Hybrid Video Coding. Thomas Wiegand: Digital Image Communication Hybrid Video Coding 1

Size: px
Start display at page:

Download "Hybrid Video Coding. Thomas Wiegand: Digital Image Communication Hybrid Video Coding 1"

Transcription

1 Hri Vieo Coing Principle of Hri Vieo Coing Moion-Compene Preicion Bi Allocion Moion Moel Moion Eimion Efficienc of Hri Vieo Coing Thom Wiegn: Digil Imge Communicion Hri Vieo Coing

2 I h een cuomr in he p o rnmi ucceive complee imge of he rnmie picure. [...] In ccornce wih hi invenion hi ifficul i voie rnmiing onl he ifference eween ucceive imge of he ojec. Thom Wiegn: Digil Imge Communicion Hri Vieo Coing

3 Hri Vieo Encoer [ ] u[ ] - Decoer Coer Conrol Inr-Frme DCT Coer Inr-Frme Decoer Conrol D DCT Coefficien u' [ ] Inr/Iner 0 ˆ [ ] Moion- Compene Preicor Moion Eimor ' [ ] Moion D Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 3

4 Hri Vieo Decoer Conrol D DCT Coefficien Decoer Inr-Frme Decoer u' [ ] Inr/Iner 0 Moion- Compene Preicor ' [ ] Moion D ˆ [ ] Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 4

5 Moion-Compene Preicion Moving ojec Sionr ckgroun Previou frme Δ Curren frme Diplce ojec ime Preicion for he luminnce ignl [] wihin he moving ojec: ˆ [ ] ( Δ from: Giro Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 5

6 Moion-Compene Preicion: Emple Frme [-] (previou Frme [] (curren Priion of frme ino lock (chemic Frme wih iplcemen vecor Difference eween moioncompene preicion n curren frme u[] Reference lock in frme Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 6

7 Re-conrine Moion Eimion Bi-re R Moion vecor re R m D Preicion error re R u Opimum re-off: D R D m R u Diplcemen error vrince Diplcemen error vrince cn e influence vi Block-ize qunizion of moion prmeer Choice of moion moel from: Giro Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 7

8 Re-Conrine Coer Conrol Efficienc incree vi ing coing moe Wh pr of he imge houl e coe uing wh meho? Prolem cn e poe : minimize iorion D ujec o re conrin R c min { D }.. R<Rc Coer Conrol uing Lgrngin opimizion: Solve n unconrine minimizion prolem λ min { D R } [Evere III 963] [Shohm Gerho 988] [Chou Lookugh Gr 989] Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 8

9 Lgrngin Opimizion in Vieo Coing A numer of inercion re ofen neglece Temporl epenenc ue o DPCM loop Spil epenenc of coing eciion Coniionl enrop coing Re-Conrine Moion Eimion [Sullivn Bker 99]: min {D m λ R m } Diorion fer moion compenion Lgrnge prmeer Numer of i for moion vecor Re-Conrine Moe Deciion [Wiegn e l. 996]: min {D λ R} Diorion fer reconrucion Lgrnge prmeer Numer of i for coing moe Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 9

10 Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 0 Cmer Moel Cmer Moel Nurl cmer-view cene re projece from he 3-D worl ino he -D imge plne A cmer moel cn e ue o ecrie projecion len n mpling z Imge plne 3D Poiion Imge poiion Focl poin F z 3-D poiion Imge poiion Imge plne Perpecive projecion moel Orhogrphic projecion moel Cn e ue when F«Z for ll coniere poin Z Y X P Z Y X P F p F p Y Z F X Z F Y X

11 Moion Moel Moion in 3-D pce correpon o iplcemen in he imge plne Moion compenion in he imge plne i conuce o provie preicion ignl for efficien vieo compreion Efficien moion-compene preicion ofen ue ie informion o rnmi he iplcemen Diplcemen mu e efficienl repreene for vieo compreion Moion moel rele 3-D moion o iplcemen uming reonle rericion of he moion n ojec in he 3-D worl Moion Moel f ( f ( : locion in previou imge : locion in curren imge : vecor of moion coefficien : iplcemen Thom Wiegn: Digil Imge Communicion Hri Vieo Coing

12 Mhemicl moel: Rericion: Perpecive Moion Moel 3 3 c c c c Roion n cling of rigi o in 3-D pce u no rnlion Trnlion roion n cling of plnr pch in 3-D Avnge: correpon o perpecive projecion moel Divnge: hperolic moion funcion Thom Wiegn: Digil Imge Communicion Hri Vieo Coing

13 Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 3 Trnlionl moion moel 4-Prmeer moion moel: rnlion zoom (ioropic Scling roion in imge plne Affine moion moel: Prolic moion moel Cn lo e viewe Tlor epnion of perpecive moion moel Orhogrphic Moion Moel Orhogrphic Moion Moel

14 Impc of he Affine Prmeer 50 rnlion cling heering Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 4

15 Impc of he Prolic Prmeer Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 5

16 Impc of he Perpecive Prmeer c c Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 6

17 Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 7 Differenil Moion Eimion Differenil Moion Eimion Aume mll iplcemen : Aperure prolem: everl oervion require Inccure for iplcemen > 0.5 pel muligri meho ierion Minimize Diplce frme ifference Horizonl n vericl grien of imge ignl S u Δ Δ Δ ( ( ( ( ˆ( ( ( ( min u B B

18 Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 8 Grien Grien-Be Affine Refinemen Be Affine Refinemen Diplcemen vecor fiel i repreene Cominion 3 3 iel em of liner equion: Sem cn e olve uing e.g. peuo-invere minimizing ( ( ( ( ( 3 3 u Δ B B u ( rg min u

19 Principle of Blockmching Suivie ever imge ino qure lock Fin one iplcemen vecor for ech lock Wihin erch rnge fin e mch h minimize n error meure. erch rnge in previou frme S k- Block of curen frme S k Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 9

20 Blockmching: : Error Meure Men qure error (um of qure error B B SSE( [ ( ( Δ] Sum of olue ifference SAD( B B ( ( Δ Approimel me performnce SAD le comple for ome rchiecure Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 0

