possile potentil rod direction. 3.3 Compute ATS From the lst rod centreline point in the trjectory, rectngulr templte is formed with width w nd height * w, nd rotte 80 deg from the perpendiculr of the predicted direction. At discrete intervls out the pixel, the ngulr 54

4 The Interntionl Archives of the Photogrmmetry, Remote Sensing nd Sptil Informtion Sciences. Vol. XXXVII. Prt B3. Beijing 008 texture signture is clculted. Selecting which texture signture s the mesure of ATS, it should judge y the rod conditions. After lot of experiment, we conclude tht, tking vrince, strnd devition or entropy s the mesure of ATS if the rod hs slient chrcteristic d) while tking men s the mesure of ATS if the rod hs ovious chrcteristic e). 3.4 Compute hed ATS compctness ATS compctness nd move forwrd one step Clculte the y Eq. (4). If the vlue is lrger thn predefined threshold T, it tells us tht the ATS is not fit ny more to trck rod, nd it needs lest squres templte mtching insted. Otherwise the direction of the limit is regrded s the rod direction, nd moves the rod trjectory one step. 3.5 Compute the chnge of the curvture Clculte the curvture of the new dded rod centreline y Eq. (5), compre it with the curvture of lst point, if the difference is lrger thn predefined threshold T, delete the new point from the rod trjectory, nd resort to mnully plot. Otherwise, predict the next rod position y prol eqution nd iterte from 3.3 if the trjectory doesn t rech to nother trjectory or the oundry of the imge. Once the user ccomplishes one rod segment or the trcker reches to one trcked rod or the oundry of imge, initilizes nother rod segment nd restrt from 3. gin until ll rods re trcked. From the opertor point of view, the procedure is s follows: the opertor hs to initilize the trcker y three input points to indicte the strting, the moving direction nd the width of the rod segment, nd then the trcker is triggered. Whenever the internl evlution of the trcking tool indictes tht the trcker might lost the rod xis or e no longer fit, it demnds for interction of the opertor. Then the opertor hs to confirm the trcker or the user must edit the extrcted rod nd put the trcker ck on the rod. finishes immeditely fter initiliztion. The snkes is slower thn profile mtching. The templte mtching is slower thn snkes ut fster thn ATS. We cn get the conclusion tht our proposed lgorithm is more roust thn other trckers. c d 5. EXPERIAMENT AND EVALUATION 4. COMPARISION OF FOUR TRACKERS To verify our lgorithm, we mke comprison etween lest squre templte mtching, lest squre profile mtching, snkes nd our trcker on sme Quickird imge of Hui rou County in Beijing, Chin, whose size is 355 y 066 pixels. On this imge, there is righter centreline on the homogenous drker rod surfce with righter ckground. The results re shown in Fig. 3. All trckers extrct the rod centreline with different precision in red colour. For profile mtching, the front prt of the pth is quite good ut the lst prt of the extrcted rod trjectory hs lrger devition due to the lrger curving of the rod. For templte mtching, the extrcted rod trjectory is good ut with some lrger devite points long the trjectory. For snkes, if there is only two seed points on centreline, the extrcted rod trjectory is quite wrong, s shown in Fig. 3(c), the up line; ut if there is 5 rod seed points, the result re quite good, s shown in Fig. 3(c), the down line. For ATS tking vrince s mesure, there is some cceptle devition in the middle prt of the rod. For ATS tking men s mesure, the extrcted rod trjectory is very good. We lso record the time needed y ech trcker. Profile mtching is so fst tht it e Fig. 3 Comprison of lgorithms ()The result of profile mtching () The result of templte mtching (c) The result of snkes (d) The result of ngulr texture signture tle stndrd devition s mesure (e) The result of ngulr texture signture tke men s mesure The lgorithm proposed here ws tested y one Quickird imge over Hefei City, An hui Province, Chin. The imge with 8 y 998 pixels contins mny different rod types such s stright rods, curves, nd crossings t different orienttions. And for ech segment, the surfce mteril is sme, ut there is sudden chnge in rdiometry, s shown in Fig. 4. The rods hve different disturing ojects such s shdows of trees nd 54

