Mesh Editing in ROI with Dual Laplacian

Size: px
Start display at page:

Download "Mesh Editing in ROI with Dual Laplacian"

Transcription

1 Mesh Edtng n ROI wth Dual Laplacan Luo Qong, Lu Bo, Ma Zhan-guo, Zhang Hong-bn College of Computer Scence, Beng Unversty of Technology, Chna lqngng@sohu.com, lubo@but.edu.cn,mzgsy@63.com,zhb@publc.bta.net.cn (a) (b) (c) (d) (e) (f) Fgure. Deform the dnosaur model: (a) the orgnal meshes; (b) (c) (d) (e) (f) are the deformed results and the ROIs are labeled wth red crcles. Abstract In ths paper, we propose a new mesh edtng method worked n the dual doman for ROI (regon of nterest). Ths method has ntutve user nterface and effcent reconstructon process. The mesh detal s represented by dual Laplacan, and the reconstructed mesh s obtaned by solvng a quadratc mnmzaton problem whch preserves the mesh detal n least square sense. Precondtoned b-conugate gradent method (PBCG) s adopted to teratvely update the postons of the dual vertces and the dual Laplacan coordnates. The experments demonstrate that our method can work effectvely and gve vsually pleasng results. Keywords--- mesh deformaton, ROI, nteractve nterface, dual Laplacan.. Introducton Mesh edtng s an actve research feld n computer graphcs and has receved much attenton recently. It s useful n a varety of applcatons n computer modelng and anmaton. Mesh edtng often requres that the global shape deform n a user specfed way whle geometrc detals are well preserved. In the past years, many mesh edtng technques were developed. Free-Form Deformaton (FFD) [] embeds the orgnal model n the control lattces and ndrectly controls the deformaton of model by the control lattces. Mult-resoluton technque [2, 3] encodes the mesh geometry as a coarsest mesh and several levels of refnement. The modfed shape s computed by addng fner level detals to the deformed coarsest mesh. Sheffer [4] represents the mesh by rotaton-nvarant pyramd coordnates. Kho [5] gves a method to mplctly control the deformaton n the regon of nterest (ROI) wth a reference curve that users sketch. Sh [6] proposes a fast multgrd algorthm for deformng meshes. Laplacan technques [7-8] cast mesh deformaton as mnmzng an energy functon whch contans terms for both detal preservaton and poston constrants. The Laplacan coordnate descrbes the mesh geometry detal whch s expressed as the dfference between a vertex and ts one-rng neghbor vertces. Snce the Laplacan coordnate s encoded n a global coordnate system, t faces the transformaton problem: the Laplacan coordnates need to be approprately transformed to ft the orentaton of detals n the deformed mesh. Kn-Chung [9] gves dual Laplacan deformaton algorthm to edt whole model, whch can avod transformaton problem to some extent. Our method s based on the dual Laplacan representaton. Generally speakng, deformaton s usually carred out n some parts of a model, whle the other parts (a maorty of the whole model) are unchanged. If takng the whole model nto consderaton, the edtng operaton may be a complex process, especally for large mesh models. Therefore, t s necessary to develop effectve edtng methods for the deformaton of ROI. Computer Graphcs, Imagng and sualsaton (CGI 2007)

2 We propose a new mesh edtng framework wth an ntutve nterface and effcent reconstructon algorthm. Deformaton s confned only n ROI whch s determned by our Water-Fllng technque. We represent the mesh surface nformaton wth dual Laplacan coordnates, and reconstruct the deformed mesh by solvng a quadratc mnmzaton problem. The resulted lnear system s solved usng the precondtoned b-conugate gradent method. Observng that drect nteracton n 3D space s often a laborous task especally for non-expert users, we propose an ntutve user nterface easy to manpulate. Experments show that our system can gve natural deformaton wth pleasng vsual effect. In ths paper, we make the followng contrbutons: A new technque named Water-Fllng that determnes the ROI effectvely wth easy manpulaton and ntutve nterface An nteractve ROI edtng mechansm based on the dual Laplacan representaton, whch satsfes the preservaton of local geometry and poston constrants The rest of the paper s organzed as follows. In Secton 2, we ntroduce the dual Laplacan representaton. Secton 3 presents our edtng framework and explans mplementaton detals. In secton 4, we show some experment results, and conclude n Secton Dual Laplacan Our method s based on the dual Laplacan representaton. Dual Laplacan follows the same prncple as Laplacan, but presents the Laplacan coordnates n dual doman. There are many ways to buld dual mesh of the prmal mesh. In our method, we choose barycenter dual mesh and take trangular mesh for the nput mesh, the dual vertces can be found by gettng the centrod of the trangular faces n prmal mesh. It s obvous that there s a one-to-one mappng between the trangular faces n prmal mesh and the dual vertex n dual mesh. As n [0], assume that trangle plane n mesh conssts of three vertces v (=, 2, 3), then the dual vertex ncluded by the trangular plane s: 3 v = v () 3 n matrx form, = I = D IJ (2) where D s the vertex-face ncdent matrx, wth only the dagonal elements nonzero. Fg. 2 shows the fxed one-rng structure of the dual vertex v. The unque decomposton of dual vertex s gven by Equaton (3) [9]: v = q + hn = w v hn,, + (3) (,2,3) Fgure 2. Illustraton of the one-rng structure of dual vertces where q s the proecton of the dual vertex v n the plane, and n s the outward unt normal, the normalzed weghts are the barycentrc coordnates w, of q correspondng to v,v,2v, and, 3 w, = =,2,3. h s the sgned magntude of the normal component. Let l denotes the Laplace operator of v, Rearrange the expresson (3): l = hn = q v = w v v (4) = 5, w, (,2,3) q, ( v, 3 hn v ) n matrx form, l = L = LD = A (5) φ ( v ) = A (6) where A = L D and φ(v) denotes the dual Laplacan coordnates of the prmal vertces v. Snce D s of full rank matrx and L has rank n d, gven the orgnal dual Laplacan coordnates l of the ROI mesh and one fxed prmal vertex poston, we can get the rest of the vertex postons by solvng the equaton (5) wthout error. The ratonale of usng the dual Laplacan to avod the transformaton problem and preserve geometry property s to decompose the global geometry nto local parameterzaton nformaton and local geometry nformaton whch are two sets of scalar data. The local 3 6 Computer Graphcs, Imagng and sualsaton (CGI 2007)

