Object Removal by Exemplar-Based Inpainting

Size: px
Start display at page:

Download "Object Removal by Exemplar-Based Inpainting"

Transcription

1 Oject Removl y Exemplr-Bsed Inpinting A. Criminisi, P. Pérez K. Toym Microsoft Reserch Ltd., Cmridge, UK Microsoft Corportion, Redmond, WA, USA Astrct A new lgorithm is proposed for removing lrge ojects from digitl imges. The chllenge is to fill in the hole tht is left ehind in visully plusile wy. In the pst, this prolem hs een ddressed y two clsses of lgorithms: (i) texture synthesis lgorithms for generting lrge imge regions from smple textures, nd (ii) inpinting techniques for filling in smll imge gps. The former work well for textures repeting twodimensionl ptterns with some stochsticity; the ltter focus on liner structures which cn e thought of s onedimensionl ptterns, such s lines nd oject contours. This pper presents novel nd efficient lgorithm tht comines the dvntges of these two pproches. We first note tht exemplr-sed texture synthesis contins the essentil process required to replicte oth texture nd structure; the success of structure propgtion, however, is highly dependent on the order in which the filling proceeds. We propose est-first lgorithm in which the confidence in the synthesized pixel vlues is propgted in mnner similr to the propgtion of informtion in inpinting. The ctul colour vlues re computed using exemplr-sed synthesis. Computtionl efficiency is chieved y locksed smpling process. A numer of exmples on rel nd synthetic imges demonstrte the effectiveness of our lgorithm in removing lrge occluding ojects s well s thin scrtches. Roustness with respect to the shpe of the mnully selected trget region is lso demonstrted. Our results compre fvorly to those otined y existing techniques. 1. Introduction This pper presents novel lgorithm for removing ojects from digitl photogrphs nd replcing them with visully plusile ckgrounds. Figure 1 shows n exmple of this tsk, where the foreground person (mnully selected s the trget region) is replced y textures smpled from the reminder of the imge. The lgorithm effectively hllucintes new colour vlues for the trget region in wy tht looks resonle to the humn eye. In previous work, severl reserchers hve considered texture synthesis s wy to fill lrge imge regions with Figure 1: Removing lrge ojects from imges. () Originl imge. () The region corresponding to the foreground person (covering out 19% of the imge) hs een mnully selected nd then utomticlly removed. Notice tht the horizontl structures of the fountin hve een synthesized in the occluded re together with the wter, grss nd rock textures. pure textures repetitive two-dimensionl texturl ptterns with moderte stochsticity. This is sed on lrge ody of texture-synthesis reserch, which seeks to replicte texture d infinitum, given smll source smple of pure texture [1, 8, 9, 10, 11, 12, 14, 15, 16, 19, 22]. Of prticulr interest re exemplr-sed techniques which cheply nd effectively generte new texture y smpling nd copying colour vlues from the source [1, 9, 10, 11, 15]. As effective s these techniques re in replicting consistent texture, they hve difficulty filling holes in photogrphs of rel-world scenes, which often consist of liner structures nd composite textures multiple textures intercting sptilly [23]. The min prolem is tht oundries etween imge regions re complex product of mutul influences etween different textures. In constrst to the twodimensionl nture of pure textures, these oundries form wht might e considered more one-dimensionl, or liner, imge structures. A numer of lgorithms specificlly ddress this issue for the tsk of imge restortion, where speckles, scrtches, nd overlid text re removed [2, 3, 4, 7, 20]. These imge inpinting techniques fill holes in imges y propgting liner structures (clled isophotes in the inpinting literture) into the trget region vi diffusion. They re inspired y the prtil differentil equtions of physicl het flow, 1

2 nd work convincingly s restortion lgorithms. Their drwck is tht the diffusion process introduces some lur, which is noticele when the lgorithm is pplied to fill lrger regions. The lgorithm presented here comines the strengths of oth pproches. As with inpinting, we py specil ttention to liner structures. But, liner structures utting the trget region only influence the fill order of wht is t core n exemplr-sed texture synthesis lgorithm. The result is n lgorithm tht hs the efficiency nd qulittive performnce of exemplr-sed texture synthesis, ut which lso respects the imge constrints imposed y surrounding liner structures. Our lgorithm uilds on very recent reserch long similr lines. The work in [5] decomposes the originl imge into two components; one of which is processed y inpinting nd the other y texture synthesis. The output imge is the sum of the two processed components. This pproch still remins limited to the removl of smll imge gps, however, s the diffusion process continues to lur the filled region (cf., [5], fig.5 top right). The utomtic switching etween pure texture- nd pure structure-mode descried in [21] is lso voided. One of the first ttempts to use exemplr-sed synthesis specificlly for oject removl ws y Hrrison [13]. There, the order in which pixel in the trget region is filled ws dictted y the level of texturedness of the pixel s neighorhood 1. Although the intuition is sound, strong liner structures were often overruled y nery noise, minimizing the vlue of the extr computtion. A relted technique drove the fill order y the locl shpe of the trget region, ut did not seek to explicitly propgte liner structure [6]. Finlly, Zlesny et l. [23] descrie n interesting lgorithm for the prllel synthesis of composite textures. They devise specil-purpose solution for the interfce etween two textures. In this pper we show tht, in fct, only one mechnism is sufficient for the synthesis of oth pure nd composite textures. Section 2 presents the key oservtion on which our lgorithm depends. Section 3 descries the detils of the lgorithm. Results on oth synthetic nd rel imgery re presented in section Exemplr-sed synthesis suffices The core of our lgorithm is n isophote-driven imgesmpling process. It is well-understood tht exemplrsed pproches perform well for two-dimensionl textures [1, 9, 15]. But, we note in ddition tht exemplrsed texture synthesis is sufficient for propgting extended liner imge structures, s well. A seprte synthesis 1 An implementtion of Hrrison s lgorithm is ville from pfh/resynthesizer/ Figure 2: Structure propgtion y exemplr-sed texture synthesis. () Originl imge, with the trget region Ω, its contour δω nd the source region Φ clerly mrked. () We wnt to synthesize the re delimited y the ptch Ψ p centred on the point p δω. (c) The most likely cndidte mtches for Ψ p lie long the oundry etween the two textures in the source region, e.g., Ψ q nd Ψ q. (d) The est mtching ptch in the cndidtes set hs een copied into the position occupied y Ψ p, thus chieving prtil filling of Ω. The trget region Ω hs, now, shrnk nd its front hs ssumed different shpe. See text for detils. mechnism is not required for hndling isophotes. Figure 2 illustrtes this point. For ese of comprison, we dopt nottion similr to tht used in the inpinting literture. The region to e filled, i.e., the trget region is indicted y Ω, nd its contour is denoted δω. The contour evolves inwrd s the lgorithm progresses, nd so we lso refer to it s the fill front. The source region, Φ, which remins fixed throughout the lgorithm, provides smples used in the filling process. We now focus on single itertion of the lgorithm to show how structure nd texture re dequtely hndled y exemplr-sed synthesis. Suppose tht the squre templte Ψ p Ω centred t the point p (fig. 2), is to e filled. The est-mtch smple from the source region comes from the ptch Ψˆq Φ, which is most similr to those prts tht re lredy filled in Ψ p. In the exmple in fig. 2, we see tht if Ψ p lies on the continution of n imge edge, the most likely est mtches will lie long the sme (or similrly coloured) edge (e.g., Ψ q nd Ψ q in fig. 2c). All tht is required to propgte the isophote inwrds is simple trnsfer of the pttern from the est-mtch source ptch (fig. 2d). Notice tht isophote orienttion is utomticlly preserved. In the figure, despite the fct tht the originl edge is not orthogonl to the trget contour δω, the propgted structure hs mintined the sme orienttion s in the source region. 3. Region-filling lgorithm We now proceed with the detils of our lgorithm. First, user selects trget region, Ω, to e removed nd filled. The source region, Φ, my e defined s the entire imge minus the trget region (Φ = I Ω), s dilted nd round the trget region, or it my e mnully specified y the user. Next, s with ll exemplr-sed texture synthesis [10], the size of the templte window Ψ must e specified. We provide defult window size of 9 9 pixels, ut in prctice require the user to set it to e slightly lrger thn the lrgest 2