5 The Interntionl Archives of the Photogrmmetry, Remote Sensing nd Sptil Informtion Sciences. Vol. XXXVII. Prt B3. Beijing 008 occlusions y vehicles, ut the shdow nd occlusion is not serious. In the procedure of trcking, there re 8 times the trcker deviting the pth, nd then the thred is cesed s soon s possile y the opertor. There re 6 times prompts notifying the user tht the trcker is no longer suitle nd it needs mnul plotting. And there re only 76 mnul input points, nd the whole process tkes 543 seconds. But if the opertor wnt mnully plot ll pth point with the sme precision s the trcker, it needs 08 inputs nd it tkes 776 seconds. In generl, the qulity of the result of mnul nd semi-utomtic plotting is equivlent, since the opertor supervises the results of the semi-utomtic system nd filures re edited online. On verge, the geometric ccurcy is comprle, too. We lso test our trcker on mny other grey scle imges with different resolution vried from 0. to.5 m, nd the results re similr in mnul input sving out 90% nd time sving out 30%. The result shows tht our trcker is quite roust when the photometric property of sme rod segment chnges suddenly, nd when the trcker reches to the junctions nd it will go on without stop. And the trcker cn detect the rod centreline of the rods in ny orienttion with moderte curvture ccurtely, nd lso works successfully for rods hve some ostcles cused y shdow nd occlusion. compctness coefficient to evlute the ptness of itself to go on trcking, so the lgorithm hs some ility of higher-level resoning. The current limittions re tht the lgorithm my not work on the rod cst y much shdow nd occlusion in complex scenes, it cn t judge the vlidity of input seeds, it cn only trck long rion rods on grey scle imgery, nd it need more computing times. These limittions re currently eing exmined now. The min contriution of this pper is tht it employs ngulr texture signture semi-utomticlly extrct rod with precise results. REFERENCES Bjcsy, R., Tvkoli, M., 976. Computer recognition of rods from stellite pictures. IEEE Trnsctions on Systerms, Mn, nd Cyernetics, 6(9), pp Bltsvis, E. P., 004. Oject extrction nd revision y imge nlysis using existing geodt nd knowledge: current sttus nd steps towrds opertionl systems.isprs Journl of Photogrmmetry & Remote Sensing, 58, pp Brzohr, M., Cooper, D. B., 996. Automtic finding min rods in eril imges y using geometric-stochstic models nd estimtion. IEEE Trnsctions on Pttern Anlysis nd Mchine Intelligence, 8(7), pp Bumgrtner, A., Hinz, S., Wiedemnn, C., 00. Efficient methods nd interfces for rod trcking. Interntionl Archives of Photogrmmetry nd Remote Sensing, 34(3B), pp Benz, U. C., Hofmnn, P., Willhuck, G., et l., 004. Multiresolution, oject-oriented fuzzy nlysis of remote sensing dt for GIS-redy informtion. ISPRS Journl of Photogrmmetry & Remote Sensing, 58, pp Doucette, P., Agouris, P., Stefnidis, A., 004. Automted rod extrction from high resolution multi-spectrl imgery. Photogrmmetric Engineering &Remote Sensing, 70(), pp Grdner, M. E., Roert, D. A., Funk, C., Noronh, V., 00. Rod extrction from AVIRIS using spectrl mixture nd Q-tree filter techniques. In: Proc. AVIRIS Airorne Geosciences Workshop, Psden, Cliforni, URL:ftp://popo.jpl.ns.gov/pu/docs/workshops/0_docs/toc.h tml (lst ccessed : April 0,007). Gemn, D., Jedynk, B., 996. An ctive testing model for trcking rods in stellite imges. IEEE Trnsction on Pttern Anlysis nd Mchine Intelligence, 8(), pp. -4.Gruen, A., 985. Adptive lest squre correltion-a Powerful Imge Mtching Technique. South Africn Journl of Photogrmmetry, Remote Sensing nd Crtogrphy, 4(3), pp Fig. 4 Semi-utomtic extrcted rod network on Quickird imge () Overview () Locl result. 6. CONCLUSIONS Gruen, A., Li, H., 995. Rod extrction from eril nd stellite imges y dynmic progrmming. ISPRS Journl of Photogrmmetry nd Remote Sensing, 50(4), pp. -0. The proposed trcker sed on ATS is very roust, ecuse it mkes est use of the rod chrcteristics on high-resolution imgery. Our lgorithm employ prol eqution to fit the trjectory of the rod nd to predict the rod position nd moving direction nd to judge whether the new dded rod point is right y check the curvture chnge, it lso utilize 543 Gruen, A., Li, H., 997. Semi-utomtic liner feture extrction y dynmic progrmming nd LSB-Snkes. Photogrmmetic Engineering nd Remote Sensing, 997, 63(8), pp

6 The Interntionl Archives of the Photogrmmetry, Remote Sensing nd Sptil Informtion Sciences. Vol. XXXVII. Prt B3. Beijing 008 Hverkmp, D., 00. Extrcting stright rod structure in urn environments using IKONOS stellite imgery. Opticl Engineering, 4(9), pp Hrvey, W., McGlone, J., MKeown, D., Irvine, J., 004. Usercentric evlution of semi-utomtic rod network extrction. Photogrmmetric Engineering nd Remote Sensing, 70(), pp Hinz, S., Bumgrtner, A., 003. Automtic extrction of urn rod network from multi-view eril imgery. ISPRS Journl of Photogrmmetry & Remote Sensing, 58, pp Hu, X., Zhng, Z., Zhng, J., 000. An pproch of semiutomted rod extrction form eril imges sed on templte mtching nd Neurl Network. Interntionl Achieves of Photogrmmetry nd Remote Sensing, Amsterdm, Netherlnds, Vol. XXXIII, Prt B3, pp Long, H., Zho, Z., 005. Urn rod extrction from highresolution opticl stellite imge. Interntionl Journl of Remote Sensing, 6(), pp Mckeown, D., Denlinger, J., 988. Coopertive methods for rod trcing in eril imgery. In: Proceedings of the IEEE Conference in Computer Vision nd Pttern Recognition, pp Ann Aror, MI. Men, J.B, 003. Stte of the rt on utomtic rod extrction for GIS updte : novel clssifiction. Pttern Recognition Letters, 4,pp Merlet, N., Zerui, J., 996. New prospects in line detection y dynmic progrmming. IEEE Trnsction on Pttern Anlysis nd Mchine Intelligence, 8(4), pp Prk, S., Kim, T., 00. Semi-utomtic rod extrction lgorithm from IKONOS imges using templte mtching. In: Proc.nd Asin Conference on Remote Sensing, Singpore, pp Shukl, V., Chndrknth, R., Rmchndrn, R., 00. Semiutomtic rod extrction lgorithm for high resolution imges using pth following pproch.in:icvgip0, Ahmdd, pp Trinder, J. C., Li, H., 997. Semi-utomtic feture extrction y snkes. In: Automtic Extrction of Mn-mde Ojects from Aeril nd Spce Imges (). Bsel, Zürich,, pp Trinder, J. C., Wng, Y. D, Sowm, Y. A., et l., 997. Artificil intelligence in 3D feture extrction. In: Automtic Extrction of Mn-mde Ojects from Aeril nd Spce Imges (), Bsel, Zürich, pp Vosselmn, G. nd de Knecht, J., 995. Rod trcing y profile mtching nd Klmn filtering. In Proceedings of the Workshop on Automtic Extrction of Mn-Mde Ojects from Aeril nd Spce Imges, pp Birkheuser, Germny. Wng, F. G., Newkirkr, R., 988. A knowledge-sed system for highwy network extrction. IEEE Trnsction on Geoscience nd Remote Sensing, 6(5), pp Zhng, Q., Couloigner, I., 006. Benefit of the ngulr texture signture for the seprtion of prking lots nd rods on high resolution multi-spectrl imgery. Pttern Recognition Letters, 7, pp Zhou, J., Bischof, W. F., Celli, T., 006. Rod trcking in eril imges sed on humn-computer interction nd Bysin filtering. ISPRS Journl of Photogrmmetry & Remote Sensing, 6, pp ACKNOWLEDGEMENTS Our reserch is funded y The Ntionl Key Bsic Reserch nd Develop Progrm under Grnt No. 0006CB Qum, L. H., 978. Rod trcking nd nomly detection in eril imgery. In: Imge Understnding Workshop, London, UK, pp