3 parameterzaton nformaton s defned by the coeffcents of the Laplace operator, and the local geometry nformaton s captured by the magntudes of the Laplacan coordnates. Both the Laplacan coeffcents and the magntudes of the Laplacan coordnates are kept unchanged as possble before and after edtng [9]. 3. Mesh edtng framework n ROI The basc dea of our framework for dual Laplacan mesh edtng n ROI s to descrbe the mesh surface detal nformaton by dual Laplacan coordnates and reconstruct the deformed mesh by preservng them n the least square sense. For a ROI mesh edtng system, there are two key problems that must be solved carefully:. how to determne the ROI; and 2. how to deal wth the boundary vertces between the ROI and the fxed component. Our solutons are descrbed n detal as follows. 3.. Water-fllng technque to determne ROI Our system supples an ntutve way for users to determne the ROI. The user begns edtng by drectly clckng two ponts on the screen, the frst pont and the last pont, whch are then proected onto the correspondng vertces n the surface of 3D model, obtanng the frst vertex and the last vertex. The system mplctly connects the two vertces wth a lne whch we name t as regon lne, and computes a cuttng plane perpendcular the regon lne at the last vertex. The ntersecton of the plane wth the surface defnes a boundary of the ROI. Then search the neghbors startng from the frst vertex and extend the search operaton to the neghbors, only when meetng the boundary the search process end. Label all the vertces of been searched and determne the regon of nterest. Ths selectng method s smlar as the water fllng phenomenon, so we called t Water-Fllng technque. Ths method works effcently only for the regon that nvolves a closed mesh at the sde of frst vertex and our system only consders ROI whch satsfes ths requrement. In general, the regons that users usually want to deform mostly satsfy ths condton, lke the leg, arm, tal or head. So Water- Fllng technque s a good choce for ROI selectng n most cases. If the regon been selected s not satsfed, users can cancel t and select other regons. The nteractve nterface s flexble for users. After determnng the ROI, The followng step s to select the deform-controllng handles n the ROI and determne ther new postons. Handles are usually a subset of vertces n ROI. (a) (c) Fgure 3. The cow model: (a) the orgnal mesh, the red part on rght back leg s the ROI, and the green pont s the selected handle; (b) the green pont s the new poston of the handle that the user chooses by hmself; (c) the deformed mesh that controlled by the handle, only the vertces n ROI are consdered and other vertces out of the ROI are kept fxed; (d) the deformed model. We have parttoned the model nto two parts now:, the fxed part (black part); 2, the ROI (red part) whch ncludes the deformaton control handles (green ponts). Fg.3 llustrates ths partton. The fxed part wll be kept unchanged n the deformaton. The green handles determne what the resulted model wll be, and the red part should be moved followng the green handles n a natural way and the new poston of vertces n red part wll be obtaned n the edtng process. The boundary vertces are regarded as handles Mesh deformaton n ROI Suppose G (K, ) denotes trangular mesh n ROI, where K denotes the connectvty and denotes the geometry postons = { v < n}, the handles are a subset of the vertces n ROI U = { u m < n}. It has been observed that the soluton behaves better f the constrants comng from the handles are satsfed n the least squares sense rather than exactly [7]. We wll process all handles n ths way. Accordng to the dual Laplacan representaton whch descrbed n part 2, we use the approach of energy mnmzaton [7] to reconstruct the resultng mesh, the new postons ' are obtaned by mnmzng the followng quadratc error functon: (b) (d) Computer Graphcs, Imagng and sualsaton (CGI 2007)

4 n 2 n 2 E( ) = φ ( v ) l + v u (7) = = m Ths quadratc error functon corresponds to an over-determned lnear sparse system of the form A = b, where A s the augmented system matrx whch defned by the prmal mesh and poston constrants, and t keeps fxed throughout the whole process. Mnmzaton of ths error functon s equal to solve the augmented lnear system n the least square T T sense, leadng to the normal equatons A A = A b n ths headng, they should be Tmes -pont boldface, ntally captalzed, flush left, wth one blank lne before, and one after. t+ n changes along wth the updated dual vertex t t t postons +, + v v, v +, and the dual, Laplacan coordnate,2 l t+,3 also changes accordngly. The teraton process wll termnate as long as the updatng rate of prmal vertex s below a threshold. 4. Expermental results We have expermented wth local mesh deformatons n ROI on some models [] (dnosaur, cow, camel, pthecanthrope and trceratops). Fgures 4-7 show some edtng results PBCG teraton Notng that both the local parameterzaton nformaton and local geometry nformaton are nonlnearly dependent on the vertex poston n prmal mesh, teratve solver for the normal equatons may be a good choce to mnmze the dstorton and get satsfactory results. We adopt the precondtoned bconugate gradent method to solve the normal equatons teratvely. Snce the matrx s a sparse matrx, t s neffcent to use general methods of lnear algebra on such problem, because most of the arthmetc operatons devoted to solvng the set of the equatons or nvertng the matrx nvolve zero operands. The PBCG method wll mprove the effcency of solvng a sparse lnear system. We adopt the two steps ntroduced n [9] to update the postons of the dual vertces and the dual Laplacan coordnates: Step. Update the dual vertex postons: T t T t b + A A = A (8) t + t+ = D (9) t where b s derved from l t and the poston of 0 current handles, s the postons of the prmal vertex and l 0 s the dual Laplacan coordnates of the prmal mesh. Step 2. Update the dual Laplacan coordnates: t+ t+ t+ l = h n ( t+ (0) t+ = w v v ), (,2,3), (a) (b) (c) (d) (e) Fgure 4. The cow model: (a) (d) are the orgnal model; (b) the runnng cow wth four legs and tal ROIs, we gan ths model wth fve operatons;(c) the shakng-tal cow wth the tal ROI; (e) deform the horns. (a) (b) (c) (d) (e) (f) Fgure 5. The camel model: (a) the orgnal mesh; (b) (c) (d) (f) are the deformed camel model, the ROIs are labeled wth red crcles. Computer Graphcs, Imagng and sualsaton (CGI 2007)