21 Blockmching: : Serch Sregie I Full erch All poile iplcemen wihin he erch rnge re compre. Compuionll epenive Highl regulr prllelizle Thom Wiegn: Digil Imge Communicion Hri Vieo Coing

22 Block mching: Serch Sregie III Compuionl Complei Block comprion D logrihmic full erch Emple: m. horizonl vericl iplcemen 6 ineger-pel ccurc - for pecil vecor (6 - wor ce from: Giro Thom Wiegn: Digil Imge Communicion Hri Vieo Coing

23 Block Comprion Spee-Up Tringle inequliie for SAD n SSE S S ( S S S lock lock S k k S k k lock N k lock ( S k k S k lock numer of erm in um Sreg:. Compue pril um for lock in curren n previou frme. Compre lock e on pril um 3. Omi full lock comprion if pril um inice wore error meure hn previou e reul Performnce: > 0 pee up of full erch lock mching repore emploing. Sum over 66 lock. Row wie lock projecion 3. Column wie lock projecion (Lin Ti IEEE Tr. Commun. M 97 Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 3 k N lock S lock k S k lock S k

24 Su-pel Trnlionl Moion Moion vecor re ofen no rerice o onl poin ino he ineger-pel gri of he reference frme Tpicl u-pel ccurcie: hlf-pel n qurer-pel Su-pel poiion re ofen eime refinemen Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 4

25 Hior of Moion Compenion Inrfrme coing: onl pil correlion eploie Complei DCT [Ahme Nrjn Ro 974] JPEG [99] incree Coniionl replenihmen H.0 [984] (DPCM clr qunizion Frme ifference coing H.0 Verion [988] Moion compenion: ineger-pel ccure iplcemen H.6 [99] Hlf-pel ccure moion compenion MPEG- [993] MPEG-/H.6 [994] Vrile lock-ize (66 & 88 moion compenion H.63 [996] MPEG-4 [999] Vrile lock-ize (66 44 n muli-frme moion compenion H.6L [00] Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 5

26 PSNR [B] Mileone in Vieo Coing Vrile lock ize (66 44 qurer-pel muli-frme moion compenion (H.6L 00 Vrile lock ize (66 88 (H qurer-pel moion compenion (MPEG Bi-re Reucion: 75% Ineger-pel moion compenion (H.6 99 Inrfrme DCT coing (JPEG 990 Hlf-pel moion compenion (MPEG- 993 MPEG- 994 Coniionl Replenihmen (H Foremn 0 Hz QCIF 00 frme Re [ki/] Frme Difference coing (H Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 6

27 SNR [B] Mileone in Vieo Coing Vrile lock ize (66 44 qurer-pel muli-frme moion compenion (H.6L 00 Viul Comprion Vrile lock ize (66 88 (H qurer-pel moion compenion (MPEG Ineger-pel moion compenion (H.6 99 Inrfrme DCT coing (JPEG 990 Hlf-pel moion compenion (MPEG- 993 MPEG- 994 Coniionl Replenihmen (H Frme Difference coing (H Re [ki/] Foremn 0 Hz QCIF 00 frme Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 7

28 00 ki/ 0 Hz Inrfrme DCT coing No moion compenion (JPEG 990 Vrile lock ize (66 44 qurer-pel muli-frme moion compenion (H.6L 00 Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 8

29 Summr Vieo coing hri of moion compenion n preicion reiul coing Lgrngin i-llocion rule pecif conn lope llocion o moion coefficien n preicion error Moion moel cn repreen vriou kin of moion In prcice: ffine or 8-prmeer moel for cmer moion rnlionl moel for mll lock Differenil meho clcule iplcemen from pil n emporl ifference in he imge ignl Block mching compue error meure for cnie iplcemen n fin e mch Spee up lock mching erch meho n clever pplicion of ringle inequli Hri vieo coing h een ricll improve enhnce moion compenion cpiliie Thom Wiegn: Digil Imge Communicion Hri Vieo Coing 9

CS 428: Fall Introduction to. Geometric Transformations (continued) Andrew Nealen, Rutgers, /20/2010 1

CS 428: Fall Introduction to. Geometric Transformations (continued) Andrew Nealen, Rutgers, /20/2010 1 CS 428: Fall 2 Inroducion o Compuer Graphic Geomeric Tranformaion (coninued) Andrew Nealen, Ruger, 2 9/2/2 Tranlaion Tranlaion are affine ranformaion The linear par i he ideni mari The 44 mari for he ranlaion

More information

Lecture 10 Splines Introduction to Splines

Lecture 10 Splines Introduction to Splines ES8 Economerics. Inroducion o Splines. Esiming Spline Mehod One. Esiming Spline Mehod To.4 Cuic Splines Lecure Splines. Inroducion o Splines Firs pplied Poirier & Grer (974) in sud of profi res in hree

More information

Grade 11 Physics Homework 3. Be prepared to defend your choices in class!

Grade 11 Physics Homework 3. Be prepared to defend your choices in class! Gre 11 Physics Homework 3 Be prepre o efen your choices in clss! 1. The grph shows he riion wih ime of he elociy of n objec. Which one of he following grphs bes represens he riion wih ime of he ccelerion

More information

Overview: motion-compensated coding

Overview: motion-compensated coding Overview: motion-compensated coding Motion-compensated prediction Motion-compensated hybrid coding Motion estimation by block-matching Motion estimation with sub-pixel accuracy Power spectral density of

More information

CS 314 Principles of Programming Languages

CS 314 Principles of Programming Languages CS 314 Principles of Progrmming Lnguges Lecure 10: Synx Direced Trnslion Zheng (Eddy) Zhng Rugers Universiy Februry 19, 2018 Clss Informion Homework 2 is sill being grded. Projec 1 nd homework 4 will be

More information

Jorge Salvador Marques, Stereo Reconstruction

Jorge Salvador Marques, Stereo Reconstruction Jorge Slvdor Mrques, Sereo Reconsrucion roblem Gol: reconsruc he D she of objecs in he scene from or more imges. Jorge Slvdor Mrques, Jorge Slvdor Mrques, secil cse f f f f b model reconsrucion, b - fb,

More information

CEE598 - Visual Sensing for Civil Infrastructure Eng. & Mgmt.