GENERATING ORTHOIMAGES FOR CLOSE-RANGE OBJECTS BY AUTOMATICALLY DETECTING BREAKLINES

GENERATING ORTHOIMAGES FOR CLOSE-RANGE OBJECTS BY AUTOMATICALLY DETECTING BREAKLINES GENEATING OTHOIMAGES FO CLOSE-ANGE OBJECTS BY AUTOMATICALLY DETECTING BEAKLINES Efstrtios Stylinidis 1, Lzros Sechidis 1, Petros Ptis 1, Spiros Sptls 2 Aristotle University of Thessloniki 1 Deprtment of

More information

COLOUR IMAGE MATCHING FOR DTM GENERATION AND HOUSE EXTRACTION

COLOUR IMAGE MATCHING FOR DTM GENERATION AND HOUSE EXTRACTION Hee Ju Prk OLOUR IMAGE MATHING FOR DTM GENERATION AND HOUSE EXTRATION Hee Ju PARK, Petr ZINMMERMANN * Swiss Federl Institute of Technology, Zuric Switzerlnd Institute for Geodesy nd Photogrmmetry heeju@ns.shingu-c.c.kr

More information

2 Computing all Intersections of a Set of Segments Line Segment Intersection

2 Computing all Intersections of a Set of Segments Line Segment Intersection 15-451/651: Design & Anlysis of Algorithms Novemer 14, 2016 Lecture #21 Sweep-Line nd Segment Intersection lst chnged: Novemer 8, 2017 1 Preliminries The sweep-line prdigm is very powerful lgorithmic design

More information

6.3 Volumes. Just as area is always positive, so is volume and our attitudes towards finding it.

6.3 Volumes. Just as area is always positive, so is volume and our attitudes towards finding it. 6.3 Volumes Just s re is lwys positive, so is volume nd our ttitudes towrds finding it. Let s review how to find the volume of regulr geometric prism, tht is, 3-dimensionl oject with two regulr fces seprted

More information

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

Before We Begin. Introduction to Spatial Domain Filtering. Introduction to Digital Image Processing. Overview (1): Administrative Details (1): Overview (): Before We Begin Administrtive detils Review some questions to consider Winter 2006 Imge Enhncement in the Sptil Domin: Bsics of Sptil Filtering, Smoothing Sptil Filters, Order Sttistics Filters

More information

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1 Mth 33 Volume Stewrt 5.2 Geometry of integrls. In this section, we will lern how to compute volumes using integrls defined by slice nlysis. First, we recll from Clculus I how to compute res. Given the

More information

USING HOUGH TRANSFORM IN LINE EXTRACTION

USING HOUGH TRANSFORM IN LINE EXTRACTION Stylinidis, Efstrtios USING HOUGH TRANSFORM IN LINE EXTRACTION Efstrtios STYLIANIDIS, Petros PATIAS The Aristotle University of Thessloniki, Deprtment of Cdstre Photogrmmetry nd Crtogrphy Univ. Box 473,

More information

CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE

CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE 3.1 Scheimpflug Configurtion nd Perspective Distortion Scheimpflug criterion were found out to be the best lyout configurtion for Stereoscopic PIV, becuse

More information

On the Detection of Step Edges in Algorithms Based on Gradient Vector Analysis

On the Detection of Step Edges in Algorithms Based on Gradient Vector Analysis On the Detection of Step Edges in Algorithms Bsed on Grdient Vector Anlysis A. Lrr6, E. Montseny Computer Engineering Dept. Universitt Rovir i Virgili Crreter de Slou sin 43006 Trrgon, Spin Emil: lrre@etse.urv.es

More information

Complete Coverage Path Planning of Mobile Robot Based on Dynamic Programming Algorithm Peng Zhou, Zhong-min Wang, Zhen-nan Li, Yang Li

Complete Coverage Path Planning of Mobile Robot Based on Dynamic Programming Algorithm Peng Zhou, Zhong-min Wang, Zhen-nan Li, Yang Li 2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) Complete Coverge Pth Plnning of Mobile Robot Bsed on Dynmic Progrmming Algorithm Peng Zhou, Zhong-min

More information

MTH 146 Conics Supplement

MTH 146 Conics Supplement 105- Review of Conics MTH 146 Conics Supplement In this section we review conics If ou ne more detils thn re present in the notes, r through section 105 of the ook Definition: A prol is the set of points

More information

P(r)dr = probability of generating a random number in the interval dr near r. For this probability idea to make sense we must have

P(r)dr = probability of generating a random number in the interval dr near r. For this probability idea to make sense we must have Rndom Numers nd Monte Crlo Methods Rndom Numer Methods The integrtion methods discussed so fr ll re sed upon mking polynomil pproximtions to the integrnd. Another clss of numericl methods relies upon using

More information

Section 10.4 Hyperbolas

Section 10.4 Hyperbolas 66 Section 10.4 Hyperbols Objective : Definition of hyperbol & hyperbols centered t (0, 0). The third type of conic we will study is the hyperbol. It is defined in the sme mnner tht we defined the prbol

More information

10.5 Graphing Quadratic Functions

10.5 Graphing Quadratic Functions 0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions

More information

Class-XI Mathematics Conic Sections Chapter-11 Chapter Notes Key Concepts

Class-XI Mathematics Conic Sections Chapter-11 Chapter Notes Key Concepts Clss-XI Mthemtics Conic Sections Chpter-11 Chpter Notes Key Concepts 1. Let be fixed verticl line nd m be nother line intersecting it t fixed point V nd inclined to it t nd ngle On rotting the line m round

More information

Fig.1. Let a source of monochromatic light be incident on a slit of finite width a, as shown in Fig. 1.