5 demonstrate that our edtng system for mesh ROI can generate pleasng vsual effect. 6. Acknowledgements (a) (b) (c) Ths work was supported by Natonal Natural Scence Foundaton of Chna (No , ) and Chna Mnstry of Educaton (No ). 7. References [] Sederber, T. W., Parry, S. R. Free-form deformaton of sold geometrc models. In Proceedngs of the 3th annual conference on computer graphcs and nteractve technques, ACM Press, 986, (d) (e) (f) Fgure 6. The pthecanthrope model: (a) the orgnal mesh; (b) the left leg steps out; (d) left arm lfts up and rght arm lfts down; (c) (e) (f) are the sde vew. [2] Zorn, D., Schroder, P., Sweldens, W. Interactve multresoluton mesh edtng. In Proceedngs of ACM SIGGRAPH 97, ACM Press, 997, [3] Guskov, I., Sweldens, W., Schroder, P. Mutresoluton sgnal processng for meshes. In Proceedngs of ACM SIGGRAPH 99, ACM Press, 999, [4] Sheffer, A., Kraevov,. Pyramd coordnates for morphng and deformaton. In Proceedngs of 3DPT (a) (b) (c) (d) Fgure 7. The trceratops model, select the two horns as ROI: (a) the orgnal mesh; (b) (c) the horns rotate wth dfferent angles; (d) the horns rotate n perpendcular drecton. Experments demonstrate that our system can obtan natural deformaton effect n ROI, satsfyng not only precse handle poston constrants but also preservng local mesh detals well. 5. Concluson We have presented an effcent method to edt surface mesh n ROI by the dual Laplacan representaton. The mesh s reconstructed by mnmzng a quadratc error functon whch nvolves both the preservaton of local geometry features and handle poston constrants. We use precondtoned bconugate gradent method to teratvely update the dual vertces poston and dual Laplacan coordnates to get the deformed mesh. The experment results [5] Kho, Y., Garland, M. Sketchng Mesh Deformatons. In Proceedngs of ACM SIGGRAPH ACM Press, 2005, [6] Sh, L., Yu, Y., Bell, N., Feng, W. A Fast Multgrd Algorthm for Mesh Deformaton. In Proceedngs of ACM SIGGRAPH ACM Press, 2006, [7] Sorkng, O., Lpman, Y., Cohen-OR, D., Alexa, M., Rossl, C., Sedel, H.-P. Laplcan surface edtng. In Processngs of the Eurographcs/ACM SIGGRAPH Symposum on Geometry Processng, Eurographcs Assocaton, ACM Press, 2004, [8] Nealen, A., Sorkng, O., Alexa, M., Cohen-Or, D. A Sketch-Based Interface for Detal-Preservng Mesh Edtng. In Proceedngs of ACM SIGGRAPH2005. ACM Press, 2005, [9] Kn-Chung, O., Chew-Lan, T., Lgang, Lu., Hongbo, F., Dual Laplacan Edtng for Meshes. IEEE Transactons on sualzaton and Computer Graphcs. 2006, [0] Taubn, G. Dual MesH Resamplng. In Processngs of Pacfc Graphcs [] Computer Graphcs, Imagng and sualsaton (CGI 2007)

High-Boost Mesh Filtering for 3-D Shape Enhancement

High-Boost Mesh Filtering for 3-D Shape Enhancement Hgh-Boost Mesh Flterng for 3-D Shape Enhancement Hrokazu Yagou Λ Alexander Belyaev y Damng We z Λ y z ; ; Shape Modelng Laboratory, Unversty of Azu, Azu-Wakamatsu 965-8580 Japan y Computer Graphcs Group,

More information

An Optimal Algorithm for Prufer Codes *

An Optimal Algorithm for Prufer Codes * J. Software Engneerng & Applcatons, 2009, 2: 111-115 do:10.4236/jsea.2009.22016 Publshed Onlne July 2009 (www.scrp.org/journal/jsea) An Optmal Algorthm for Prufer Codes * Xaodong Wang 1, 2, Le Wang 3,

More information

Parameterization of Quadrilateral Meshes

Parameterization of Quadrilateral Meshes Parameterzaton of Quadrlateral Meshes L Lu 1, CaMng Zhang 1,, and Frank Cheng 3 1 School of Computer Scence and Technology, Shandong Unversty, Jnan, Chna Department of Computer Scence and Technology, Shandong

More information

Parallelism for Nested Loops with Non-uniform and Flow Dependences

Parallelism for Nested Loops with Non-uniform and Flow Dependences Parallelsm for Nested Loops wth Non-unform and Flow Dependences Sam-Jn Jeong Dept. of Informaton & Communcaton Engneerng, Cheonan Unversty, 5, Anseo-dong, Cheonan, Chungnam, 330-80, Korea. seong@cheonan.ac.kr

More information

2D Shape Deformation Based on Rigid Square Matching

2D Shape Deformation Based on Rigid Square Matching D Shape Deformaton Based on Rgd Square Matchng A. Author Author s Afflaton Author s E-Mal Author s Webste B. Author Author s Afflaton Author s E-Mal Author s Webste C. Author Author s Afflaton Author s

More information

D shape manipulation via topology-aware rigid grid. Introduction. By Wenwu Yang and Jieqing Feng *

D shape manipulation via topology-aware rigid grid. Introduction. By Wenwu Yang and Jieqing Feng * COMPUTER ANIMATION AND VIRTUAL WORLDS Comp. Anm. Vrtual Worlds 2009; 20: 175 184 Publshed onlne 1 June 2009 n Wley InterScence (www.nterscence.wley.com).285 2D shape manpulaton va topology-aware rgd grd

More information

Chapter 6 Programmng the fnte element method Inow turn to the man subject of ths book: The mplementaton of the fnte element algorthm n computer programs. In order to make my dscusson as straghtforward

More information

Feature-Preserving Mesh Denoising via Bilateral Normal Filtering

Feature-Preserving Mesh Denoising via Bilateral Normal Filtering Feature-Preservng Mesh Denosng va Blateral Normal Flterng Ka-Wah Lee, Wen-Png Wang Computer Graphcs Group Department of Computer Scence, The Unversty of Hong Kong kwlee@cs.hku.hk, wenpng@cs.hku.hk Abstract

More information

Support Vector Machines

Support Vector Machines /9/207 MIST.6060 Busness Intellgence and Data Mnng What are Support Vector Machnes? Support Vector Machnes Support Vector Machnes (SVMs) are supervsed learnng technques that analyze data and recognze patterns.

More information

Hermite Splines in Lie Groups as Products of Geodesics

Hermite Splines in Lie Groups as Products of Geodesics Hermte Splnes n Le Groups as Products of Geodescs Ethan Eade Updated May 28, 2017 1 Introducton 1.1 Goal Ths document defnes a curve n the Le group G parametrzed by tme and by structural parameters n the

More information

An Image Fusion Approach Based on Segmentation Region

An Image Fusion Approach Based on Segmentation Region Rong Wang, L-Qun Gao, Shu Yang, Yu-Hua Cha, and Yan-Chun Lu An Image Fuson Approach Based On Segmentaton Regon An Image Fuson Approach Based on Segmentaton Regon Rong Wang, L-Qun Gao, Shu Yang 3, Yu-Hua

More information

Quality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation

Quality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation Intellgent Informaton Management, 013, 5, 191-195 Publshed Onlne November 013 (http://www.scrp.org/journal/m) http://dx.do.org/10.36/m.013.5601 Qualty Improvement Algorthm for Tetrahedral Mesh Based on

More information

Wavefront Reconstructor

Wavefront Reconstructor A Dstrbuted Smplex B-Splne Based Wavefront Reconstructor Coen de Vsser and Mchel Verhaegen 14-12-201212 2012 Delft Unversty of Technology Contents Introducton Wavefront reconstructon usng Smplex B-Splnes

More information

Range images. Range image registration. Examples of sampling patterns. Range images and range surfaces

Range images. Range image registration. Examples of sampling patterns. Range images and range surfaces Range mages For many structured lght scanners, the range data forms a hghly regular pattern known as a range mage. he samplng pattern s determned by the specfc scanner. Range mage regstraton 1 Examples

More information

A Binarization Algorithm specialized on Document Images and Photos

A Binarization Algorithm specialized on Document Images and Photos A Bnarzaton Algorthm specalzed on Document mages and Photos Ergna Kavalleratou Dept. of nformaton and Communcaton Systems Engneerng Unversty of the Aegean kavalleratou@aegean.gr Abstract n ths paper, a

More information

Barycentric Coordinates. From: Mean Value Coordinates for Closed Triangular Meshes by Ju et al.