3 Figure 3: Nottion digrm. Given the ptch Ψ p, n p is the norml to the contour δω of the trget region Ω nd Ip is the isophote (direction nd intensity) t point p. The entire imge is denoted with I. distinguishle texture element, or texel, in the source region. Once these prmeters re determined, the reminder of the region-filling process is completely utomtic. In our lgorithm, ech pixel mintins colour vlue (or empty, if the pixel is unfilled) nd confidence vlue, which reflects our confidence in the pixel vlue, nd which is frozen once pixel hs een filled. During the course of the lgorithm, ptches long the fill front re lso given temporry priority vlue, which determines the order in which they re filled. Then, our lgorithm itertes the following three steps until ll pixels hve een filled: 1. Computing ptch priorities. Filling order is crucil to non-prmetric texture synthesis [1, 6, 10, 13]. Thus fr, the defult fvourite hs een the onion peel method, where the trget region is synthesized from the outside inwrd, in concentric lyers. To our knowledge, however, designing fill order which explicitly encourges propgtion of liner structure (together with texture) hs never een explored. Our lgorithm performs this tsk through est-first filling lgorithm tht depends entirely on the priority vlues tht re ssigned to ech ptch on the fill front. The priority computtion is ised towrd those ptches which re on the continution of strong edges nd which re surrounded y high-confidence pixels. Given ptch Ψ p centred t the point p for some p δω (see fig. 3), its priority P (p) is defined s the product of two terms: P (p) = C(p)D(p). (1) We cll C(p) the confidence term nd D(p) the dt term, nd they re defined s follows: q Ψ C(p) = p Ω C(q), D(p) = I p n p Ψ p α where Ψ p is the re of Ψ p, α is normliztion fctor (e.g., α = 255 for typicl grey-level imge), nd n p is unit vector orthogonl to the front δω in the point p. The priority is computed for every order ptch, with distinct ptches for ech pixel on the oundry of the trget region. During initiliztion, the function C(p) is set to C(p) = 0 p Ω, nd C(p) = 1 p I Ω. The confidence term C(p) my e thought of s mesure of the mount of relile informtion surrounding the pixel p. The intention is to fill first those ptches which hve more of their pixels lredy filled, with dditionl preference given to pixels tht were filled erly on (or tht were never prt of the trget region). This utomticlly incorportes preference towrds certin shpes long the fill front. For exmple, ptches tht include corners nd thin tendrils of the trget region will tend to e filled first, s they re surrounded y more pixels from the originl imge. These ptches provide more relile informtion ginst which to mtch. Conversely, ptches t the tip of peninsuls of filled pixels jutting into the trget region will tend to e set side until more of the surrounding pixels re filled in. At corse level, the term C(p) of (1) pproximtely enforces the desirle concentric fill order. As filling proceeds, pixels in the outer lyers of the trget region will tend to e chrcterized y greter confidence vlues, nd therefore e filled erlier; pixels in the centre of the trget region will hve lesser confidence vlues. The dt term D(p) is function of the strength of isophotes hitting the front δω t ech itertion. This term oosts the priority of ptch tht n isophote flows into. This fctor is of fundmentl importnce in our lgorithm ecuse it encourges liner structures to e synthesized first, nd, therefore propgted securely into the trget region. Broken lines tend to connect, thus relizing the Connectivity Principle of vision psychology [7, 17] (cf., fig. 4, fig. 7d, fig. 8 nd fig. 13d). There is delicte lnce etween the confidence nd dt terms. The dt term tends to push isophotes rpidly inwrd, while the confidence term tends to suppress precisely this sort of incursion into the trget region. As presented in the results section, this lnce is hndled grcefully vi the mechnism of single priority computtion for ll ptches on the fill front. Since the fill order of the trget region is dictted solely y the priority function P (p), we void hving to predefine n ritrry fill order s done in existing ptch-sed pproches [9, 19]. Our fill order is function of imge properties, resulting in n orgnic synthesis process tht elimintes the risk of roken-structure rtefcts (fig. 7c) nd lso reduces locky rtefcts without n expensive ptch-cutting step [9] or lur-inducing lending step [19]. 2. Propgting texture nd structure informtion. Once ll priorities on the fill front hve een computed, the ptch Ψˆp with highest priority is found. We then fill it with dt extrcted from the source region Φ. In trditionl inpinting techniques, pixel-vlue inform- 3