CEE598 - Visual Sensing for Civil Infrastructure Eng. & Mgmt. CEE598 - Visul Sensing for Civil Infrsrucure Eng. & Mgm. Session 2 Review of Liner Algebr nd Geomeric Trnsformions Mni Golprvr-Frd Deprmen of Civil nd Environmenl Engineering Deprmen of Compuer Science

More information

RULES OF DIFFERENTIATION LESSON PLAN. C2 Topic Overview CALCULUS

RULES OF DIFFERENTIATION LESSON PLAN. C2 Topic Overview CALCULUS CALCULUS C Topic Overview C RULES OF DIFFERENTIATION In pracice we o no carry ou iffereniaion from fir principle (a ecribe in Topic C Inroucion o Differeniaion). Inea we ue a e of rule ha allow u o obain

More information

Procedure Abstraction

Procedure Abstraction Compiler Design Procedure Absrcion Hwnsoo Hn Conrol Absrcion Procedures hve well-defined conrol-flow The Algol-60 procedure cll Invoked cll sie, wih some se of cul prmeers Conrol reurns o cll sie, immediely

More information

3D Image Representation through Hierarchical Tensor Decomposition, Based on SVD with Elementary Tensor of size 2 2 2

3D Image Representation through Hierarchical Tensor Decomposition, Based on SVD with Elementary Tensor of size 2 2 2 WSEAS RASACIOS on SIGAL ROCESSIG Roumen Kouncev, Roumin Kouncev 3D Imge Represenion roug Hierrcicl ensor Decomposiion, Bse on SVD wi Elemenry ensor of size ROUME KOUCHEV Rio Communicions n Vieo ecnologies

More information

the marginal product. Using the rule for differentiating a power function,

the marginal product. Using the rule for differentiating a power function, 3 Augu 07 Chaper 3 Derivaive ha economi ue 3 Rule for differeniaion The chain rule Economi ofen work wih funcion of variable ha are hemelve funcion of oher variable For example, conider a monopoly elling

More information

Sound Insulation Analysis of Automotive Soundproof Material using Urethane and Rubber

Sound Insulation Analysis of Automotive Soundproof Material using Urethane and Rubber Jornl o Technology nd Socil Science JTSS Sond Inlion Anlyi o Aomoive Sondproo Meril ing Urehne nd Rer Yohio row,, Tey Ozki,, oyki kizmi 3,c Fcly o Science nd Engineering, Teikyo Univeriy, - Toyoodi, Unomiy

More information

Data Structures and Algorithms. The material for this lecture is drawn, in part, from The Practice of Programming (Kernighan & Pike) Chapter 2

Data Structures and Algorithms. The material for this lecture is drawn, in part, from The Practice of Programming (Kernighan & Pike) Chapter 2 Daa Srucures and Algorihms The maerial for his lecure is drawn, in par, from The Pracice of Programming (Kernighan & Pike) Chaper 2 1 Moivaing Quoaion Every program depends on algorihms and daa srucures,

More information

4. Minimax and planning problems

4. Minimax and planning problems CS/ECE/ISyE 524 Inroducion o Opimizaion Spring 2017 18 4. Minima and planning problems ˆ Opimizing piecewise linear funcions ˆ Minima problems ˆ Eample: Chebyshev cener ˆ Muli-period planning problems

More information

Fisheye Lens Distortion Correction on Multicore and Hardware Accelerator Platforms

Fisheye Lens Distortion Correction on Multicore and Hardware Accelerator Platforms Fiheye Len Diorion Correcion on Mulicore and Hardware Acceleraor Plaform Konani Dalouka 1 Chrio D. Anonopoulo 1 Nikolao Sek M. Bella 1 Chai 1 Deparmen of Compuer and Communicaion Engineering Univeriy of

More information

8.2 Areas in the Plane

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

More information

EECS 487: Interactive Computer Graphics

EECS 487: Interactive Computer Graphics EECS 487: Ineracive Compuer Graphics Lecure 7: B-splines curves Raional Bézier and NURBS Cubic Splines A represenaion of cubic spline consiss of: four conrol poins (why four?) hese are compleely user specified

More information

Fill in the following table for the functions shown below.

Fill in the following table for the functions shown below. By: Carl H. Durney and Neil E. Coer Example 1 EX: Fill in he following able for he funcions shown below. he funcion is odd he funcion is even he funcion has shif-flip symmery he funcion has quarer-wave

More information

CL-Path in B-Spline Form with Global Error Control for 3-Axis Sculptured Surface Machining

CL-Path in B-Spline Form with Global Error Control for 3-Axis Sculptured Surface Machining n Inernionl onference on Mechnicl, Proucion n Auomobile Engineering (IMPAE'0) Singpore April 8-9, 0 -Ph in B-Spline Form wih Globl Error onrol for 3-Axis Sculpure Surfce Mchining Mqsoo Ahme. Khn, n Zezhong.

More information

Giving credit where credit is due

Giving credit where credit is due JEP 84H Foundtion of omputer tem Proceor rchitecture II: ogic eign r. teve Goddrd goddrd@ce.unl.edu Giving credit where credit i due Mot of lide for thi lecture re ed on lide creted r. rnt, rnegie Mellon

More information

DEFINITION OF THE LAPLACE TRANSFORM

DEFINITION OF THE LAPLACE TRANSFORM 74 CHAPER 7 HE LAPLACE RANSFORM 7 DEFINIION OF HE LAPLACE RANSFORM REVIEW MAERIAL Improper inegral wih infinie limi of inegraio Inegraion y par and parial fracion decompoiion INRODUCION In elemenary calculu

More information

Overview: motion estimation. Differential motion estimation

Overview: motion estimation. Differential motion estimation Overview: motion estimation Differential methods Fast algorithms for Sub-pel accuracy Rate-constrained motion estimation Bernd Girod: EE368b Image Video Compression Motion Estimation no. 1 Differential