Fig.1. Let a source of monochromatic light be incident on a slit of finite width a, as shown in Fig. 1. Answer on Question #5692, Physics, Optics Stte slient fetures of single slit Frunhofer diffrction pttern. The slit is verticl nd illuminted by point source. Also, obtin n expression for intensity distribution

More information

Hyperbolas. Definition of Hyperbola

Hyperbolas. Definition of Hyperbola CHAT Pre-Clculus Hyperols The third type of conic is clled hyperol. For n ellipse, the sum of the distnces from the foci nd point on the ellipse is fixed numer. For hyperol, the difference of the distnces

More information

Semi-Automatic Technique for 3D Building Model Generation

Semi-Automatic Technique for 3D Building Model Generation Ngw El-ASHMAWY, Egypt Key words: DTM, DSM, 3D Building Model, Phoogrmmetry, Remote Sensing. SUMMARY Three Dimensionl Building models re excessively used in vrious pplictions. Digitl Surfce Model is the

More information

Stained Glass Design. Teaching Goals:

Stained Glass Design. Teaching Goals: Stined Glss Design Time required 45-90 minutes Teching Gols: 1. Students pply grphic methods to design vrious shpes on the plne.. Students pply geometric trnsformtions of grphs of functions in order to

More information

Agilent Mass Hunter Software

Agilent Mass Hunter Software Agilent Mss Hunter Softwre Quick Strt Guide Use this guide to get strted with the Mss Hunter softwre. Wht is Mss Hunter Softwre? Mss Hunter is n integrl prt of Agilent TOF softwre (version A.02.00). Mss

More information

Lecture 10 Evolutionary Computation: Evolution strategies and genetic programming

Lecture 10 Evolutionary Computation: Evolution strategies and genetic programming Lecture 10 Evolutionry Computtion: Evolution strtegies nd genetic progrmming Evolution strtegies Genetic progrmming Summry Negnevitsky, Person Eduction, 2011 1 Evolution Strtegies Another pproch to simulting

More information

CS321 Languages and Compiler Design I. Winter 2012 Lecture 5

CS321 Languages and Compiler Design I. Winter 2012 Lecture 5 CS321 Lnguges nd Compiler Design I Winter 2012 Lecture 5 1 FINITE AUTOMATA A non-deterministic finite utomton (NFA) consists of: An input lphet Σ, e.g. Σ =,. A set of sttes S, e.g. S = {1, 3, 5, 7, 11,

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION Supplementry Figure y (m) x (m) prllel perpendiculr Distnce (m) Bird Stndrd devition for distnce (m) c 6 prllel perpendiculr 4 doi:.8/nture99 SUPPLEMENTARY FIGURE Confirmtion tht movement within the flock

More information

Fig.25: the Role of LEX

Fig.25: the Role of LEX The Lnguge for Specifying Lexicl Anlyzer We shll now study how to uild lexicl nlyzer from specifiction of tokens in the form of list of regulr expressions The discussion centers round the design of n existing

More information

Slides for Data Mining by I. H. Witten and E. Frank

Slides for Data Mining by I. H. Witten and E. Frank Slides for Dt Mining y I. H. Witten nd E. Frnk Simplicity first Simple lgorithms often work very well! There re mny kinds of simple structure, eg: One ttriute does ll the work All ttriutes contriute eqully

More information

In the last lecture, we discussed how valid tokens may be specified by regular expressions.

In the last lecture, we discussed how valid tokens may be specified by regular expressions. LECTURE 5 Scnning SYNTAX ANALYSIS We know from our previous lectures tht the process of verifying the syntx of the progrm is performed in two stges: Scnning: Identifying nd verifying tokens in progrm.

More information

Graphing Conic Sections

Graphing Conic Sections Grphing Conic Sections Definition of Circle Set of ll points in plne tht re n equl distnce, clled the rdius, from fixed point in tht plne, clled the center. Grphing Circle (x h) 2 + (y k) 2 = r 2 where

More information

DECISION LEVEL FUSION OF LIDAR DATA AND AERIAL COLOR IMAGERY BASED ON BAYESIAN THEORY FOR URBAN AREA CLASSIFICATION

DECISION LEVEL FUSION OF LIDAR DATA AND AERIAL COLOR IMAGERY BASED ON BAYESIAN THEORY FOR URBAN AREA CLASSIFICATION DECISION LEVEL FUSION OF LIDAR DATA AND AERIAL COLOR IMAGERY BASED ON BAYESIAN THEORY FOR URBAN AREA CLASSIFICATION H. Rstiveis* School of Surveying nd Geosptil Engineering, Fculty of Engineering, University

More information

What are suffix trees?

What are suffix trees? Suffix Trees 1 Wht re suffix trees? Allow lgorithm designers to store very lrge mount of informtion out strings while still keeping within liner spce Allow users to serch for new strings in the originl

More information

such that the S i cover S, or equivalently S

such that the S i cover S, or equivalently S MATH 55 Triple Integrls Fll 16 1. Definition Given solid in spce, prtition of consists of finite set of solis = { 1,, n } such tht the i cover, or equivlently n i. Furthermore, for ech i, intersects i

More information

L. Yaroslavsky. Fundamentals of Digital Image Processing. Course

L. Yaroslavsky. Fundamentals of Digital Image Processing. Course L. Yroslvsky. Fundmentls of Digitl Imge Processing. Course 0555.330 Lecture. Imge enhncement.. Imge enhncement s n imge processing tsk. Clssifiction of imge enhncement methods Imge enhncement is processing

More information

Dr. D.M. Akbar Hussain

Dr. D.M. Akbar Hussain Dr. D.M. Akr Hussin Lexicl Anlysis. Bsic Ide: Red the source code nd generte tokens, it is similr wht humns will do to red in; just tking on the input nd reking it down in pieces. Ech token is sequence

More information

MATH 2530: WORKSHEET 7. x 2 y dz dy dx =

MATH 2530: WORKSHEET 7. x 2 y dz dy dx = MATH 253: WORKSHT 7 () Wrm-up: () Review: polr coordintes, integrls involving polr coordintes, triple Riemnn sums, triple integrls, the pplictions of triple integrls (especilly to volume), nd cylindricl

More information

8.2 Areas in the Plane

8.2 Areas in the Plane 39 Chpter 8 Applictions of Definite Integrls 8. Ares in the Plne Wht ou will lern out... Are Between Curves Are Enclosed Intersecting Curves Boundries with Chnging Functions Integrting with Respect to

More information

International Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2016)

International Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2016) \ Interntionl Conference on Mechnics, Mterils nd tructurl Engineering (ICMME 2016) Reserch on the Method to Clibrte tructure Prmeters of Line tructured Light Vision ensor Mingng Niu1,, Kngnin Zho1, b,

More information

MA1008. Calculus and Linear Algebra for Engineers. Course Notes for Section B. Stephen Wills. Department of Mathematics. University College Cork