4 c d e f g Figure 4: Reliztion of the Connectivity Principle [7, 17] on synthetic exmple. () Originl imge, the Knizs tringle with rndom noise dded. () The occluding white tringle in the originl imge hs een mnully selected s the trget region (24% of totl imge re) nd mrked in red. (c...f) Different stges of the filling process. (d) Notice tht strong edges re pushed inside the trget region first nd tht shrp ppendices (e.g., the vertices of the red tringle) re rpidly smoothed. (f) When no structures hit the front δω the trget region evolves in roughly circulr shpe. (g) The output imge where the trget region hs een filled, i.e., the occluding tringle removed. Little imperfections re present in the curvture of the circles in the reconstructed res, while the sides of the internl tringle hve een correctly connected. The lur typicl of diffusion techniques is completely voided. See figs. 7, 8, 13 for further exmples of structurl continution. tion is propgted vi diffusion. As noted previously, diffusion necessrily leds to imge smoothing, which results in lurry fill-in, especilly of lrge regions (see fig. 10f). On the contrry, we propgte imge texture y direct smpling of the source region. Similr to [10], we serch in the source region for tht ptch which is most similr to Ψˆp. 2 Formlly, Ψˆq = rg min Ψ q Φ d(ψˆp, Ψ q ) (2) where the distnce d(ψ, Ψ ) etween two generic ptches Ψ nd Ψ is simply defined s the sum of squred differences (SSD) of the lredy filled pixels in the two ptches. We use the CIE L colour spce ecuse of its property of perceptul uniformity [18]. Hving found the source exemplr Ψˆq, the vlue of ech pixel-to-e-filled, p p Ψˆp Ω, is copied from its corresponding position inside Ψˆq. This suffices to chieve the propgtion of oth structure nd texture informtion from the source Φ to the trget region Ω, one ptch t time (cf., fig. 2d). In fct, we note tht ny further mnipultion of the pixel vlues (e.g., dding noise, smoothing nd so forth) tht does not explicitly depend upon sttistics of the source region, is fr more likely to degrde visul similrity etween the filled region nd the source region, thn to improve it. 3. Updting confidence vlues. After the ptch Ψˆp hs een filled with new pixel vlues, the confidence C(p) is updted in the re delimited y Ψˆp s follows: C(q) = C(ˆp) q Ψˆp Ω. This simple updte rule llows us to mesure the reltive confidence of ptches on the fill front, without imgespecific prmeters. As filling proceeds, confidence vlues decy, indicting tht we re less sure of the colour vlues of pixels ner the centre of the trget region. 2 Vlid ptches Ψˆq must e entirely contined in Φ. Extrct the mnully selected initil front δω 0. Repet until done: 1. Identify the fill front δω t. If Ω t =, exit. 1. Compute priorities P (p) p δω t. 2. Find the ptch Ψˆp with the mximum priority, i.e., Ψˆp ˆp = rg mx p δω t P (p) 2. Find the exemplr Ψˆq Φ tht minimizes d(ψˆp, Ψˆq ). 2c. Copy imge dt from Ψˆq to Ψˆp. 3. Updte C(p) p p Ψˆp Ω Tle 1: Region filling lgorithm. A pseudo-code description of the lgorithmic steps is shown in tle 1. The superscript t indictes the current itertion. 4. Results nd comprisons Here we pply our lgorithm to vriety of imges, rnging from purely synthetic imges to full-colour photogrphs tht include complex textures. Where possile, we mke side-y-side comprisons to previously proposed methods. In other cses, we hope the reder will refer to the originl source of our test imges (mny re tken from previous literture on inpinting nd texture synthesis) nd compre these results with the results of erlier work. In ll of the experiments, the ptch size ws set to e greter thn the lrgest texel or the thickest structure (e.g., edges) in the source region. Furthermore, unless otherwise stted the source region hs een set to e Φ = I Ω. All experiments were run on 2.5GHz Pentium IV with 1GB of RAM. The Knizs tringle. We perform our first experiment on the well-known Knizs tringle [17] to show how the lgorithm works on structure-rich synthetic imge. As shown in fig. 4, our lgorithm deforms the fill front δω under the ction of two forces: isophote continution (the dt term, D(p)) nd the pressure from surrounding filled pixels (the confidence term, C(p)). 4

5 c d Figure 7: Onion peel vs. structure-guided filling. () Originl imge. () The trget region hs een selected nd mrked in red. (c) Results of filling y concentric lyers. (d) Results of filling with our lgorithm. Thnks to the dt term in (1) the pole is reconstructed correctly. The shrp liner structures of the incomplete green tringle re grown into the trget region. But lso, no single structurl element domintes ll of the others; this lnce mong competing isophotes is chieved through the nturlly decying confidence vlues (in n erlier version of our lgorithm which lcked this lnce, runwy structures led to lrge-scle rtefcts.) Figures 4e,f lso show the effect of the confidence term in smoothing shrp ppendices such s the vertices of the trget region (in red). As descried ove, the confidence is propgted in mnner similr to the front-propgtion lgorithms used in inpinting. We stress, however, tht unlike inpinting, it is the confidence vlues tht re propgted long the front (nd which determine fill order), not colour vlues themselves, which re smpled from the source region. Finlly, we note tht despite the lrge size of the removed region, edges nd lines in the filled region re s shrp s ny found in the source region. There is no lurring from diffusion processes. This is property of exemplr-sed texture synthesis. The effect of different filling strtegies. Figures 5, 6 nd 7 demonstrte the effect of different filling strtegies. Figure 5f shows how our filling lgorithm chieves the est structurl continution in simple, synthetic imge. Figure 6 further demonstrtes the vlidity of our lgorithm on n eril photogrph. The pixel trget region hs een selected to strddle two different textures (fig. 6). The reminder of the imge in fig. 6 ws used s source for ll the experiments in fig. 6. With rster-scn synthesis (fig. 6c) not only does the top region (the river) grow into the ottom one (the city re), ut visile sems lso pper t the ottom of the trget region. This prolem is only prtilly ddressed y concentric filling (fig 6d). Similrly, in fig. 6e the sophisticted ordering proposed y Hrrison [13] only modertely succeeds in preventing this phenomenon. In ll of these cses, the primry difficulty is tht since the (eventul) texture oundry is the most constrined prt Figure 8: Comprison with trditionl structure inpinting. () Originl imge. () Oject removl nd structure recovery vi our lgorithm; to e compred with fig.4 in [4]. of the trget region, it should e filled first. But, unless this is explicitly ddressed in determining the fill order, the texture oundry is often the lst prt to e filled. The lgorithm proposed in this pper is designed to ddress this prolem, nd thus more nturlly extends the contour etween the two textures s well s the verticl grey rod. In the exmple in fig. 6, our lgorithm fills the trget region in only 2 seconds, on Pentium IV, 2.52GHz, 1GB RAM. Hrrison s resynthesizer [13], which is the nerest in qulity, requires pproximtely 45 seconds. Figure 7 shows yet nother comprison etween the concentric filling strtegy nd the proposed lgorithm. In the presence of concve trget regions, the onion peel filling my led to visile rtefcts such s unrelisticlly roken structures (see the pole in fig. 7c). Conversely, the presence of the dt term of (1) encourges the edges of the pole to grow first inside the trget region nd thus correctly reconstruct the complete pole (fig. 7d). This exmple demonstrtes the roustness of the proposed lgorithm with respect to the shpe of the selected trget region. Comprisons with inpinting. We now turn to some exmples from the inpinting literture. The first two exmples show tht our pproch works t lest s well s inpinting. The first (fig. 8) is synthesized imge of two ellipses [4]. The occluding white torus is removed from the input imge nd two drk ckground ellipses reconstructed vi our lgorithm (fig. 8). This exmple ws chosen y uthors of the originl work on inpinting to illustrte the structure propgtion cpilities of their lgorithm. Our results re visully identicl to those otined y inpinting ([4], fig.4). We now compre results of the restortion of n hnddrwn imge. In fig. 9 the im is to remove the foreground text. Our results (fig. 9) re mostly indistinguishle with those otined y trditionl inpinting 3. This exmple demonstrtes the effectiveness of oth techniques in imge restortion pplictions. It is in rel photogrphs with lrge ojects to remove, 3 5