More information

A High-Performance Area-Efficient Multifunction Interpolator

A High-Performance Area-Efficient Multifunction Interpolator A High-Performance Area-Efficien Mulifuncion Inerpolaor ARITH Suar Oberman Michael Siu Ouline Wha i a GPU? Targe applicaion and floaing poin Shader microarchiecure High-order funcion Aribue inerpolaion

More information

Systems & Biomedical Engineering Department. Transformation

Systems & Biomedical Engineering Department. Transformation Sem & Biomedical Engineering Deparmen SBE 36B: Compuer Sem III Compuer Graphic Tranformaion Dr. Aman Eldeib Spring 28 Tranformaion Tranformaion i a fundamenal corner one of compuer graphic and i a cenral

More information

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

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

More information

WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM - ACCELERATED GEOMETRY ACCELERATED. Should conjectures always be stated?

WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM - ACCELERATED GEOMETRY ACCELERATED. Should conjectures always be stated? AYNESBORO AREA SCOOL DISTRICT CURRICULUM - ACCELERATED GEOMETRY ACCELERATED UNIT: Cher Bsics of Geomery NO. OF : 6 UNIT ESSENTIAL QUESTIONS: ow re he undefined erms used o esblish definiions in geomery?

More information

Algebra II Notes Unit Ten: Conic Sections

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

More information

Parametric equations 8A

Parametric equations 8A Parameric equaions 8A a so () y () Susiue () ino (): y ( ) y 5, So he domain of f() is 6. y, So he range of f() is y 7. d so () y () Susiue () ino (): y y, 0 So he domain of f() is. 5 so 5 () y () Susiue

More information

Overview Capturing Still Images Recording Videos Various Features Advanced Features

Overview Capturing Still Images Recording Videos Various Features Advanced Features Overview... - Viewfiner Inicators... -3 Switching s... -5 Capturing Still Images... -6 Capturing Still Images... -6 Recoring Vieos... -8 Recoring Vieos... -8 Various Features... -0 Using Smile Moe... -0

More information

Image warping Li Zhang CS559

Image warping Li Zhang CS559 Wha is an image Image arping Li Zhang S559 We can hink of an image as a funcion, f: R 2 R: f(, ) gives he inensi a posiion (, ) defined over a recangle, ih a finie range: f: [a,b][c,d] [,] f Slides solen

More information

4.2 Implicit Differentiation

4.2 Implicit Differentiation 6 Chapter 4 More Derivatives 4. Implicit Differentiation What ou will learn about... Implicitl Define Functions Lenses, Tangents, an Normal Lines Derivatives of Higher Orer Rational Powers of Differentiable

More information

Maximum Flows: Polynomial Algorithms

Maximum Flows: Polynomial Algorithms Maximum Flow: Polynomial Algorihm Algorihm Augmening pah Algorihm - Labeling Algorihm - Capaciy Scaling Algorihm - Shore Augmening Pah Algorihm Preflow-Puh Algorihm - FIFO Preflow-Puh Algorihm - Highe

More information

Texture Mapping. Texture Mapping. Map textures to surfaces. Trompe L Oeil ( Deceive the Eye ) Texture map. The texture

Texture Mapping. Texture Mapping. Map textures to surfaces. Trompe L Oeil ( Deceive the Eye ) Texture map. The texture CSCI 48 Compuer Graphic Lecure Texure Mapping A way of adding urface deail Texure Mapping February 5, 22 Jernej Barbic Univeriy of Souhern California Texure Mapping + Shading Filering and Mipmap Non-color

More information

Flow graph/networks MAX FLOW APPLICATIONS. Flow constraints. Max flow problem 4/26/12

Flow graph/networks MAX FLOW APPLICATIONS. Flow constraints. Max flow problem 4/26/12 4// low graph/nework MX LOW PPLIION 30, pring 0 avid Kauchak low nework direced, weighed graph (V, ) poiive edge weigh indicaing he capaciy (generally, aume ineger) conain a ingle ource V wih no incoming

More information

The Laplace Transform

The Laplace Transform 7 he Laplace ranform 7 Definiion of he Laplace ranform 7 Invere ranform and ranform of Derivaive 7 Invere ranform 7 ranform of Derivaive 73 Operaional Properie I 73 ranlaion on he -Axi 73 ranlaion on he

More information

Camera Overview Capturing Still Images Recording Videos Various Features Advanced Features

Camera Overview Capturing Still Images Recording Videos Various Features Advanced Features Overview... - Viewfiner Inicators... -3 Switching s... -5 Capturing Still Images... -6 Capturing Still Images... -6 Recoring Vieos... -8 Recoring Vieos... -8 Various Features... -0 Using Smile Moe... -0

More information

USING ARTIFICIAL NEURAL NETWORKS TO APPROXIMATE A DISCRETE EVENT STOCHASTIC SIMULATION MODEL

USING ARTIFICIAL NEURAL NETWORKS TO APPROXIMATE A DISCRETE EVENT STOCHASTIC SIMULATION MODEL USING ARTIFICIAL NEURAL NETWORKS TO APPROXIMATE A DISCRETE EVENT STOCHASTIC SIMULATION MODEL Robert A. Kilmer Department of Sytem Engineering Unite State Military Acaemy Wet Point, NY 1996 Alice E. Smith

More information

geometric transformations

geometric transformations geomeric ranformaion comuer grahic ranform 28 fabio ellacini linear algebra review marice noaion baic oeraion mari-vecor mulilicaion comuer grahic ranform 28 fabio ellacini 2 marice noaion for marice and

More information

INFORMATION SECURITY

INFORMATION SECURITY ISSN 2075-078. Science-Base Technologies 203. 2 (8) 79 INFORMATION SECRITY DC 629.39 THE METHOD OF TIME SPENT ESTIMATING ON PROCESSING AND TRANSMISSION OF COMPRESSED VIDEO STREAM A. Leah I. Cheremsoy 2

More information

Energy/Performance Design of Memory Hierarchies for Processor-in-Memory Chips

Energy/Performance Design of Memory Hierarchies for Processor-in-Memory Chips Energy/Performnce Design of Memory Hierrchies for Processor-in-Memory Chips Michel Hung, Jose Renu, Seung-Moon Yoo, Josep Torrells Deprmen of Compuer Science Deprmen of Elecricl n Compuer Engineering Universiy

More information

Rou$ng. Rou$ng: Mapping Link to Path. Data and Control Planes. Rou$ng vs. Forwarding. Rou$ng Protocols. What Does the Protocol Compute?