MA1008. Calculus and Linear Algebra for Engineers. Course Notes for Section B. Stephen Wills. Department of Mathematics. University College Cork MA1008 Clculus nd Liner Algebr for Engineers Course Notes for Section B Stephen Wills Deprtment of Mthemtics University College Cork s.wills@ucc.ie http://euclid.ucc.ie/pges/stff/wills/teching/m1008/ma1008.html

More information

CS143 Handout 07 Summer 2011 June 24 th, 2011 Written Set 1: Lexical Analysis

CS143 Handout 07 Summer 2011 June 24 th, 2011 Written Set 1: Lexical Analysis CS143 Hndout 07 Summer 2011 June 24 th, 2011 Written Set 1: Lexicl Anlysis In this first written ssignment, you'll get the chnce to ply round with the vrious constructions tht come up when doing lexicl

More information

COMP 423 lecture 11 Jan. 28, 2008

COMP 423 lecture 11 Jan. 28, 2008 COMP 423 lecture 11 Jn. 28, 2008 Up to now, we hve looked t how some symols in n lphet occur more frequently thn others nd how we cn sve its y using code such tht the codewords for more frequently occuring

More information

Video-rate Image Segmentation by means of Region Splitting and Merging

Video-rate Image Segmentation by means of Region Splitting and Merging Video-rte Imge Segmenttion y mens of Region Splitting nd Merging Knur Anej, Florence Lguzet, Lionel Lcssgne, Alin Merigot Institute for Fundmentl Electronics, University of Pris South Orsy, Frnce knur.nej@gmil.com,

More information

Objective: Students will understand what it means to describe, graph and write the equation of a parabola. Parabolas

Objective: Students will understand what it means to describe, graph and write the equation of a parabola. Parabolas Pge 1 of 8 Ojective: Students will understnd wht it mens to descrie, grph nd write the eqution of prol. Prols Prol: collection of ll points P in plne tht re the sme distnce from fixed point, the focus

More information

Spectral Analysis of MCDF Operations in Image Processing

Spectral Analysis of MCDF Operations in Image Processing 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

More information

1 Quad-Edge Construction Operators

1 Quad-Edge Construction Operators CS48: Computer Grphics Hndout # Geometric Modeling Originl Hndout #5 Stnford University Tuesdy, 8 December 99 Originl Lecture #5: 9 November 99 Topics: Mnipultions with Qud-Edge Dt Structures Scribe: Mike

More information

Computer Vision and Image Understanding

Computer Vision and Image Understanding Computer Vision nd Imge Understnding 116 (2012) 25 37 Contents lists ville t SciVerse ScienceDirect Computer Vision nd Imge Understnding journl homepge: www.elsevier.com/locte/cviu A systemtic pproch for

More information

If f(x, y) is a surface that lies above r(t), we can think about the area between the surface and the curve.

If f(x, y) is a surface that lies above r(t), we can think about the area between the surface and the curve. Line Integrls The ide of line integrl is very similr to tht of single integrls. If the function f(x) is bove the x-xis on the intervl [, b], then the integrl of f(x) over [, b] is the re under f over the

More information

called the vertex. The line through the focus perpendicular to the directrix is called the axis of the parabola.

called the vertex. The line through the focus perpendicular to the directrix is called the axis of the parabola. Review of conic sections Conic sections re grphs of the form REVIEW OF CONIC SECTIONS prols ellipses hperols P(, ) F(, p) O p =_p REVIEW OF CONIC SECTIONS In this section we give geometric definitions

More information

The Greedy Method. The Greedy Method

The Greedy Method. The Greedy Method Lists nd Itertors /8/26 Presenttion for use with the textook, Algorithm Design nd Applictions, y M. T. Goodrich nd R. Tmssi, Wiley, 25 The Greedy Method The Greedy Method The greedy method is generl lgorithm

More information

Analysis of Computed Diffraction Pattern Diagram for Measuring Yarn Twist Angle

Analysis of Computed Diffraction Pattern Diagram for Measuring Yarn Twist Angle Textiles nd Light ndustril Science nd Technology (TLST) Volume 3, 2014 DO: 10.14355/tlist.2014.0301.01 http://www.tlist-journl.org Anlysis of Computed Diffrction Pttern Digrm for Mesuring Yrn Twist Angle

More information

9.1 apply the distance and midpoint formulas

9.1 apply the distance and midpoint formulas 9.1 pply the distnce nd midpoint formuls DISTANCE FORMULA MIDPOINT FORMULA To find the midpoint between two points x, y nd x y 1 1,, we Exmple 1: Find the distnce between the two points. Then, find the

More information

From Dependencies to Evaluation Strategies

From Dependencies to Evaluation Strategies From Dependencies to Evlution Strtegies Possile strtegies: 1 let the user define the evlution order 2 utomtic strtegy sed on the dependencies: use locl dependencies to determine which ttriutes to compute

More information

Tilt-Sensing with Kionix MEMS Accelerometers

Tilt-Sensing with Kionix MEMS Accelerometers Tilt-Sensing with Kionix MEMS Accelerometers Introduction Tilt/Inclintion sensing is common ppliction for low-g ccelerometers. This ppliction note describes how to use Kionix MEMS low-g ccelerometers to

More information

Area & Volume. Chapter 6.1 & 6.2 September 25, y = 1! x 2. Back to Area:

Area & Volume. Chapter 6.1 & 6.2 September 25, y = 1! x 2. Back to Area: Bck to Are: Are & Volume Chpter 6. & 6. Septemer 5, 6 We cn clculte the re etween the x-xis nd continuous function f on the intervl [,] using the definite integrl:! f x = lim$ f x * i )%x n i= Where fx

More information

Computing offsets of freeform curves using quadratic trigonometric splines

Computing offsets of freeform curves using quadratic trigonometric splines Computing offsets of freeform curves using qudrtic trigonometric splines JIULONG GU, JAE-DEUK YUN, YOONG-HO JUNG*, TAE-GYEONG KIM,JEONG-WOON LEE, BONG-JUN KIM School of Mechnicl Engineering Pusn Ntionl

More information

4452 Mathematical Modeling Lecture 4: Lagrange Multipliers

4452 Mathematical Modeling Lecture 4: Lagrange Multipliers Mth Modeling Lecture 4: Lgrnge Multipliers Pge 4452 Mthemticl Modeling Lecture 4: Lgrnge Multipliers Lgrnge multipliers re high powered mthemticl technique to find the mximum nd minimum of multidimensionl

More information

Machine vision system for surface inspection on brushed industrial parts.