6 c d e f Figure 5: Effect of filling order on synthetic imge. () The originl imge; () The trget region hs een selected nd mrked in lck; (c) Filling the trget region in rster-scn order; (d) Filling y concentric lyers; (e) The result of pplying Hrrison s technique which took 2 45 ; (f) Filling with our lgorithm which took 5. Notice tht even though the tringle upper vertex is not complete our technique performs etter thn the others. c d e f Figure 6: Effect of filling order on n eril photogrph. () The originl imge, n eril view of London. () The trget region hs een selected nd mrked in red; Notice tht it strddles two different textures; (c) Filling with rster-scn order; (d) Filling y concentric lyers; (e) The result of pplying Hrrison s technique (performed in 45 ); (f) Filling with our lgorithm (performed in 2 ). See text for detils. Figure 11 compres our lgorithm to the recent texture nd structure inpinting technique descried in [5]. Figure 11(ottom right) shows tht lso our lgorithm ccomplishes the propgtion of structure nd texture inside the selected trget region. Moreover, the lck of diffusion steps voids lurring propgted structures (see the verticl edge in the encircled region) nd mkes the lgorithm more computtionlly efficient. Figure 9: Imge restortion exmple. () Originl imge. The text occupies 9% of the totl imge re. () Result of text removl vi our lgorithm. however, tht the rel dvntges of our pproch ecome pprent. Figure 10 shows n exmple on rel photogrph, of ungee jumper in mid-jump (from [4], fig.8). In the originl work, the thin ungee cord is removed from the imge vi inpinting. In order to prove the cpilities of our lgorithm we removed the entire ungee jumper (fig. 10e). Structures such s the shore line nd the edge of the house hve een utomticlly propgted into the trget region long with plusile textures of shruery, wter nd roof tiles; nd ll this with no priori model of nything specific to this imge. For comprison, figure 10f shows the result of filling the sme trget region (fig. 10) y imge inpinting 4. Considerle lur is introduced into the trget region ecuse of inpinting s use of diffusion to propgte colour vlues; nd high-frequency texturl informtion is entirely sent ,000 itertions were run using the implementtion in j/inpinting/ Synthesizing composite textures. Fig. 12 demonstrtes tht our lgorithm ehves well lso t the oundry etween two different textures, such s the ones nlyzed in [23]. The trget region selected in fig. 12c strddles two different textures. The qulity of the knitting in the contour reconstructed vi our pproch (fig. 12d) is similr to the originl imge nd to the results otined in the originl work (fig. 12), ut gin, this hs een ccomplished without complicted texture models or seprte oundryspecific texture synthesis lgorithm. Further exmples on photogrphs. We show two more exmples on photogrphs of rel scenes. Figure 13 demonstrtes, gin, the dvntge of the proposed pproch in preventing structurl rtefcts (cf., 7d). While the onion-peel pproch produces deformed horizon, our lgorithm reconstructs the oundry etween sky nd se s convincing stright line. Finlly, in fig. 14, the foreground person hs een mnully selected nd the corresponding region filled in utomticlly. The filled region in the output imge convincingly mimics the complex ckground texture with no prominent rtefcts (fig. 14f). During the filling process the topologicl chnges of the trget region re hndled effortlessly. 6