Rou$ng. Rou$ng: Mapping Link to Path. Data and Control Planes. Rou$ng vs. Forwarding. Rou$ng Protocols. What Does the Protocol Compute? Ro$ng: Mapping Link o Pah Ro$ng Jennifer Reford COS : Comper Nework Lecre: MW 0-0:0am in Archiecre N0 hgp://www.c.princeon.ed/core/archie/pr/co/ link eion pah name addre Daa and Conrol Plane daa plane

More information

M y. Image Warping. Targil 7 : Image Warping. Image Warping. 2D Geometric Transformations. image filtering: change range of image g(x) = T(f(x))

M y. Image Warping. Targil 7 : Image Warping. Image Warping. 2D Geometric Transformations. image filtering: change range of image g(x) = T(f(x)) Hebrew Universi Image Processing - 6 Image Warping Hebrew Universi Image Processing - 6 argil 7 : Image Warping D Geomeric ransormaions hp://www.jere-marin.com Man slides rom Seve Seiz and Aleei Eros Image

More information

MTH 146 Conics Supplement

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

More information

Nearest-Neighbor and Fault-Tolerant Quantum Circuit Implementation

Nearest-Neighbor and Fault-Tolerant Quantum Circuit Implementation Neres-Neighbor nd Ful-olern Qunum Circui Implemenion Lxmidhr Biswl, Chndn Bndyopdhyy, Anupm Chopdhyy 2, Rober Wille 3, Rolf Drechsler 4, fizur Rhmn Indin Insiue of Engineering cience nd echnology hibpur,

More information

Implementing Ray Casting in Tetrahedral Meshes with Programmable Graphics Hardware (Technical Report)

Implementing Ray Casting in Tetrahedral Meshes with Programmable Graphics Hardware (Technical Report) Implemening Ray Casing in Terahedral Meshes wih Programmable Graphics Hardware (Technical Repor) Marin Kraus, Thomas Erl March 28, 2002 1 Inroducion Alhough cell-projecion, e.g., [3, 2], and resampling,

More information

Interactive Rendering of Atmospheric Scattering Effects Using Graphics Hardware

Interactive Rendering of Atmospheric Scattering Effects Using Graphics Hardware Ineracive Rendering of Amopheric Scaering Effec Uing Graphic Hardware Yohinori Dobahi Tuyohi Yamamoo Tomoyui Nihia Hoaido Univeriy Hoaido Univeriy Toyo Univeriy Overview Inroducion - moivaion - previou

More information

Hybrid Signal-based and Geometry-based Prediction for Haptic Data Reduction

Hybrid Signal-based and Geometry-based Prediction for Haptic Data Reduction Hybri Signal-base an Geomery-base Preicion for Hapic Daa Reucion Xiao Xu, Julius Kammerl, Rahul Chauhari an Eckehar Seinbach nsiue for Meia Technology, Technische Universiä München, Germany Email: {xiao.xu,

More information

Camera Overview Capturing Still Images Recording Videos Various Features Advanced Features

Camera Overview Capturing Still Images Recording Videos Various Features Advanced Features Overview... -2 Viewfiner Inicators... -3 Switching s... -4 Capturing Still Images... -5 Capturing Still Images... -5 Recoring Vieos... - Recoring Vieos... - Various Features... -9 Continuous Shooting...

More information

Spline Curves. Color Interpolation. Normal Interpolation. Last Time? Today. glshademodel (GL_SMOOTH); Adjacency Data Structures. Mesh Simplification

Spline Curves. Color Interpolation. Normal Interpolation. Last Time? Today. glshademodel (GL_SMOOTH); Adjacency Data Structures. Mesh Simplification Las Time? Adjacency Daa Srucures Spline Curves Geomeric & opologic informaion Dynamic allocaion Efficiency of access Mesh Simplificaion edge collapse/verex spli geomorphs progressive ransmission view-dependen

More information

Motion estimation. Announcements. Outline. Motion estimation

Motion estimation. Announcements. Outline. Motion estimation Annoncemens Moion esimaion Projec # is e on ne Tesa sbmission mechanism will be annonce laer his week. graing: reor is imoran resls goo/ba iscssions on imlemenaion inerface feares ec. Digial Visal Effecs

More information

Dimmer time switch AlphaLux³ D / 27

Dimmer time switch AlphaLux³ D / 27 Dimmer ime swich AlphaLux³ D2 426 26 / 27! Safey noes This produc should be insalled in line wih insallaion rules, preferably by a qualified elecrician. Incorrec insallaion and use can lead o risk of elecric

More information

See chapter 8 in the textbook. Dr Muhammad Al Salamah, Industrial Engineering, KFUPM

See chapter 8 in the textbook. Dr Muhammad Al Salamah, Industrial Engineering, KFUPM Goal programming Objective of the topic: Indentify indutrial baed ituation where two or more objective function are required. Write a multi objective function model dla a goal LP Ue weighting um and preemptive

More information

WORKSHOP 9 HEX MESH USING SWEEP VECTOR

WORKSHOP 9 HEX MESH USING SWEEP VECTOR WORKSHOP 9 HEX MESH USING SWEEP VECTOR WS9-1 WS9-2 Prolem Desription This exerise involves importing urve geometry from n IGES file. The urves re use to rete other urves. From the urves trimme surfes re

More information

Camera Overview Capturing Still Images Recording Videos Various Features Advanced Features

Camera Overview Capturing Still Images Recording Videos Various Features Advanced Features Overview... -2 Viewfiner Inicators... -3 Capturing Still Images... -5 Capturing Still Images... -5 Recoring Vieos... - Recoring Vieos... - Various Features... -9 Continuous Shooting... -9 A Frames to Images...