Barycentric Coordinates. From: Mean Value Coordinates for Closed Triangular Meshes by Ju et al. Barycentrc Coordnates From: Mean Value Coordnates for Closed Trangular Meshes by Ju et al. Motvaton Data nterpolaton from the vertces of a boundary polygon to ts nteror Boundary value problems Shadng Space

More information

Simplification of 3D Meshes

Simplification of 3D Meshes Smplfcaton of 3D Meshes Addy Ngan /4/00 Outlne Motvaton Taxonomy of smplfcaton methods Hoppe et al, Mesh optmzaton Hoppe, Progressve meshes Smplfcaton of 3D Meshes 1 Motvaton Hgh detaled meshes becomng

More information

Learning the Kernel Parameters in Kernel Minimum Distance Classifier

Learning the Kernel Parameters in Kernel Minimum Distance Classifier Learnng the Kernel Parameters n Kernel Mnmum Dstance Classfer Daoqang Zhang 1,, Songcan Chen and Zh-Hua Zhou 1* 1 Natonal Laboratory for Novel Software Technology Nanjng Unversty, Nanjng 193, Chna Department

More information

Polyhedral Surface Smoothing with Simultaneous Mesh Regularization

Polyhedral Surface Smoothing with Simultaneous Mesh Regularization olyhedral Surface Smoothng wth Smultaneous Mesh Regularzaton Yutaka Ohtake The Unversty of Azu Azu-Wakamatsu Cty Fukushma 965-8580 Japan d800@u-azu.ac.jp Alexander G. Belyaev The Unversty of Azu Azu-Wakamatsu

More information

Modeling, Manipulating, and Visualizing Continuous Volumetric Data: A Novel Spline-based Approach

Modeling, Manipulating, and Visualizing Continuous Volumetric Data: A Novel Spline-based Approach Modelng, Manpulatng, and Vsualzng Contnuous Volumetrc Data: A Novel Splne-based Approach Jng Hua Center for Vsual Computng, Department of Computer Scence SUNY at Stony Brook Talk Outlne Introducton and

More information

TN348: Openlab Module - Colocalization

TN348: Openlab Module - Colocalization TN348: Openlab Module - Colocalzaton Topc The Colocalzaton module provdes the faclty to vsualze and quantfy colocalzaton between pars of mages. The Colocalzaton wndow contans a prevew of the two mages

More information

Tsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance

Tsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance Tsnghua Unversty at TAC 2009: Summarzng Mult-documents by Informaton Dstance Chong Long, Mnle Huang, Xaoyan Zhu State Key Laboratory of Intellgent Technology and Systems, Tsnghua Natonal Laboratory for

More information

A Fast Content-Based Multimedia Retrieval Technique Using Compressed Data

A Fast Content-Based Multimedia Retrieval Technique Using Compressed Data A Fast Content-Based Multmeda Retreval Technque Usng Compressed Data Borko Furht and Pornvt Saksobhavvat NSF Multmeda Laboratory Florda Atlantc Unversty, Boca Raton, Florda 3343 ABSTRACT In ths paper,

More information

R s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes

R s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes SPH3UW Unt 7.3 Sphercal Concave Mrrors Page 1 of 1 Notes Physcs Tool box Concave Mrror If the reflectng surface takes place on the nner surface of the sphercal shape so that the centre of the mrror bulges

More information

Analysis of Continuous Beams in General

Analysis of Continuous Beams in General Analyss of Contnuous Beams n General Contnuous beams consdered here are prsmatc, rgdly connected to each beam segment and supported at varous ponts along the beam. onts are selected at ponts of support,

More information

Facial Model Improvement Using 3D Texture Mapping Feedback

Facial Model Improvement Using 3D Texture Mapping Feedback Facal Model Improvement Usng 3D Texture Mappng Feedback Yongje Lu, Anup Basu and Jong-Seong Km* Department of Computng Scence, Unversty of Alberta, *Andong Unversty, South Korea {yongje, anup}@cs.ualberta.ca,

More information

For instance, ; the five basic number-sets are increasingly more n A B & B A A = B (1)

For instance, ; the five basic number-sets are increasingly more n A B & B A A = B (1) Secton 1.2 Subsets and the Boolean operatons on sets If every element of the set A s an element of the set B, we say that A s a subset of B, or that A s contaned n B, or that B contans A, and we wrte A

More information

Preconditioning Parallel Sparse Iterative Solvers for Circuit Simulation

Preconditioning Parallel Sparse Iterative Solvers for Circuit Simulation Precondtonng Parallel Sparse Iteratve Solvers for Crcut Smulaton A. Basermann, U. Jaekel, and K. Hachya 1 Introducton One mportant mathematcal problem n smulaton of large electrcal crcuts s the soluton

More information

Fair Triangle Mesh Generation with Discrete Elastica

Fair Triangle Mesh Generation with Discrete Elastica Far Trangle Mesh Generaton wth Dscrete Elastca Shn Yoshzawa, and Alexander G. Belyaev, Computer Graphcs Group, Max-Planck-Insttut für Informatk, 66123 Saarbrücken, Germany Phone: [+49](681)9325-414 Fax:

More information

The Codesign Challenge

The Codesign Challenge ECE 4530 Codesgn Challenge Fall 2007 Hardware/Software Codesgn The Codesgn Challenge Objectves In the codesgn challenge, your task s to accelerate a gven software reference mplementaton as fast as possble.