7 c d e f Figure 10: Removing lrge ojects from photogrphs. () Originl imge (from [4]), pix. () The trget region (in white) covers 12% of the totl imge re. (c,d) Different stges of the filling process. Notice how the isophotes hitting the oundry of the trget region re propgted inwrds while thin ppendices (e.g., the rms) in the trget region tend to dispper quickly. (e) The finl imge where the ungee jumper hs een completely removed nd the occluded region reconstructed y our utomtic lgorithm (performed in 18, to e compred with 10 of Hrrison s resynthesizer). (f) The result of region filling y trditionl imge inpinting. Notice the lur introduced y the diffusion process nd the complete lck of texture in the synthesized re. 5. Conclusion nd future work This pper hs presented novel lgorithm for removing lrge ojects from digitl photogrphs. The result of oject removl is n imge in which the selected oject hs een replced y visully plusile ckground tht mimics the ppernce of the source region. Our pproch employs n exemplr-sed texture synthesis technique modulted y unified scheme for determining the fill order of the trget region. Pixels mintin confidence vlue, which together with imge isophotes, influence their fill priority. The technique is cple of propgting oth liner structure nd two-dimensionl texture into the trget region. Comprtive experiments show tht creful selection of the fill order is necessry nd sufficient to hndle this tsk. Our method performs t lest s well s previous techniques designed for the restortion of smll scrtches, nd in instnces in which lrger ojects re removed, it drmticlly outperforms erlier work in terms of oth perceptul qulity nd computtionl efficiency. Currently, we re investigting extensions for more ccurte propgtion of curved structures in still photogrphs nd for oject removl from video, which promise to impose n entirely new set of chllenges. Acknowledgements. The uthors would like to thnk M. Gngnet, A. Blke nd P. Anndn for inspiring discussions; nd G. Spiro, M. Bertlmio, L. vn Gool nd A. Zlesny for mking some of their imges ville. References [1] M. Ashikhmin. Synthesizing nturl textures. In Proc. ACM Symp. on Interctive 3D Grphics, pp , Reserch Tringle Prk, NC, Mr [2] C. Bllester, V. Cselles, J. Verder, M. Bertlmio, nd G. Spiro. A vritionl model for filling-in gry level nd color imges. In Proc. ICCV, pp. I: 10 16, Vncouver, Cnd, Jun Figure 11: Comprison with texture nd structure inpinting. (Top) Originl imge (from [5]). The trget regions re mrked in white. (Bottom left) Region filling vi the inpinting lgorithm in [5]. Notice the lur of the edge in the circled region. (Bottom right) The result of our lgorithm. Both structure nd texture hve een nicely propgted inside the trget region. The edge in the circled region is noticely shrper. [3] M. Bertlmio, A.L. Bertozzi, nd G. Spiro. Nvier-stokes, fluid dynmics, nd imge nd video inpinting. In Proc. Conf. Comp. Vision Pttern Rec., pp. I: , Hwi, Dec [4] M. Bertlmio, G. Spiro, V. Cselles, nd C. Bllester. Imge inpinting. In Proc. ACM Conf. Comp. Grphics (SIGGRAPH), pp , New Orlens, LU, Jul guille/inpinting.htm. [5] M. Bertlmio, L. Vese, G. Spiro, nd S. Osher. Simultneous structure nd texture imge inpinting. to pper, guille/inpinting.htm. [6] R. Bornrd, E. Lecn, L. Lorelli, nd J-H. Chenot. Missing dt correction in still imges nd imge sequences. In ACM Multimedi, Frnce, Dec [7] T. F. Chn nd J. Shen. Non-texture inpinting y curvture-driven diffusions (CDD). J. Visul Comm. Imge Rep., 4(12), [8] J.S. de Bonet. Multiresolution smpling procedure for nlysis nd synthesis of texture imges. In Proc. ACM Conf. Comp. Grphics (SIGGRAPH), volume 31, pp , [9] A. Efros nd W.T. Freemn. Imge quilting for texture synthesis nd trnsfer. In Proc. ACM Conf. Comp. Grphics (SIGGRAPH), pp , Eugene Fiume, Aug

8 c Figure 12: Comprison with prllel composite texture synthesis. () Originl imge, the fur of zer (from [23]). () The result of the synthesis lgorithm descried in [23]. (c) Originl imge with the trget region mrked in red (22% of totl imge size). (d) The trget region hs een filled vi our lgorithm. The knitting effect long the oundry etween the two textures is correctly reproduced y our technique. [10] A. Efros nd T. Leung. Texture synthesis y non-prmetric smpling. In Proc. ICCV, pp , Kerkyr, Greece, Sep [11] W.T. Freemn, E.C. Psztor, nd O.T. Crmichel. Lerning lowlevel vision. Int. J. Computer Vision, 40(1):25 47, [12] D. Grer. Computtionl Models for Texture Anlysis nd Texture Synthesis. PhD thesis, Univ. of Southern Cliforni, USA, [13] P. Hrrison. A non-hierrchicl procedure for re-synthesis of complex texture. In Proc. Int. Conf. Centrl Europe Comp. Grphics, Visu. nd Comp. Vision, Plzen, Czech Repulic, Fe [14] D.J. Heeger nd J.R. Bergen. Pyrmid-sed texture nlysis/synthesis. In Proc. ACM Conf. Comp. Grphics (SIGGRAPH), volume 29, pp , Los Angeles, CA, [15] A. Hertzmnn, C. Jcos, N. Oliver, B. Curless, nd D. Slesin. Imge nlogies. In Proc. ACM Conf. Comp. Grphics (SIGGRAPH), Eugene Fiume, Aug [16] H. Igehy nd L. Pereir. Imge replcement through texture synthesis. In Proc. Int. Conf. Imge Processing, pp. III: , [17] G. Knizs. Orgniztion in Vision. Preger, New York, [18] J. M. Ksson nd W. Plouffe. An nlysis of selected computer interchnge color spces. In ACM Trnsctions on Grphics, volume 11, pp , Oct [19] L. Ling, C. Liu, Y.-Q. Xu, B. Guo, nd H.-Y. Shum. Rel-time texture synthesis y ptch-sed smpling. In ACM Trnsctions on Grphics, [20] S. Msnou nd J.-M. Morel. Level lines sed disocclusion. In Int. Conf. Imge Processing, Chicgo, [21] S. Rne, G. Spiro, nd M. Bertlmio. Structure nd texture fillingin of missing imge locks in wireless trnsmission nd compression pplictions. In IEEE. Trns. Imge Processing, to pper. [22] L.-W. Wey nd M. Levoy. Fst texture synthesis using treestructured vector quntiztion. In Proc. ACM Conf. Comp. Grphics (SIGGRAPH), [23] A. Zlesny, V. Ferrri, G. Cenen, nd L. vn Gool. Prllel composite texture synthesis. In Texture 2002 workshop - (in conjunction with ECCV02), Copenhgen, Denmrk, Jun d c Figure 13: Concentric-lyer filling vs. the proposed guided filling lgorithm. () Originl imge. () The mnully selected trget region (20% of the totl imge re, in red). (c) The result of filling y concentric lyers. The deformtion of the horizon is cused y the fct tht in the concentric lyers filling sky nd se grow inwrds t the sme speed. Thus, the reconstructed sky-se oundry tends to follow the skeleton of the selected trget region. (d) The result of filling y the proposed lgorithm. The horizon is correctly reconstructed s stright line. c e Figure 14: Removing lrge ojects from photogrphs. () Originl imge. () The trget region (10% of the totl imge re) hs een lnked out. (c...e) Intermedite stges of the filling process. (f) The trget region hs een completely filled nd the selected oject removed. The source region hs een utomticlly selected s nd round the trget region. The edges of the stones hve een nicely propgted inside the trget region together with the wter texture. d d f 8