More information

Curves & Surfaces. Last Time? Today. Readings for Today (pick one) Limitations of Polygonal Meshes. Today. Adjacency Data Structures

Curves & Surfaces. Last Time? Today. Readings for Today (pick one) Limitations of Polygonal Meshes. Today. Adjacency Data Structures Las Time? Adjacency Daa Srucures Geomeric & opologic informaion Dynamic allocaion Efficiency of access Curves & Surfaces Mesh Simplificaion edge collapse/verex spli geomorphs progressive ransmission view-dependen

More information

AlphaGo Overview. Overview. Digression: Zero sum, alternating move games. Original AlphaGo approach. Recent AlphaGo Zero approach 10/24/17

AlphaGo Overview. Overview. Digression: Zero sum, alternating move games. Original AlphaGo approach. Recent AlphaGo Zero approach 10/24/17 AlphGo Overview Ron Prr CompSci 590.2 Duke Univerity Overview Digreion: Zero um, lternting move gme Originl AlphGo pproch Recent AlphGo Zero pproch 1 2 Alternting move, zero-um, 2-plyer gme Ordinry bellmn

More information

Video streaming over Vajda Tamás

Video streaming over Vajda Tamás Video sreaming over 802.11 Vajda Tamás Video No all bis are creaed equal Group of Picures (GoP) Video Sequence Slice Macroblock Picure (Frame) Inra (I) frames, Prediced (P) Frames or Bidirecional (B) Frames.

More information

Lighting and Shading

Lighting and Shading ighting an Shaing 4 th ~ 5 th Week, 29 Why We Nee Shaing Suppoe we buil a moel of a phere uing many polygon an color it with glcolor We get omething like But we want Why oe the image of a real phere look

More information

Image warping/morphing

Image warping/morphing Image arping/morphing Image arping Digial Visual Effecs Yung-Yu Chuang ih slides b Richard Szeliski, Seve Seiz, Tom Funkhouser and leei Efros Image formaion Sampling and quanizaion B Wha is an image We

More information

CENG 477 Introduction to Computer Graphics. Modeling Transformations

CENG 477 Introduction to Computer Graphics. Modeling Transformations CENG 477 Inroducion o Compuer Graphics Modeling Transformaions Modeling Transformaions Model coordinaes o World coordinaes: Model coordinaes: All shapes wih heir local coordinaes and sies. world World

More information

Control Flow Analysis

Control Flow Analysis Control Flow Analyi Efficiency Control Flow Analyi Type an Effect ytem Data Flow Analyi Abtract Interpretation Correctne Control Flow Analyi p.1/35 Control Flow Analyi Flow information i eential for the

More information

Geometric Transformations Hearn & Baker Chapter 5. Some slides are taken from Robert Thomsons notes.

Geometric Transformations Hearn & Baker Chapter 5. Some slides are taken from Robert Thomsons notes. Geometric Tranformation Hearn & Baker Chapter 5 Some lie are taken from Robert Thomon note. OVERVIEW Two imenional tranformation Matri repreentation Invere tranformation Three imenional tranformation OpenGL

More information

Describing motion. Unit 6.1. context. Fact File. Distance and displacement. Science

Describing motion. Unit 6.1. context. Fact File. Distance and displacement. Science Uni 6. conex Eeryhing in he uniere i in moion all he ime. We are moing a 00 km/h a he Earh pin on i axi and orbi he Sun. The Sun orbi he cenre of our galaxy, he Milky Way. Eer ince he Big Decribing moion

More information

Describing Combinational circuits in BSV

Describing Combinational circuits in BSV Decriing Comintionl circuit in BSV Arvind Computer Science & Artificil Intelligence L. Mchuett Intitute of Technology Ferury 13, 2018 http://cg.cil.mit.edu/6.s084 L03-1 Three imple comintionl circuit NOT

More information

Enhancement of Noisy Speech Using Sliding Discrete Cosine Transform

Enhancement of Noisy Speech Using Sliding Discrete Cosine Transform Enhancemen of Noiy Speech Uing Sliding Dicree Coine Tranform Vialy Kober Deparmen of Compuer Science, Diviion of Applied Phyic CICESE, Enenada, B.C. 860, Mexico vober@cicee.mx Abrac. Denoiing of peech

More information

Chapter Six Chapter Six

Chapter Six Chapter Six Chaper Si Chaper Si 0 CHAPTER SIX ConcepTess and Answers and Commens for Secion.. Which of he following graphs (a) (d) could represen an aniderivaive of he funcion shown in Figure.? Figure. (a) (b) (c)

More information

Numerical Solution of ODE

Numerical Solution of ODE Numerical Soluion of ODE Euler and Implici Euler resar; wih(deools): wih(plos): The package ploools conains more funcions for ploing, especially a funcion o draw a single line: wih(ploools): wih(linearalgebra):

More information

Viewing Transformations I Comp 535

Viewing Transformations I Comp 535 Viewing Transformations I Comp 535 Motivation Want to see our virtual 3-D worl on a 2-D screen 2 Graphics Pipeline Moel Space Moel Transformations Worl Space Viewing Transformation Ee/Camera Space Projection

More information

Programming (was due Friday) Last day to submit for late credit was yesterday. Today 6-7pm in AA204 All you need is a writing utensil and an ID

Programming (was due Friday) Last day to submit for late credit was yesterday. Today 6-7pm in AA204 All you need is a writing utensil and an ID Announcement Aignment Pogmming ( ue Fi Lt to umit fo lte ceit ete Aignment Theo ue net Wene Pogmming Mitem To 6-7m in AA04 All ou nee i iting utenil n n ID (no ook/note/clculto etc. You cnnot leve the

More information

Principles of MRI EE225E / BIO265. Lecture 10. Instructor: Miki Lustig UC Berkeley, EECS. M. Lustig, EECS UC Berkeley