More information

Proper Choice of Data Used for the Estimation of Datum Transformation Parameters

Proper Choice of Data Used for the Estimation of Datum Transformation Parameters Proper Choce of Data Used for the Estmaton of Datum Transformaton Parameters Hakan S. KUTOGLU, Turkey Key words: Coordnate systems; transformaton; estmaton, relablty. SUMMARY Advances n technologes and

More information

Introduction to Geometrical Optics - a 2D ray tracing Excel model for spherical mirrors - Part 2

Introduction to Geometrical Optics - a 2D ray tracing Excel model for spherical mirrors - Part 2 Introducton to Geometrcal Optcs - a D ra tracng Ecel model for sphercal mrrors - Part b George ungu - Ths s a tutoral eplanng the creaton of an eact D ra tracng model for both sphercal concave and sphercal

More information

2x x l. Module 3: Element Properties Lecture 4: Lagrange and Serendipity Elements

2x x l. Module 3: Element Properties Lecture 4: Lagrange and Serendipity Elements Module 3: Element Propertes Lecture : Lagrange and Serendpty Elements 5 In last lecture note, the nterpolaton functons are derved on the bass of assumed polynomal from Pascal s trangle for the fled varable.

More information

Load Balancing for Hex-Cell Interconnection Network

Load Balancing for Hex-Cell Interconnection Network Int. J. Communcatons, Network and System Scences,,, - Publshed Onlne Aprl n ScRes. http://www.scrp.org/journal/jcns http://dx.do.org/./jcns.. Load Balancng for Hex-Cell Interconnecton Network Saher Manaseer,

More information

What are the camera parameters? Where are the light sources? What is the mapping from radiance to pixel color? Want to solve for 3D geometry

What are the camera parameters? Where are the light sources? What is the mapping from radiance to pixel color? Want to solve for 3D geometry Today: Calbraton What are the camera parameters? Where are the lght sources? What s the mappng from radance to pel color? Why Calbrate? Want to solve for D geometry Alternatve approach Solve for D shape

More information

VISUAL SELECTION OF SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES

VISUAL SELECTION OF SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES UbCC 2011, Volume 6, 5002981-x manuscrpts OPEN ACCES UbCC Journal ISSN 1992-8424 www.ubcc.org VISUAL SELECTION OF SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES

More information

Robust Curvature Estimation and Geometry Analysis of 3D point Cloud Surfaces

Robust Curvature Estimation and Geometry Analysis of 3D point Cloud Surfaces Robust Curvature Estmaton and Geometry Analyss of 3D pont Cloud Surfaces Xaopeng ZHANG, Hongjun LI, Zhangln CHENG, Ykuan ZHANG Sno-French Laboratory LIAMA, Insttute of Automaton, CAS, Bejng 100190, Chna

More information

The Theory and Application of an Adaptive Moving Least. Squares for Non-uniform Samples

The Theory and Application of an Adaptive Moving Least. Squares for Non-uniform Samples Xanpng Huang, Qng Tan, Janfe Mao, L Jang, Ronghua Lang The Theory and Applcaton of an Adaptve Movng Least Squares for Non-unform Samples Xanpng Huang, Qng Tan, Janfe Mao*, L Jang, Ronghua Lang College

More information

Cluster Analysis of Electrical Behavior

Cluster Analysis of Electrical Behavior Journal of Computer and Communcatons, 205, 3, 88-93 Publshed Onlne May 205 n ScRes. http://www.scrp.org/ournal/cc http://dx.do.org/0.4236/cc.205.350 Cluster Analyss of Electrcal Behavor Ln Lu Ln Lu, School

More information

3D MODEL DEFORMATION ALONG A PARAMETRIC SURFACE

3D MODEL DEFORMATION ALONG A PARAMETRIC SURFACE 3D MODEL DEFORMATION ALONG A PARAMETRIC URFACE Bng-Yu Chen * Yutaka Ono * Henry Johan * Masaak Ish * Tomoyuk Nshta * Jeqng Feng * The Unversty of Tokyo 7-3-1, Hongo, Bunkyo-ku, Tokyo, 133-0033 Japan Zheang

More information

Nonlocal Mumford-Shah Model for Image Segmentation

Nonlocal Mumford-Shah Model for Image Segmentation for Image Segmentaton 1 College of Informaton Engneerng, Qngdao Unversty, Qngdao, 266000,Chna E-mal:ccluxaoq@163.com ebo e 23 College of Informaton Engneerng, Qngdao Unversty, Qngdao, 266000,Chna E-mal:

More information

A Fast Visual Tracking Algorithm Based on Circle Pixels Matching

A Fast Visual Tracking Algorithm Based on Circle Pixels Matching A Fast Vsual Trackng Algorthm Based on Crcle Pxels Matchng Zhqang Hou hou_zhq@sohu.com Chongzhao Han czhan@mal.xjtu.edu.cn Ln Zheng Abstract: A fast vsual trackng algorthm based on crcle pxels matchng

More information

Smoothing Spline ANOVA for variable screening

Smoothing Spline ANOVA for variable screening Smoothng Splne ANOVA for varable screenng a useful tool for metamodels tranng and mult-objectve optmzaton L. Rcco, E. Rgon, A. Turco Outlne RSM Introducton Possble couplng Test case MOO MOO wth Game Theory

More information

The Shortest Path of Touring Lines given in the Plane

The Shortest Path of Touring Lines given in the Plane Send Orders for Reprnts to reprnts@benthamscence.ae 262 The Open Cybernetcs & Systemcs Journal, 2015, 9, 262-267 The Shortest Path of Tourng Lnes gven n the Plane Open Access Ljuan Wang 1,2, Dandan He

More information

As-Rigid-As-Possible Shape Manipulation

As-Rigid-As-Possible Shape Manipulation As-Rgd-As-Possble Shape Manpulaton akeo Igarash 1, 3 omer Moscovch John F. Hughes 1 he Unversty of okyo Brown Unversty 3 PRESO, JS Abstract We present an nteractve system that lets a user move and deform

More information

Content Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers

Content Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers IOSR Journal of Electroncs and Communcaton Engneerng (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue, Ver. IV (Mar - Apr. 04), PP 0-07 Content Based Image Retreval Usng -D Dscrete Wavelet wth

More information

The Research of Ellipse Parameter Fitting Algorithm of Ultrasonic Imaging Logging in the Casing Hole

The Research of Ellipse Parameter Fitting Algorithm of Ultrasonic Imaging Logging in the Casing Hole Appled Mathematcs, 04, 5, 37-3 Publshed Onlne May 04 n ScRes. http://www.scrp.org/journal/am http://dx.do.org/0.436/am.04.584 The Research of Ellpse Parameter Fttng Algorthm of Ultrasonc Imagng Loggng

More information

Interpolation of the Irregular Curve Network of Ship Hull Form Using Subdivision Surfaces

Interpolation of the Irregular Curve Network of Ship Hull Form Using Subdivision Surfaces 7 Interpolaton of the Irregular Curve Network of Shp Hull Form Usng Subdvson Surfaces Kyu-Yeul Lee, Doo-Yeoun Cho and Tae-Wan Km Seoul Natonal Unversty, kylee@snu.ac.kr,whendus@snu.ac.kr,taewan}@snu.ac.kr