Machine vision system for surface inspection on brushed industrial parts. Mchine vision system for surfce inspection on rushed industril prts. Nicols Bonnot, Rlph Seulin, Frederic Merienne Lortoire Le2i, CNRS UMR 5158, University of Burgundy, Le Creusot, Frnce. ABSTRACT This

More information

Topics in Analytic Geometry

Topics in Analytic Geometry Nme Chpter 10 Topics in Anltic Geometr Section 10.1 Lines Objective: In this lesson ou lerned how to find the inclintion of line, the ngle between two lines, nd the distnce between point nd line. Importnt

More information

TOWARDS GRADIENT BASED AERODYNAMIC OPTIMIZATION OF WIND TURBINE BLADES USING OVERSET GRIDS

TOWARDS GRADIENT BASED AERODYNAMIC OPTIMIZATION OF WIND TURBINE BLADES USING OVERSET GRIDS TOWARDS GRADIENT BASED AERODYNAMIC OPTIMIZATION OF WIND TURBINE BLADES USING OVERSET GRIDS S. H. Jongsm E. T. A. vn de Weide H. W. M. Hoeijmkers Overset symposium 10-18-2012 Deprtment of mechnicl engineering

More information

ZZ - Advanced Math Review 2017

ZZ - Advanced Math Review 2017 ZZ - Advnced Mth Review Mtrix Multipliction Given! nd! find the sum of the elements of the product BA First, rewrite the mtrices in the correct order to multiply The product is BA hs order x since B is

More information

A multiview 3D modeling system based on stereo vision techniques

A multiview 3D modeling system based on stereo vision techniques Mchine Vision nd Applictions (2005) 16: 148 156 Digitl Oject Identifier (DOI) 10.1007/s00138-004-0165-2 Mchine Vision nd Applictions A multiview 3D modeling system sed on stereo vision techniques Soon-Yong

More information

Alignment of Long Sequences. BMI/CS Spring 2012 Colin Dewey

Alignment of Long Sequences. BMI/CS Spring 2012 Colin Dewey Alignment of Long Sequences BMI/CS 776 www.biostt.wisc.edu/bmi776/ Spring 2012 Colin Dewey cdewey@biostt.wisc.edu Gols for Lecture the key concepts to understnd re the following how lrge-scle lignment

More information

Chapter 2 Sensitivity Analysis: Differential Calculus of Models

Chapter 2 Sensitivity Analysis: Differential Calculus of Models Chpter 2 Sensitivity Anlysis: Differentil Clculus of Models Abstrct Models in remote sensing nd in science nd engineering, in generl re, essentilly, functions of discrete model input prmeters, nd/or functionls

More information

Presentation Martin Randers

Presentation Martin Randers Presenttion Mrtin Rnders Outline Introduction Algorithms Implementtion nd experiments Memory consumption Summry Introduction Introduction Evolution of species cn e modelled in trees Trees consist of nodes

More information

Section 9.2 Hyperbolas

Section 9.2 Hyperbolas Section 9. Hperols 597 Section 9. Hperols In the lst section, we lerned tht plnets hve pproimtel ellipticl orits round the sun. When n oject like comet is moving quickl, it is le to escpe the grvittionl

More information

Vulnerability Analysis of Electric Power Communication Network. Yucong Wu

Vulnerability Analysis of Electric Power Communication Network. Yucong Wu 2nd Interntionl Conference on Advnces in Mechnicl Engineering nd Industril Informtics (AMEII 2016 Vulnerbility Anlysis of Electric Power Communiction Network Yucong Wu Deprtment of Telecommunictions Engineering,

More information

Math 35 Review Sheet, Spring 2014

Math 35 Review Sheet, Spring 2014 Mth 35 Review heet, pring 2014 For the finl exm, do ny 12 of the 15 questions in 3 hours. They re worth 8 points ech, mking 96, with 4 more points for netness! Put ll your work nd nswers in the provided

More information

HOPC: A NOVEL SIMILARITY METRIC BASED ON GEOMETRIC STRUCTURAL PROPERTIES FOR MULTI-MODAL REMOTE SENSING IMAGE MATCHING

HOPC: A NOVEL SIMILARITY METRIC BASED ON GEOMETRIC STRUCTURAL PROPERTIES FOR MULTI-MODAL REMOTE SENSING IMAGE MATCHING ISPRS Annls of the Photogrmmetry, Remote Sensing nd Sptil Informtion Sciences, Volume III-1, 216 XXIII ISPRS Congress, 12 19 July 216, Prgue, Czech Republic : A NOVEL SILARITY METRIC BASED ON GEOMETRIC

More information

Image Segmentation Using Wavelet and watershed transform

Image Segmentation Using Wavelet and watershed transform Imge Segmenttion Using Wvelet nd wtershed trnsform Atollh Hdddi, Mhmod R. Shei, Mohmmd J. Vldn Zoej, Ali mohmmdzdeh Fculty of Geodesy nd Geomtics Engineering, K. N. Toosi University of Technology, Vli_Asr

More information

Algorithm Design (5) Text Search

Algorithm Design (5) Text Search Algorithm Design (5) Text Serch Tkshi Chikym School of Engineering The University of Tokyo Text Serch Find sustring tht mtches the given key string in text dt of lrge mount Key string: chr x[m] Text Dt:

More information

Statistical classification of spatial relationships among mathematical symbols

Statistical classification of spatial relationships among mathematical symbols 2009 10th Interntionl Conference on Document Anlysis nd Recognition Sttisticl clssifiction of sptil reltionships mong mthemticl symbols Wl Aly, Seiichi Uchid Deprtment of Intelligent Systems, Kyushu University

More information

If you are at the university, either physically or via the VPN, you can download the chapters of this book as PDFs.