Principles of MRI EE225E / BIO265. Lecture 10. Instructor: Miki Lustig UC Berkeley, EECS. M. Lustig, EECS UC Berkeley Principles of MRI Lecure 0 EE225E / BIO265 Insrucor: Miki Lusig UC Berkeley, EECS Bloch Eq. For Recepion No B() : 2 4 Ṁ x Ṁ y Ṁ z 3 5 = 2 6 4 T 2 ~ G ~r 0 ~G ~r T 2 0 0 0 T 3 2 7 5 4 M x M y M z 3 5 +

More information

Projection & Interaction

Projection & Interaction Projecion & Ineracion Algebra of projecion Canonical viewing volume rackball inerface ransform Hierarchies Preview of Assignmen #2 Lecure 8 Comp 236 Spring 25 Projecions Our lives are grealy simplified

More information

Subband coding of image sequences using multiple vector quantizers. Emanuel Martins, Vitor Silva and Luís de Sá

Subband coding of image sequences using multiple vector quantizers. Emanuel Martins, Vitor Silva and Luís de Sá Sund coding of imge sequences using multiple vector quntizers Emnuel Mrtins, Vitor Silv nd Luís de Sá Instituto de Telecomunicções, Deprtmento de Engenhri Electrotécnic Pólo II d Universidde de Coimr,

More information

CS559: Computer Graphics

CS559: Computer Graphics CS559: Computer Grphic Lecture 7: Texture Mpping Li Zhng Spring 008 Mn lide from Rvi Rmmoorthi, Columbi Univ, Greg Humphre, UVA nd Rolee Wolfe, DePul tutoril teching texture mpping viull, Jingi Yu, U Kentuck.

More information

REACTION ENUMERATION & CONDENSATION OF DOMAIN-LEVEL STRAND DISPLACEMENT SYSTEMS. Stefan Badelt DNA and Natural Algorithms (DNA) Group, Caltech

REACTION ENUMERATION & CONDENSATION OF DOMAIN-LEVEL STRAND DISPLACEMENT SYSTEMS. Stefan Badelt DNA and Natural Algorithms (DNA) Group, Caltech REACTION ENUMERATION & CONDENSATION OF DOMAIN-LEVEL STRAND DISPLACEMENT SYSTEMS Sefn Bdel DNA nd Nurl Algorihms (DNA) Group, Clech Fe 14 h, 2018 33rd TBI Winerseminr, Bled, Sloveni Grun, Bdel, Srm, Shin,

More information

Frequency Domain Parameter Estimation of a Synchronous Generator Using Bi-objective Genetic Algorithms

Frequency Domain Parameter Estimation of a Synchronous Generator Using Bi-objective Genetic Algorithms Proceeings of the 7th WSEAS International Conference on Simulation, Moelling an Optimization, Beijing, China, September 15-17, 2007 429 Frequenc Domain Parameter Estimation of a Snchronous Generator Using

More information

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

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

More information

Day-Night Long Range Camera System

Day-Night Long Range Camera System United Vision Solutions Day-Night Long Range Camera System Our camera system designed for long range surveillance 24/7 utilized the most advance optical sensors and lenses EV3000-P-EMCCD 1000 Hi-Resolution

More information

Data Structures and Algorithms

Data Structures and Algorithms Daa Srucures and Algorihms The maerial for his lecure is drawn, in ar, from The Pracice of Programming (Kernighan & Pike) Chaer 2 1 Goals of his Lecure Hel you learn (or refresh your memory) abou: Common

More information

STEREO PLANE MATCHING TECHNIQUE

STEREO PLANE MATCHING TECHNIQUE STEREO PLANE MATCHING TECHNIQUE Commission III KEY WORDS: Sereo Maching, Surface Modeling, Projecive Transformaion, Homography ABSTRACT: This paper presens a new ype of sereo maching algorihm called Sereo

More information

MATH Differential Equations September 15, 2008 Project 1, Fall 2008 Due: September 24, 2008

MATH Differential Equations September 15, 2008 Project 1, Fall 2008 Due: September 24, 2008 MATH 5 - Differenial Equaions Sepember 15, 8 Projec 1, Fall 8 Due: Sepember 4, 8 Lab 1.3 - Logisics Populaion Models wih Harvesing For his projec we consider lab 1.3 of Differenial Equaions pages 146 o

More information

In-HouseTrainingProgramme

In-HouseTrainingProgramme In-HouseTriningProgrmme Ocober2015-Mrch2015 KolkCluser MesgefromMr.DerekMichelShhEVP&Hed-MMHIC DerColegues Keepinginmindhecompe veenvironmenndlimiedopporuni esvilbleinhe presenmrkeiishigh meweriseoheoccsionndreinforceoursndofbeinghe

More information

Section 9.2 Hyperbolas

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

More information

Wiley Plus. Assignment 1 is online:

Wiley Plus. Assignment 1 is online: Wile Plus Assignmen 1 is online: 6 problems from chapers and 3 1D and D Kinemaics Due Monda Ocober 5 Before 11 pm! Chaper II: Kinemaics In One Dimension Displacemen Speed and Veloci Acceleraion Equaions

More information

Today. Quiz Introduction to pipelining

Today. Quiz Introduction to pipelining Pipelining 1 Tody Quiz Inroduion o pipelining 2 Pipelining 10ns (10ns) 20ns (10ns) 30ns (10ns) Wh s he leny for one uni of work? Wh s he hroughpu? Pipelining 1.Brek up he logi wih lhes ino pipeline sges

More information

In fmri a Dual Echo Time EPI Pulse Sequence Can Induce Sources of Error in Dynamic Magnetic Field Maps

In fmri a Dual Echo Time EPI Pulse Sequence Can Induce Sources of Error in Dynamic Magnetic Field Maps In fmri a Dual Echo Time EPI Pulse Sequence Can Induce Sources of Error in Dynamic Magneic Field Maps A. D. Hahn 1, A. S. Nencka 1 and D. B. Rowe 2,1 1 Medical College of Wisconsin, Milwaukee, WI, Unied

More information

Diffraction I Version 1.0 : March 12, 2019

Diffraction I Version 1.0 : March 12, 2019 Diffraction I Interference an Diffraction of Light Through Slit: The Jut Give Me The Formulae Verion! Steve Smith March 12, 2019 Content 1 Introuction 3 1.1 Huygen Principle.............................................