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

Reasoning to Solve Equations and Inequalities

Reasoning to Solve Equations and Inequalities Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

Gaze Manipulation for One-to-one Teleconferencing

Gaze Manipulation for One-to-one Teleconferencing Gze Mnipultion for One-to-one Teleconferencing A. Criminisi, J. Shotton, A. Blke, P.H.S. Torr Microsoft Reserch Ltd, Cmridge, UK Astrct A new lgorithm is proposed for novel view genertion in one-toone

More information

Gaze Manipulation for One-to-one Teleconferencing

Gaze Manipulation for One-to-one Teleconferencing Gze Mnipultion for One-to-one Teleconferencing A. Criminisi, J. Shotton, A. Blke, P.H.S. Torr Microsoft Reserch Ltd, Cmridge, UK Astrct A new lgorithm is proposed for novel view genertion in one-toone

More information

Square Roots Teacher Notes

Square Roots Teacher Notes Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this

More information

Multiblending: displaying overlapping windows simultaneously without the drawbacks of alpha blending

Multiblending: displaying overlapping windows simultaneously without the drawbacks of alpha blending Multilending: displying overlpping windows simultneously without the drwcks of lph lending Ptrick Budisch Microsoft Reserch One Microsoft Wy, Redmond, WA 98052, USA ABSTRACT Alph lending llows the simultneous

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions. Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

More information

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one. 5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324 A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................

More information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

Regular Sets and Expressions

Regular Sets and Expressions Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite

More information

The Math Learning Center PO Box 12929, Salem, Oregon 97309 0929 Math Learning Center

The Math Learning Center PO Box 12929, Salem, Oregon 97309 0929  Math Learning Center Resource Overview Quntile Mesure: Skill or Concept: 1010Q Determine perimeter using concrete models, nonstndrd units, nd stndrd units. (QT M 146) Use models to develop formuls for finding res of tringles,

More information

Assuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C;

Assuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C; B-26 Appendix B The Bsics of Logic Design Check Yourself ALU n [Arthritic Logic Unit or (rre) Arithmetic Logic Unit] A rndom-numer genertor supplied s stndrd with ll computer systems Stn Kelly-Bootle,

More information

APPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS

APPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS APPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS TABLE OF FIGURES Figure 1: Spectrl Response of CMOS Imge Sensor...3 Figure 2: Byer CFA Ptterns...4

More information

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful Pentominoes Bruce Bguley Cscde Mth Systems, LLC Astrct. Pentominoes nd their reltives the polyominoes, polycues, nd polyhypercues will e used to explore nd pply vrious importnt mthemticl concepts. In this

More information

Math 135 Circles and Completing the Square Examples

Math 135 Circles and Completing the Square Examples Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

A Network Management System for Power-Line Communications and its Verification by Simulation

A Network Management System for Power-Line Communications and its Verification by Simulation A Network Mngement System for Power-Line Communictions nd its Verifiction y Simultion Mrkus Seeck, Gerd Bumiller GmH Unterschluerscher-Huptstr. 10, D-90613 Großhersdorf, Germny Phone: +49 9105 9960-51,

More information

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3. The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only

More information

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001 CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

Econ 4721 Money and Banking Problem Set 2 Answer Key

Econ 4721 Money and Banking Problem Set 2 Answer Key Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in

More information

Small Business Networking

Small Business Networking Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

STUDY ON 3D TEXTURED BUILDING MODEL BASED ON ADS40 IMAGE AND 3D MODEL

STUDY ON 3D TEXTURED BUILDING MODEL BASED ON ADS40 IMAGE AND 3D MODEL STUDY ON 3D TEXTURED BUILDING MODEL BASED ON ADS4 IMAGE AND 3D MODEL Liu Zhen,, *, Gong Peng c, Shi Peijun Ssgw T d College of Resource Science & Technology, Beijing Norml University,1875, liuzhen@nu.edu.cn

More information

Helicopter Theme and Variations

Helicopter Theme and Variations Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the

More information

RTL Power Optimization with Gate-level Accuracy

RTL Power Optimization with Gate-level Accuracy RTL Power Optimiztion with Gte-level Accurcy Qi Wng Cdence Design Systems, Inc Sumit Roy Clypto Design Systems, Inc 555 River Oks Prkwy, Sn Jose 95125 2903 Bunker Hill Lne, Suite 208, SntClr 95054 qwng@cdence.com

More information

Concept Formation Using Graph Grammars

Concept Formation Using Graph Grammars Concept Formtion Using Grph Grmmrs Istvn Jonyer, Lwrence B. Holder nd Dine J. Cook Deprtment of Computer Science nd Engineering University of Texs t Arlington Box 19015 (416 Ytes St.), Arlington, TX 76019-0015

More information

AntiSpyware Enterprise Module 8.5

AntiSpyware Enterprise Module 8.5 AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility

More information

Radius of the Earth - Radii Used in Geodesy James R. Clynch February 2006

Radius of the Earth - Radii Used in Geodesy James R. Clynch February 2006 dius of the Erth - dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives

More information

T H E S E C U R E T R A N S M I S S I O N P R O T O C O L O F S E N S O R A D H O C N E T W O R K

T H E S E C U R E T R A N S M I S S I O N P R O T O C O L O F S E N S O R A D H O C N E T W O R K Z E S Z Y T Y N A U K O W E A K A D E M I I M A R Y N A R K I W O J E N N E J S C I E N T I F I C J O U R N A L O F P O L I S H N A V A L A C A D E M Y 2015 (LVI) 4 (203) A n d r z e j M r c z k DOI: 10.5604/0860889X.1187607

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

5 a LAN 6 a gateway 7 a modem

5 a LAN 6 a gateway 7 a modem STARTER With the help of this digrm, try to descrie the function of these components of typicl network system: 1 file server 2 ridge 3 router 4 ckone 5 LAN 6 gtewy 7 modem Another Novell LAN Router Internet

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the

More information

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks

More information

GFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI Softwre www.gfi.com GFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI MilArchiver 6 C2C Archive One Policy Mnger Who we re Generl fetures Supports

More information

Factoring Trinomials of the Form. x 2 b x c. Example 1 Factoring Trinomials. The product of 4 and 2 is 8. The sum of 3 and 2 is 5.