More information

Dynamic wetting property investigation of AFM tips in micro/nanoscale

Dynamic wetting property investigation of AFM tips in micro/nanoscale Dynamc wettng property nvestgaton of AFM tps n mcro/nanoscale The wettng propertes of AFM probe tps are of concern n AFM tp related force measurement, fabrcaton, and manpulaton technques, such as dp-pen

More information

GSLM Operations Research II Fall 13/14

GSLM Operations Research II Fall 13/14 GSLM 58 Operatons Research II Fall /4 6. Separable Programmng Consder a general NLP mn f(x) s.t. g j (x) b j j =. m. Defnton 6.. The NLP s a separable program f ts objectve functon and all constrants are

More information

Electrical analysis of light-weight, triangular weave reflector antennas

Electrical analysis of light-weight, triangular weave reflector antennas Electrcal analyss of lght-weght, trangular weave reflector antennas Knud Pontoppdan TICRA Laederstraede 34 DK-121 Copenhagen K Denmark Emal: kp@tcra.com INTRODUCTION The new lght-weght reflector antenna

More information

An efficient method to build panoramic image mosaics

An efficient method to build panoramic image mosaics An effcent method to buld panoramc mage mosacs Pattern Recognton Letters vol. 4 003 Dae-Hyun Km Yong-In Yoon Jong-Soo Cho School of Electrcal Engneerng and Computer Scence Kyungpook Natonal Unv. Abstract

More information

An Approach in Coloring Semi-Regular Tilings on the Hyperbolic Plane

An Approach in Coloring Semi-Regular Tilings on the Hyperbolic Plane An Approach n Colorng Sem-Regular Tlngs on the Hyperbolc Plane Ma Louse Antonette N De Las Peñas, mlp@mathscmathadmueduph Glenn R Lago, glago@yahoocom Math Department, Ateneo de Manla Unversty, Loyola

More information

A 3D Paper-Cutting Oriented Mesh Trimming Algorithm

A 3D Paper-Cutting Oriented Mesh Trimming Algorithm ISSN 1000-9825, CODEN RUXUEW E-mal: jos@scasaccn Journal of Software, Vol17, Supplement, November 2006, pp169 175 http://wwwjosorgcn 2006 by of Journal of Software All rghts reserved Tel/Fax: +86-10-62562563

More information

NAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics

NAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics Introducton G10 NAG Fortran Lbrary Chapter Introducton G10 Smoothng n Statstcs Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Smoothng Methods... 2 2.2 Smoothng Splnes and Regresson

More information

Harmonic Coordinates for Character Articulation PIXAR

Harmonic Coordinates for Character Articulation PIXAR Harmonc Coordnates for Character Artculaton PIXAR Pushkar Josh Mark Meyer Tony DeRose Bran Green Tom Sanock We have a complex source mesh nsde of a smpler cage mesh We want vertex deformatons appled to

More information

Registration of Expressions Data using a 3D Morphable Model

Registration of Expressions Data using a 3D Morphable Model Regstraton of Expressons Data usng a 3D Morphable Model Curzo Basso DISI, Unverstà d Genova, Italy Emal: curzo.basso@ds.unge.t Thomas Vetter Departement Informatk, Unverstät Basel, Swtzerland Emal: thomas.vetter@unbas.ch

More information

An Application of the Dulmage-Mendelsohn Decomposition to Sparse Null Space Bases of Full Row Rank Matrices

An Application of the Dulmage-Mendelsohn Decomposition to Sparse Null Space Bases of Full Row Rank Matrices Internatonal Mathematcal Forum, Vol 7, 2012, no 52, 2549-2554 An Applcaton of the Dulmage-Mendelsohn Decomposton to Sparse Null Space Bases of Full Row Rank Matrces Mostafa Khorramzadeh Department of Mathematcal

More information

In the planar case, one possibility to create a high quality. curve that interpolates a given set of points is to use a clothoid spline,

In the planar case, one possibility to create a high quality. curve that interpolates a given set of points is to use a clothoid spline, Dscrete Farng of Curves and Surfaces Based on Lnear Curvature Dstrbuton R. Schneder and L. Kobbelt Abstract. In the planar case, one possblty to create a hgh qualty curve that nterpolates a gven set of

More information

Mathematics 256 a course in differential equations for engineering students

Mathematics 256 a course in differential equations for engineering students Mathematcs 56 a course n dfferental equatons for engneerng students Chapter 5. More effcent methods of numercal soluton Euler s method s qute neffcent. Because the error s essentally proportonal to the

More information

Lobachevsky State University of Nizhni Novgorod. Polyhedron. Quick Start Guide

Lobachevsky State University of Nizhni Novgorod. Polyhedron. Quick Start Guide Lobachevsky State Unversty of Nzhn Novgorod Polyhedron Quck Start Gude Nzhn Novgorod 2016 Contents Specfcaton of Polyhedron software... 3 Theoretcal background... 4 1. Interface of Polyhedron... 6 1.1.

More information

Related-Mode Attacks on CTR Encryption Mode

Related-Mode Attacks on CTR Encryption Mode Internatonal Journal of Network Securty, Vol.4, No.3, PP.282 287, May 2007 282 Related-Mode Attacks on CTR Encrypton Mode Dayn Wang, Dongda Ln, and Wenlng Wu (Correspondng author: Dayn Wang) Key Laboratory

More information

3D Face Reconstruction With Local Feature Refinement

3D Face Reconstruction With Local Feature Refinement ternatonal Journal of Multmeda and Ubqutous Engneerng Vol.9, No.8 (014), pp.59-7 http://dx.do.org/10.1457/jmue.014.9.8.06 3D Face Reconstructon Wth Local Feature Refnement Rudy Adpranata 1, Kartka Gunad

More information

The Greedy Method. Outline and Reading. Change Money Problem. Greedy Algorithms. Applications of the Greedy Strategy. The Greedy Method Technique

The Greedy Method. Outline and Reading. Change Money Problem. Greedy Algorithms. Applications of the Greedy Strategy. The Greedy Method Technique //00 :0 AM Outlne and Readng The Greedy Method The Greedy Method Technque (secton.) Fractonal Knapsack Problem (secton..) Task Schedulng (secton..) Mnmum Spannng Trees (secton.) Change Money Problem Greedy

More information

3D Face Reconstruction With Local Feature Refinement. Abstract

3D Face Reconstruction With Local Feature Refinement. Abstract , pp.6-74 http://dx.do.org/0.457/jmue.04.9.8.06 3D Face Reconstructon Wth Local Feature Refnement Rudy Adpranata, Kartka Gunad and Wendy Gunawan 3, formatcs Department, Petra Chrstan Unversty, Surabaya,