If you are at the university, either physically or via the VPN, you can download the chapters of this book as PDFs. Lecture 5 Wlks, Trils, Pths nd Connectedness Reding: Some of the mteril in this lecture comes from Section 1.2 of Dieter Jungnickel (2008), Grphs, Networks nd Algorithms, 3rd edition, which is ville online

More information

A New Learning Algorithm for the MAXQ Hierarchical Reinforcement Learning Method

A New Learning Algorithm for the MAXQ Hierarchical Reinforcement Learning Method A New Lerning Algorithm for the MAXQ Hierrchicl Reinforcement Lerning Method Frzneh Mirzzdeh 1, Bbk Behsz 2, nd Hmid Beigy 1 1 Deprtment of Computer Engineering, Shrif University of Technology, Tehrn,

More information

Grade 7/8 Math Circles Geometric Arithmetic October 31, 2012

Grade 7/8 Math Circles Geometric Arithmetic October 31, 2012 Fculty of Mthemtics Wterloo, Ontrio N2L 3G1 Grde 7/8 Mth Circles Geometric Arithmetic Octoer 31, 2012 Centre for Eduction in Mthemtics nd Computing Ancient Greece hs given irth to some of the most importnt

More information

INTRODUCTION TO SIMPLICIAL COMPLEXES

INTRODUCTION TO SIMPLICIAL COMPLEXES INTRODUCTION TO SIMPLICIAL COMPLEXES CASEY KELLEHER AND ALESSANDRA PANTANO 0.1. Introduction. In this ctivity set we re going to introduce notion from Algebric Topology clled simplicil homology. The min

More information

II. THE ALGORITHM. A. Depth Map Processing

II. THE ALGORITHM. A. Depth Map Processing Lerning Plnr Geometric Scene Context Using Stereo Vision Pul G. Bumstrck, Bryn D. Brudevold, nd Pul D. Reynolds {pbumstrck,brynb,pulr2}@stnford.edu CS229 Finl Project Report December 15, 2006 Abstrct A

More information

Study Sheet ( )

Study Sheet ( ) Key Terms prol circle Ellipse hyperol directrix focus focl length xis of symmetry vertex Study Sheet (11.1-11.4) Conic Section A conic section is section of cone. The ellipse, prol, nd hyperol, long with

More information

A Sparse Grid Representation for Dynamic Three-Dimensional Worlds

A Sparse Grid Representation for Dynamic Three-Dimensional Worlds A Sprse Grid Representtion for Dynmic Three-Dimensionl Worlds Nthn R. Sturtevnt Deprtment of Computer Science University of Denver Denver, CO, 80208 sturtevnt@cs.du.edu Astrct Grid representtions offer

More information

Object-based extraction of buildings from very high resolution satellite images: A case study of Ho Chi Minh City, Viet Nam

Object-based extraction of buildings from very high resolution satellite images: A case study of Ho Chi Minh City, Viet Nam Object-bsed extrction of buildings from very high resolution stellite imges: A cse study of Ho Chi Minh City, Viet Nm T. T. Vu nd M. Mtsuok Erthquke Disster Mitigtion Reserch Center (EDM), Ntionl Reserch

More information

Naming 3D objects. 1 Name the 3D objects labelled in these models. Use the word bank to help you.

Naming 3D objects. 1 Name the 3D objects labelled in these models. Use the word bank to help you. Nming 3D ojects 1 Nme the 3D ojects lelled in these models. Use the word nk to help you. Word nk cue prism sphere cone cylinder pyrmid D A C F A B C D cone cylinder cue cylinder E B E prism F cue G G pyrmid

More information

Information Retrieval and Organisation

Information Retrieval and Organisation Informtion Retrievl nd Orgnistion Suffix Trees dpted from http://www.mth.tu.c.il/~himk/seminr02/suffixtrees.ppt Dell Zhng Birkeck, University of London Trie A tree representing set of strings { } eef d

More information

Lexical Analysis: Constructing a Scanner from Regular Expressions

Lexical Analysis: Constructing a Scanner from Regular Expressions Lexicl Anlysis: Constructing Scnner from Regulr Expressions Gol Show how to construct FA to recognize ny RE This Lecture Convert RE to n nondeterministic finite utomton (NFA) Use Thompson s construction

More information

CS201 Discussion 10 DRAWTREE + TRIES

CS201 Discussion 10 DRAWTREE + TRIES CS201 Discussion 10 DRAWTREE + TRIES DrwTree First instinct: recursion As very generic structure, we could tckle this problem s follows: drw(): Find the root drw(root) drw(root): Write the line for the

More information

this grammar generates the following language: Because this symbol will also be used in a later step, it receives the

this grammar generates the following language: Because this symbol will also be used in a later step, it receives the LR() nlysis Drwcks of LR(). Look-hed symols s eplined efore, concerning LR(), it is possile to consult the net set to determine, in the reduction sttes, for which symols it would e possile to perform reductions.

More information

Pythagoras theorem and trigonometry (2)

Pythagoras theorem and trigonometry (2) HPTR 10 Pythgors theorem nd trigonometry (2) 31 HPTR Liner equtions In hpter 19, Pythgors theorem nd trigonometry were used to find the lengths of sides nd the sizes of ngles in right-ngled tringles. These

More information

INVESTIGATION OF RESAMPLING EFFECTS ON IRS-1D PAN DATA

INVESTIGATION OF RESAMPLING EFFECTS ON IRS-1D PAN DATA INVESTIGATION OF RESAMPLING EFFECTS ON IRS-D PAN DATA Smpth Kumr P.,*, Onkr Dikshit nd YVS Murthy Geo-Informtics Division, Ntionl Remote Sensing Agency, Hyderd, Indi.-(smpth_k, murthy_yvs)@nrs.gov.in Deprtment

More information

Algebra II Notes Unit Ten: Conic Sections

Algebra II Notes Unit Ten: Conic Sections Sllus Ojective: 0. The student will sketch the grph of conic section with centers either t or not t the origin. (PARABOLAS) Review: The Midpoint Formul The midpoint M of the line segment connecting the

More information

Introduction Transformation formulae Polar graphs Standard curves Polar equations Test GRAPHS INU0114/514 (MATHS 1)

Introduction Transformation formulae Polar graphs Standard curves Polar equations Test GRAPHS INU0114/514 (MATHS 1) POLAR EQUATIONS AND GRAPHS GEOMETRY INU4/54 (MATHS ) Dr Adrin Jnnett MIMA CMth FRAS Polr equtions nd grphs / 6 Adrin Jnnett Objectives The purpose of this presenttion is to cover the following topics:

More information

CS481: Bioinformatics Algorithms

CS481: Bioinformatics Algorithms CS481: Bioinformtics Algorithms Cn Alkn EA509 clkn@cs.ilkent.edu.tr http://www.cs.ilkent.edu.tr/~clkn/teching/cs481/ EXACT STRING MATCHING Fingerprint ide Assume: We cn compute fingerprint f(p) of P in

More information

Philosophy Of Creating Macros In Accumark CAD System

Philosophy Of Creating Macros In Accumark CAD System Philosophy Of Creting Mcros In Accumrk CAD System Mrie Nejedl Astrct: - The rticle discusses promising method of creting documenttion in design preprtion of clothing production using the "Mcro" module.