More information

A METHOD OF MODELING DEFORMATION OF AN OBJECT EMPLOYING SURROUNDING VIDEO CAMERAS

A METHOD OF MODELING DEFORMATION OF AN OBJECT EMPLOYING SURROUNDING VIDEO CAMERAS A METHOD OF MODELING DEFORMATION OF AN OBJECT EMLOYING SURROUNDING IDEO CAMERAS Joo Kooi TAN, Seiji ISHIKAWA Deparmen of Mechanical and Conrol Engineering Kushu Insiue of Technolog, Japan ehelan@is.cnl.kuech.ac.jp,

More information

6.8 Shortest Paths. Chapter 6. Dynamic Programming. Shortest Paths: Failed Attempts. Shortest Paths

6.8 Shortest Paths. Chapter 6. Dynamic Programming. Shortest Paths: Failed Attempts. Shortest Paths 1 Chaper.8 Shore Pah Dynamic Programming Slide by Kein Wayne. Copyrigh 5 Pearon-Addion Weley. All righ reered. Shore Pah Shore Pah: Failed Aemp Shore pah problem. Gien a direced graph G = (V, E), wih edge

More information

Assignment 2. Due Monday Feb. 12, 10:00pm.

Assignment 2. Due Monday Feb. 12, 10:00pm. Faculy of rs and Science Universiy of Torono CSC 358 - Inroducion o Compuer Neworks, Winer 218, LEC11 ssignmen 2 Due Monday Feb. 12, 1:pm. 1 Quesion 1 (2 Poins): Go-ack n RQ In his quesion, we review how

More information

Mapping and Navigation

Mapping and Navigation Mapping an Navigation Januar 6 th, 5 Ewin Olson Wh buil a map? Time! Plaing fiel is big, robot is slow Driving aroun perimeter takes a minute! Scoring takes time often ~ secons to line up to a mouse hole.

More information

6.823 Computer System Architecture. Problem Set #3 Spring 2002

6.823 Computer System Architecture. Problem Set #3 Spring 2002 6.823 Computer System Architecture Problem Set #3 Spring 2002 Stuents are strongly encourage to collaborate in groups of up to three people. A group shoul han in only one copy of the solution to the problem

More information

Order code M F Type of relay

Order code M F Type of relay elay niversal MF for Curren Monioring elay niversal MF2 for Curren Monioring Sandard ype Large conac gap, swiching volage herefore 400 VAC Monioring of DC and AC currens Order Code Order code M F 2 0 40

More information

Timers CT Range. CT-D Range. Electronic timers. CT-D Range. Phone: Fax: Web: -

Timers CT Range. CT-D Range. Electronic timers. CT-D Range. Phone: Fax: Web:  - CT-D Range Timers CT-D Range Elecronic imers Characerisics Diversiy: mulifuncion imers 0 single-funcion imers Conrol supply volages: Wide range: -0 V AC/DC Muli range: -8 V DC, 7 ime ranges from 0.0s o

More information

EFFICIENT ON-LINE TESTING METHOD FOR A FLOATING-POINT ADDER

EFFICIENT ON-LINE TESTING METHOD FOR A FLOATING-POINT ADDER FFICINT ON-LIN TSTING MTHOD FOR A FLOATING-POINT ADDR A. Droz, M. Lobachev Department of Computer Systems, Oessa State Polytechnic University, Oessa, Ukraine Droz@ukr.net, Lobachev@ukr.net Abstract In

More information

Vocabulary Check. 410 Chapter 4 Trigonometry

Vocabulary Check. 410 Chapter 4 Trigonometry 40 pter 4 Trigonometr etion 4.8 pplitions n Moels You soul e le to solve rigt tringles. You soul e le to solve rigt tringle pplitions. You soul e le to solve pplitions of simple rmoni motion. Voulr ek.

More information

Try It. Implicit and Explicit Functions. Video. Exploration A. Differentiating with Respect to x

Try It. Implicit and Explicit Functions. Video. Exploration A. Differentiating with Respect to x SECTION 5 Implicit Differentiation Section 5 Implicit Differentiation Distinguish between functions written in implicit form an eplicit form Use implicit ifferentiation to fin the erivative of a function

More information

Projective geometry- 2D

Projective geometry- 2D Projecive geomer- D Acknowledgemens Marc Pollefes: for allowing e use of is ecellen slides on is opic p://www.cs.unc.edu/~marc/mvg/ Ricard Harle and Andrew Zisserman, "Muliple View Geomer in Compuer Vision"

More information

Image interpolation. A reinterpretation of low-pass filtering. Image Interpolation

Image interpolation. A reinterpretation of low-pass filtering. Image Interpolation Imge interpoltion A reinterprettion of low-pss filtering Imge Interpoltion Introduction Wht is imge interpoltion? (D-A conversion) Wh do we need it? Interpoltion Techniques 1D zero-order, first-order,

More information

Exercises of PIV. incomplete draft, version 0.0. October 2009

Exercises of PIV. incomplete draft, version 0.0. October 2009 Exercises of PIV incomplete raft, version 0.0 October 2009 1 Images Images are signals efine in 2D or 3D omains. They can be vector value (e.g., color images), real (monocromatic images), complex or binary

More information

Shortest Path Algorithms. Lecture I: Shortest Path Algorithms. Example. Graphs and Matrices. Setting: Dr Kieran T. Herley.

Shortest Path Algorithms. Lecture I: Shortest Path Algorithms. Example. Graphs and Matrices. Setting: Dr Kieran T. Herley. Shores Pah Algorihms Background Seing: Lecure I: Shores Pah Algorihms Dr Kieran T. Herle Deparmen of Compuer Science Universi College Cork Ocober 201 direced graph, real edge weighs Le he lengh of a pah

More information