More information

Direction Fields over Point-Sampled Geometry

Direction Fields over Point-Sampled Geometry Drecton Felds over Pont-Sampled Geometry Marc Alexa Tobas Klug Carsten Stoll Interactve Graphcs Systems Group Department of Computer Scence Technsche Unverstät Darmstadt Fraunhoferstr. 5 64283 Darmstadt,

More information

A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS

A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS Proceedngs of the Wnter Smulaton Conference M E Kuhl, N M Steger, F B Armstrong, and J A Jones, eds A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS Mark W Brantley Chun-Hung

More information

Line Clipping by Convex and Nonconvex Polyhedra in E 3

Line Clipping by Convex and Nonconvex Polyhedra in E 3 Lne Clppng by Convex and Nonconvex Polyhedra n E 3 Václav Skala 1 Department of Informatcs and Computer Scence Unversty of West Bohema Unverztní 22, Box 314, 306 14 Plzeò Czech Republc e-mal: skala@kv.zcu.cz

More information

Problem Set 3 Solutions

Problem Set 3 Solutions Introducton to Algorthms October 4, 2002 Massachusetts Insttute of Technology 6046J/18410J Professors Erk Demane and Shaf Goldwasser Handout 14 Problem Set 3 Solutons (Exercses were not to be turned n,

More information

Real-time Motion Capture System Using One Video Camera Based on Color and Edge Distribution

Real-time Motion Capture System Using One Video Camera Based on Color and Edge Distribution Real-tme Moton Capture System Usng One Vdeo Camera Based on Color and Edge Dstrbuton YOSHIAKI AKAZAWA, YOSHIHIRO OKADA, AND KOICHI NIIJIMA Graduate School of Informaton Scence and Electrcal Engneerng,

More information

Structure from Motion

Structure from Motion Structure from Moton Structure from Moton For now, statc scene and movng camera Equvalentl, rgdl movng scene and statc camera Lmtng case of stereo wth man cameras Lmtng case of multvew camera calbraton

More information

Optimization Methods: Integer Programming Integer Linear Programming 1. Module 7 Lecture Notes 1. Integer Linear Programming

Optimization Methods: Integer Programming Integer Linear Programming 1. Module 7 Lecture Notes 1. Integer Linear Programming Optzaton Methods: Integer Prograng Integer Lnear Prograng Module Lecture Notes Integer Lnear Prograng Introducton In all the prevous lectures n lnear prograng dscussed so far, the desgn varables consdered

More information

Corner-Based Image Alignment using Pyramid Structure with Gradient Vector Similarity

Corner-Based Image Alignment using Pyramid Structure with Gradient Vector Similarity Journal of Sgnal and Informaton Processng, 013, 4, 114-119 do:10.436/jsp.013.43b00 Publshed Onlne August 013 (http://www.scrp.org/journal/jsp) Corner-Based Image Algnment usng Pyramd Structure wth Gradent

More information

1. Introduction. 2. Related Work

1. Introduction. 2. Related Work ASIAGRAPH 008 PROCEEDINGS Curvature Estmaton of 3D Pont Cloud Surfaces Through the Fttng of Normal Secton Curvatures Xaopeng Zhang* /LIAMA-NLPR, Insttute of Automaton, CAS; Hongjun L /LIAMA-NLPR, Insttute

More information

FiberMesh: Designing Freeform Surfaces with 3D Curves

FiberMesh: Designing Freeform Surfaces with 3D Curves To appear n the ACM SIGGRAPH conference proceedngs FberMesh: Desgnng Freeform Surfaces wth 3D Curves Andrew Nealen TU Berln Takeo Igarash The Unversty of Tokyo / PRESTO JST Olga Sorkne TU Berln Marc Alexa

More information

Type-2 Fuzzy Non-uniform Rational B-spline Model with Type-2 Fuzzy Data

Type-2 Fuzzy Non-uniform Rational B-spline Model with Type-2 Fuzzy Data Malaysan Journal of Mathematcal Scences 11(S) Aprl : 35 46 (2017) Specal Issue: The 2nd Internatonal Conference and Workshop on Mathematcal Analyss (ICWOMA 2016) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES

More information

12/2/2009. Announcements. Parametric / Non-parametric. Case-Based Reasoning. Nearest-Neighbor on Images. Nearest-Neighbor Classification

12/2/2009. Announcements. Parametric / Non-parametric. Case-Based Reasoning. Nearest-Neighbor on Images. Nearest-Neighbor Classification Introducton to Artfcal Intellgence V22.0472-001 Fall 2009 Lecture 24: Nearest-Neghbors & Support Vector Machnes Rob Fergus Dept of Computer Scence, Courant Insttute, NYU Sldes from Danel Yeung, John DeNero

More information

3D As-Rigid-As-Possible Deformations Using MLS

3D As-Rigid-As-Possible Deformations Using MLS myjournal manuscrpt No. (wll be nserted by the edtor) 3D As-Rgd-As-Possble Deformatons Usng MLS Alvaro Cuno, Claudo Esperança, Antono Olvera, Paulo Roma Cavalcant Systems Engneerng and Computer Scence

More information

6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour

6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour 6.854 Advanced Algorthms Petar Maymounkov Problem Set 11 (November 23, 2005) Wth: Benjamn Rossman, Oren Wemann, and Pouya Kheradpour Problem 1. We reduce vertex cover to MAX-SAT wth weghts, such that the

More information

Fast Computation of Shortest Path for Visiting Segments in the Plane

Fast Computation of Shortest Path for Visiting Segments in the Plane Send Orders for Reprnts to reprnts@benthamscence.ae 4 The Open Cybernetcs & Systemcs Journal, 04, 8, 4-9 Open Access Fast Computaton of Shortest Path for Vstng Segments n the Plane Ljuan Wang,, Bo Jang

More information

A Newton-Type Method for Constrained Least-Squares Data-Fitting with Easy-to-Control Rational Curves

A Newton-Type Method for Constrained Least-Squares Data-Fitting with Easy-to-Control Rational Curves A Newton-Type Method for Constraned Least-Squares Data-Fttng wth Easy-to-Control Ratonal Curves G. Cascola a, L. Roman b, a Department of Mathematcs, Unversty of Bologna, P.zza d Porta San Donato 5, 4017

More information

FiberMesh: Designing Freeform Surfaces with 3D Curves

FiberMesh: Designing Freeform Surfaces with 3D Curves FberMesh: Desgnng Freeform Surfaces wth 3D Curves Andrew Nealen TU Berln Takeo Igarash The Unversty of Tokyo / PRESTO JST Olga Sorkne TU Berln Marc Alexa TU Berln Fgure 1: Modelng results usng FIBERMESH.