Factoring Trinomials of the Form. x 2 b x c. Example 1 Factoring Trinomials. The product of 4 and 2 is 8. The sum of 3 and 2 is 5. Section P.6 Fctoring Trinomils 6 P.6 Fctoring Trinomils Wht you should lern: Fctor trinomils of the form 2 c Fctor trinomils of the form 2 c Fctor trinomils y grouping Fctor perfect squre trinomils Select

More information

SPH simulation of fluid-structure interaction problems

SPH simulation of fluid-structure interaction problems Diprtimento di ingegneri idrulic e mientle SPH simultion of fluid-structure interction prolems C. Antoci, M. Gllti, S. Siill Reserch project Prolem: deformtion of plte due to the ction of fluid (lrge displcement

More information

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1. Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose

More information

VMware Horizon Mirage Web Manager Guide

VMware Horizon Mirage Web Manager Guide VMwre Horizon Mirge We Mnger Guide Horizon Mirge 4.3 This document supports the version of ech product listed nd supports ll susequent versions until the document is replced y new edition. To check for

More information

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn 33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of

More information

Experiment 6: Friction

Experiment 6: Friction Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht

More information

** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand

** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl

More information

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of

More information

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Learner-oriented distance education supporting service system model and applied research

Learner-oriented distance education supporting service system model and applied research SHS Web of Conferences 24, 02001 (2016) DOI: 10.1051/ shsconf/20162402001 C Owned by the uthors, published by EDP Sciences, 2016 Lerner-oriented distnce eduction supporting service system model nd pplied

More information

Integration. 148 Chapter 7 Integration

Integration. 148 Chapter 7 Integration 48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but

More information

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999 Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control Chpter 5 Configurtion of ISDN Protocols This chpter provides instructions for configuring the ISDN protocols in the SP201 for signling conversion. Use the sections tht reflect the softwre you re configuring.

More information

Neighborhood Based Fast Graph Search in Large Networks

Neighborhood Based Fast Graph Search in Large Networks Neighborhood Bsed Fst Grph Serch in Lrge Networks Arijit Khn Dept. of Computer Science University of Cliforni Snt Brbr, CA 9306 rijitkhn@cs.ucsb.edu Ziyu Gun Dept. of Computer Science University of Cliforni

More information

COVER CROP VARIETY AND SEEDING RATE EFFECTS ON WINTER WEED SEED PRODUCTION

COVER CROP VARIETY AND SEEDING RATE EFFECTS ON WINTER WEED SEED PRODUCTION COVER CROP VARIETY AND SEEDING RATE EFFECTS ON WINTER WEED SEED PRODUCTION Nthn S. Boyd nd Eric B. Brennn, USDA-ARS, Orgnic Reserch Progrm, 1636 E. Alisl Street, Slins, CA 93905 Astrct Weed mngement is

More information

Simulation of operation modes of isochronous cyclotron by a new interative method

Simulation of operation modes of isochronous cyclotron by a new interative method NUKLEONIKA 27;52(1):29 34 ORIGINAL PAPER Simultion of opertion modes of isochronous cyclotron y new intertive method Ryszrd Trszkiewicz, Mrek Tlch, Jcek Sulikowski, Henryk Doruch, Tdeusz Norys, Artur Srok,

More information

Rethinking Virtual Network Embedding: Substrate Support for Path Splitting and Migration

Rethinking Virtual Network Embedding: Substrate Support for Path Splitting and Migration Rethinking Virtul Network Emedding: Sustrte Support for Pth Splitting nd Migrtion Minln Yu, Yung Yi, Jennifer Rexford, Mung Ching Princeton University Princeton, NJ {minlnyu,yyi,jrex,chingm}@princeton.edu

More information

A Note on Complement of Trapezoidal Fuzzy Numbers Using the α-cut Method

A Note on Complement of Trapezoidal Fuzzy Numbers Using the α-cut Method Interntionl Journl of Applictions of Fuzzy Sets nd Artificil Intelligence ISSN - Vol. - A Note on Complement of Trpezoidl Fuzzy Numers Using the α-cut Method D. Stephen Dingr K. Jivgn PG nd Reserch Deprtment

More information

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.

More information

UNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics STRATEGIC SECOND SOURCING IN A VERTICAL STRUCTURE

UNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics STRATEGIC SECOND SOURCING IN A VERTICAL STRUCTURE UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 04/15 STRATEGC SECOND SOURCNG N A VERTCAL STRUCTURE By Arijit Mukherjee September 004 DP 04/15 SSN 10-438 UNVERSTY OF NOTTNGHAM Discussion

More information

Outline of the Lecture. Software Testing. Unit & Integration Testing. Components. Lecture Notes 3 (of 4)

Outline of the Lecture. Software Testing. Unit & Integration Testing. Components. Lecture Notes 3 (of 4) Outline of the Lecture Softwre Testing Lecture Notes 3 (of 4) Integrtion Testing Top-down ottom-up ig-ng Sndwich System Testing cceptnce Testing istriution of ults in lrge Industril Softwre System (ISST

More information

Rotational Equilibrium: A Question of Balance

Rotational Equilibrium: A Question of Balance Prt of the IEEE Techer In-Service Progrm - Lesson Focus Demonstrte the concept of rottionl equilirium. Lesson Synopsis The Rottionl Equilirium ctivity encourges students to explore the sic concepts of

More information

Hillsborough Township Public Schools Mathematics Department Computer Programming 1

Hillsborough Township Public Schools Mathematics Department Computer Programming 1 Essentil Unit 1 Introduction to Progrmming Pcing: 15 dys Common Unit Test Wht re the ethicl implictions for ming in tody s world? There re ethicl responsibilities to consider when writing computer s. Citizenship,

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Vector differentiation. Chapters 6, 7

Vector differentiation. Chapters 6, 7 Chpter 2 Vectors Courtesy NASA/JPL-Cltech Summry (see exmples in Hw 1, 2, 3) Circ 1900 A.D., J. Willird Gis invented useful comintion of mgnitude nd direction clled vectors nd their higher-dimensionl counterprts

More information

Section A-4 Rational Expressions: Basic Operations

Section A-4 Rational Expressions: Basic Operations A- Appendi A A BASIC ALGEBRA REVIEW 7. Construction. A rectngulr open-topped bo is to be constructed out of 9- by 6-inch sheets of thin crdbord by cutting -inch squres out of ech corner nd bending the