More information

2014 Haskell January Test Regular Expressions and Finite Automata

2014 Haskell January Test Regular Expressions and Finite Automata 0 Hskell Jnury Test Regulr Expressions nd Finite Automt This test comprises four prts nd the mximum mrk is 5. Prts I, II nd III re worth 3 of the 5 mrks vilble. The 0 Hskell Progrmming Prize will be wrded

More information

9 Graph Cutting Procedures

9 Graph Cutting Procedures 9 Grph Cutting Procedures Lst clss we begn looking t how to embed rbitrry metrics into distributions of trees, nd proved the following theorem due to Brtl (1996): Theorem 9.1 (Brtl (1996)) Given metric

More information

Conic Sections Parabola Objective: Define conic section, parabola, draw a parabola, standard equations and their graphs

Conic Sections Parabola Objective: Define conic section, parabola, draw a parabola, standard equations and their graphs Conic Sections Prol Ojective: Define conic section, prol, drw prol, stndrd equtions nd their grphs The curves creted y intersecting doule npped right circulr cone with plne re clled conic sections. If

More information

AN EFFICIENT MULTI-SCALE SEGMENTATION FOR HIGH-RESOLUTION REMOTE SENSING IMAGERY BASED ON STATISTICAL REGION MERGING AND MINIMUM HETEROGENEITY RULE

AN EFFICIENT MULTI-SCALE SEGMENTATION FOR HIGH-RESOLUTION REMOTE SENSING IMAGERY BASED ON STATISTICAL REGION MERGING AND MINIMUM HETEROGENEITY RULE AN EFFICIENT MULTI-SCALE SEGMENTATION FOR HIGH-RESOLUTION REMOTE SENSING IMAGERY BASED ON STATISTICAL REGION MERGING AND MINIMUM HETEROGENEITY RULE H. T. Li H.Y. Gu b Y. S. Hn J. H. Yng S. S. Hn b Institute

More information

Announcements. CS 188: Artificial Intelligence Fall Recap: Search. Today. General Tree Search. Uniform Cost. Lecture 3: A* Search 9/4/2007

Announcements. CS 188: Artificial Intelligence Fall Recap: Search. Today. General Tree Search. Uniform Cost. Lecture 3: A* Search 9/4/2007 CS 88: Artificil Intelligence Fll 2007 Lecture : A* Serch 9/4/2007 Dn Klein UC Berkeley Mny slides over the course dpted from either Sturt Russell or Andrew Moore Announcements Sections: New section 06:

More information

LETKF compared to 4DVAR for assimilation of surface pressure observations in IFS

LETKF compared to 4DVAR for assimilation of surface pressure observations in IFS LETKF compred to 4DVAR for ssimiltion of surfce pressure oservtions in IFS Pu Escrià, Mssimo Bonvit, Mts Hmrud, Lrs Isksen nd Pul Poli Interntionl Conference on Ensemle Methods in Geophysicl Sciences Toulouse,

More information

Unit #9 : Definite Integral Properties, Fundamental Theorem of Calculus

Unit #9 : Definite Integral Properties, Fundamental Theorem of Calculus Unit #9 : Definite Integrl Properties, Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl

More information

Today. CS 188: Artificial Intelligence Fall Recap: Search. Example: Pancake Problem. Example: Pancake Problem. General Tree Search.

Today. CS 188: Artificial Intelligence Fall Recap: Search. Example: Pancake Problem. Example: Pancake Problem. General Tree Search. CS 88: Artificil Intelligence Fll 00 Lecture : A* Serch 9//00 A* Serch rph Serch Tody Heuristic Design Dn Klein UC Berkeley Multiple slides from Sturt Russell or Andrew Moore Recp: Serch Exmple: Pncke

More information

50 AMC LECTURES Lecture 2 Analytic Geometry Distance and Lines. can be calculated by the following formula:

50 AMC LECTURES Lecture 2 Analytic Geometry Distance and Lines. can be calculated by the following formula: 5 AMC LECTURES Lecture Anlytic Geometry Distnce nd Lines BASIC KNOWLEDGE. Distnce formul The distnce (d) between two points P ( x, y) nd P ( x, y) cn be clculted by the following formul: d ( x y () x )

More information

Announcements. CS 188: Artificial Intelligence Fall Recap: Search. Today. Example: Pancake Problem. Example: Pancake Problem

Announcements. CS 188: Artificial Intelligence Fall Recap: Search. Today. Example: Pancake Problem. Example: Pancake Problem Announcements Project : erch It s live! Due 9/. trt erly nd sk questions. It s longer thn most! Need prtner? Come up fter clss or try Pizz ections: cn go to ny, ut hve priority in your own C 88: Artificil

More information

OUTPUT DELIVERY SYSTEM

OUTPUT DELIVERY SYSTEM Differences in ODS formtting for HTML with Proc Print nd Proc Report Lur L. M. Thornton, USDA-ARS, Animl Improvement Progrms Lortory, Beltsville, MD ABSTRACT While Proc Print is terrific tool for dt checking

More information

Systems I. Logic Design I. Topics Digital logic Logic gates Simple combinational logic circuits

Systems I. Logic Design I. Topics Digital logic Logic gates Simple combinational logic circuits Systems I Logic Design I Topics Digitl logic Logic gtes Simple comintionl logic circuits Simple C sttement.. C = + ; Wht pieces of hrdwre do you think you might need? Storge - for vlues,, C Computtion

More information

Lily Yen and Mogens Hansen

Lily Yen and Mogens Hansen SKOLID / SKOLID No. 8 Lily Yen nd Mogens Hnsen Skolid hs joined Mthemticl Myhem which is eing reformtted s stnd-lone mthemtics journl for high school students. Solutions to prolems tht ppered in the lst

More information