More information

Radial Basis Functions

Radial Basis Functions Radal Bass Functons Mesh Reconstructon Input: pont cloud Output: water-tght manfold mesh Explct Connectvty estmaton Implct Sgned dstance functon estmaton Image from: Reconstructon and Representaton of

More information

Feature-Preserving Denoising of Point-Sampled Surfaces

Feature-Preserving Denoising of Point-Sampled Surfaces Feature-Preservng Denosng of Pont-Sampled Surfaces Jfang L College of Computer Scence and Informaton Technology Zhejang Wanl Unversty Nngbo 315100 Chna Abstract: Based on samplng lkelhood and feature ntensty,

More information

High resolution 3D Tau-p transform by matching pursuit Weiping Cao* and Warren S. Ross, Shearwater GeoServices

High resolution 3D Tau-p transform by matching pursuit Weiping Cao* and Warren S. Ross, Shearwater GeoServices Hgh resoluton 3D Tau-p transform by matchng pursut Wepng Cao* and Warren S. Ross, Shearwater GeoServces Summary The 3D Tau-p transform s of vtal sgnfcance for processng sesmc data acqured wth modern wde

More information

MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION

MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION Paulo Quntlano 1 & Antono Santa-Rosa 1 Federal Polce Department, Brasla, Brazl. E-mals: quntlano.pqs@dpf.gov.br and

More information

Machine Learning 9. week

Machine Learning 9. week Machne Learnng 9. week Mappng Concept Radal Bass Functons (RBF) RBF Networks 1 Mappng It s probably the best scenaro for the classfcaton of two dataset s to separate them lnearly. As you see n the below

More information

Outline. Type of Machine Learning. Examples of Application. Unsupervised Learning

Outline. Type of Machine Learning. Examples of Application. Unsupervised Learning Outlne Artfcal Intellgence and ts applcatons Lecture 8 Unsupervsed Learnng Professor Danel Yeung danyeung@eee.org Dr. Patrck Chan patrckchan@eee.org South Chna Unversty of Technology, Chna Introducton

More information

Injective Shape Deformations Using Cube-Like Cages

Injective Shape Deformations Using Cube-Like Cages 309 Injectve Shape Deformatons Usng Cube-Lke Cages Jr Kosnka 1 and Mchael Barton 2 1 Unversty of Oslo, jr.kosnka@cma.uo.no 2 Technon, barton@cs.technon.ac.l ABSTRACT The present paper nvestgates an applcaton

More information

Hybrid Non-Blind Color Image Watermarking

Hybrid Non-Blind Color Image Watermarking Hybrd Non-Blnd Color Image Watermarkng Ms C.N.Sujatha 1, Dr. P. Satyanarayana 2 1 Assocate Professor, Dept. of ECE, SNIST, Yamnampet, Ghatkesar Hyderabad-501301, Telangana 2 Professor, Dept. of ECE, AITS,

More information

AP PHYSICS B 2008 SCORING GUIDELINES

AP PHYSICS B 2008 SCORING GUIDELINES AP PHYSICS B 2008 SCORING GUIDELINES General Notes About 2008 AP Physcs Scorng Gudelnes 1. The solutons contan the most common method of solvng the free-response questons and the allocaton of ponts for

More information

Smooth Approximation to Surface Meshes of Arbitrary Topology with Locally Blended Radial Basis Functions

Smooth Approximation to Surface Meshes of Arbitrary Topology with Locally Blended Radial Basis Functions 587 Smooth Approxmaton to Surface eshes of Arbtrary Topology wth Locally Blended Radal Bass Functons ngyong Pang 1,, Weyn a 1, Zhgeng Pan and Fuyan Zhang 1 Cty Unversty of Hong Kong, mewma@ctyu.edu.hk

More information

Accounting for the Use of Different Length Scale Factors in x, y and z Directions

Accounting for the Use of Different Length Scale Factors in x, y and z Directions 1 Accountng for the Use of Dfferent Length Scale Factors n x, y and z Drectons Taha Soch (taha.soch@kcl.ac.uk) Imagng Scences & Bomedcal Engneerng, Kng s College London, The Rayne Insttute, St Thomas Hosptal,

More information

IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 17, NO. 10, OCTOBER

IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 17, NO. 10, OCTOBER IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 17, NO. 10, OCTOBER 2011 1531 Partwse Cross-Parameterzaton va Nonregular Convex Hull Domans Hua-Yu Wu, Chunhong Pan, Hongbn Zha, Qng Yang,

More information

Active Contours/Snakes

Active Contours/Snakes Actve Contours/Snakes Erkut Erdem Acknowledgement: The sldes are adapted from the sldes prepared by K. Grauman of Unversty of Texas at Austn Fttng: Edges vs. boundares Edges useful sgnal to ndcate occludng

More information

Control strategies for network efficiency and resilience with route choice

Control strategies for network efficiency and resilience with route choice Control strateges for networ effcency and reslence wth route choce Andy Chow Ru Sha Centre for Transport Studes Unversty College London, UK Centralsed strateges UK 1 Centralsed strateges Some effectve

More information

Finite Element Analysis of Rubber Sealing Ring Resilience Behavior Qu Jia 1,a, Chen Geng 1,b and Yang Yuwei 2,c

Finite Element Analysis of Rubber Sealing Ring Resilience Behavior Qu Jia 1,a, Chen Geng 1,b and Yang Yuwei 2,c Advanced Materals Research Onlne: 03-06-3 ISSN: 66-8985, Vol. 705, pp 40-44 do:0.408/www.scentfc.net/amr.705.40 03 Trans Tech Publcatons, Swtzerland Fnte Element Analyss of Rubber Sealng Rng Reslence Behavor

More information

Shape Representation Robust to the Sketching Order Using Distance Map and Direction Histogram

Shape Representation Robust to the Sketching Order Using Distance Map and Direction Histogram Shape Representaton Robust to the Sketchng Order Usng Dstance Map and Drecton Hstogram Department of Computer Scence Yonse Unversty Kwon Yun CONTENTS Revew Topc Proposed Method System Overvew Sketch Normalzaton

More information

THE PULL-PUSH ALGORITHM REVISITED

THE PULL-PUSH ALGORITHM REVISITED THE PULL-PUSH ALGORITHM REVISITED Improvements, Computaton of Pont Denstes, and GPU Implementaton Martn Kraus Computer Graphcs & Vsualzaton Group, Technsche Unverstät München, Boltzmannstraße 3, 85748

More information

A high precision collaborative vision measurement of gear chamfering profile

A high precision collaborative vision measurement of gear chamfering profile Internatonal Conference on Advances n Mechancal Engneerng and Industral Informatcs (AMEII 05) A hgh precson collaboratve vson measurement of gear chamferng profle Conglng Zhou, a, Zengpu Xu, b, Chunmng

More information