More information

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2 7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6

More information

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems Gene Expression Progrmming: A New Adptive Algorithm for Solving Prolems Cândid Ferreir Deprtmento de Ciêncis Agráris Universidde dos Açores 9701-851 Terr-Chã Angr do Heroísmo, Portugl Complex Systems,

More information

Software Cost Estimation Model Based on Integration of Multi-agent and Case-Based Reasoning

Software Cost Estimation Model Based on Integration of Multi-agent and Case-Based Reasoning Journl of Computer Science 2 (3): 276-282, 2006 ISSN 1549-3636 2006 Science Publictions Softwre Cost Estimtion Model Bsed on Integrtion of Multi-gent nd Cse-Bsed Resoning Hsn Al-Skrn Informtion Technology

More information

Space Vector Pulse Width Modulation Based Induction Motor with V/F Control

Space Vector Pulse Width Modulation Based Induction Motor with V/F Control Interntionl Journl of Science nd Reserch (IJSR) Spce Vector Pulse Width Modultion Bsed Induction Motor with V/F Control Vikrmrjn Jmbulingm Electricl nd Electronics Engineering, VIT University, Indi Abstrct:

More information

Matrix Inverse and Condition

Matrix Inverse and Condition Mtrix Inverse nd Condition Berlin Chen Deprtment of Computer Science & Informtion Engineering Ntionl Tiwn Norml University Reference: 1. Applied Numericl Methods with MATLAB for Engineers, Chpter 11 &

More information

All pay auctions with certain and uncertain prizes a comment

All pay auctions with certain and uncertain prizes a comment CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 1-2015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin

More information

Vendor Rating for Service Desk Selection

Vendor Rating for Service Desk Selection Vendor Presented By DATE Using the scores of 0, 1, 2, or 3, plese rte the vendor's presenttion on how well they demonstrted the functionl requirements in the res below. Also consider how efficient nd functionl

More information

SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Basic Algebra

SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Basic Algebra SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mthemtics Bsic Alger. Opertions nd Epressions. Common Mistkes. Division of Algeric Epressions. Eponentil Functions nd Logrithms. Opertions nd their Inverses. Mnipulting

More information

Pure C4. Revision Notes

Pure C4. Revision Notes Pure C4 Revision Notes Mrch 0 Contents Core 4 Alger Prtil frctions Coordinte Geometry 5 Prmetric equtions 5 Conversion from prmetric to Crtesin form 6 Are under curve given prmetriclly 7 Sequences nd

More information

Real Time Robust L1 Tracker Using Accelerated Proximal Gradient Approach

Real Time Robust L1 Tracker Using Accelerated Proximal Gradient Approach Rel Time Robust 1 Trcker Using Accelerted Proximl Grdient Approch Chenglong Bo 1,YiWu 2, Hibin ing 2, nd Hui Ji 1 1 Deprtment of Mthemtics, Ntionl University of Singpore, Singpore,11976 2 Deprtment of

More information

Introducing Kashef for Application Monitoring

Introducing Kashef for Application Monitoring WextWise 2010 Introducing Kshef for Appliction The Cse for Rel-time monitoring of dtcenter helth is criticl IT process serving vriety of needs. Avilbility requirements of 6 nd 7 nines of tody SOA oriented

More information

Integration by Substitution

Integration by Substitution Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is

More information

An Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process

An Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct

More information

Value Function Approximation using Multiple Aggregation for Multiattribute Resource Management

Value Function Approximation using Multiple Aggregation for Multiattribute Resource Management Journl of Mchine Lerning Reserch 9 (2008) 2079-2 Submitted 8/08; Published 0/08 Vlue Function Approximtion using Multiple Aggregtion for Multittribute Resource Mngement Abrhm George Wrren B. Powell Deprtment

More information

The Acoustic Design of Soundproofing Doors and Windows

The Acoustic Design of Soundproofing Doors and Windows 3 The Open Acoustics Journl, 1, 3, 3-37 The Acoustic Design of Soundproofing Doors nd Windows Open Access Nishimur Yuy,1, Nguyen Huy Qung, Nishimur Sohei 1, Nishimur Tsuyoshi 3 nd Yno Tkshi 1 Kummoto Ntionl

More information

Application-Level Traffic Monitoring and an Analysis on IP Networks

Application-Level Traffic Monitoring and an Analysis on IP Networks Appliction-Level Trffic Monitoring nd n Anlysis on IP Networks Myung-Sup Kim, Young J. Won, nd Jmes Won-Ki Hong Trditionl trffic identifiction methods bsed on wellknown port numbers re not pproprite for

More information

Plotting and Graphing

Plotting and Graphing Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured

More information

JaERM Software-as-a-Solution Package

JaERM Software-as-a-Solution Package JERM Softwre-s--Solution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock

More information

Protocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff

Protocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff Protocol Anlysis 17-654/17-764 Anlysis of Softwre Artifcts Kevin Bierhoff Tke-Awys Protocols define temporl ordering of events Cn often be cptured with stte mchines Protocol nlysis needs to py ttention

More information

The remaining two sides of the right triangle are called the legs of the right triangle.

The remaining two sides of the right triangle are called the legs of the right triangle. 10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right

More information

SPECIAL PRODUCTS AND FACTORIZATION

SPECIAL PRODUCTS AND FACTORIZATION MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come

More information

Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity

Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University

More information

GFI MilArchiver 6 vs Quest Softwre Archive Mnger GFI Softwre www.gfi.com GFI MilArchiver 6 vs Quest Softwre Archive Mnger GFI MilArchiver 6 Quest Softwre Archive Mnger Who we re Generl fetures Supports

More information

Distributions. (corresponding to the cumulative distribution function for the discrete case).

Distributions. (corresponding to the cumulative distribution function for the discrete case). Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive

More information

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive

More information

Decision Rule Extraction from Trained Neural Networks Using Rough Sets

Decision Rule Extraction from Trained Neural Networks Using Rough Sets Decision Rule Extrction from Trined Neurl Networks Using Rough Sets Alin Lzr nd Ishwr K. Sethi Vision nd Neurl Networks Lbortory Deprtment of Computer Science Wyne Stte University Detroit, MI 48 ABSTRACT

More information

Unit 6: Exponents and Radicals

Unit 6: Exponents and Radicals Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -

More information