数学建模美赛模拟论文--博物馆安全问题.pdf

MuseumMuseumMuseumMuseum securitysecuritysecuritysecurity SummarySummarySummarySummary This paper discussesthe cameras that youwilluseare too big for the taste of museum curators who want to have as few cameras as possible interfering with theart exhibitions We can summarize the paper into three problems The first oneisdesign a procedure to place cameras in choice locations around the museum in order to provide the best possible coverage Secondly propose strategy can be easily modified to accommodate some extra security concern The third oneisdiscuss a strategy to place a limited number of cameras in an optimal way then propose possible additional security precautions For the first question Based on the increasing number of cameras we design the most reasonable arrangement ans calculate the critical value of the visible range in order to have as few cameras as possible interfering with theartexhibitions we use the inverse method to establish a corresponding number of different range cameras The conclusions are as follows when the exhibition hall area belongs to the intervalis from 0 to 307 7507 with 2 cameras when the intervalisfrom 307 7507 to 405 5233 with 3 cameras when the intervalisfrom 405 52331 to 440 2350 with 4 cameras when the intervalisfrom 1440 2350 to 1581 8854 with 5 cameras when the areais the largest 3000 use 9 cameras the above data units are square feet Basedonthe question one the second questionisspecial protection object in some museum exhibitiononcamera number and position adjusted slightly the camera can clearly monitor some extra security concern For the last one according to the important degree of exhibits of the exhibition hallis divided into A B and C due to the limited numberofcamera we take priority to install a showroom ensure no blind area secondly install theBhall finally ifthereis a surplusisinstalled at the C exhibitionhallor gallery Weplace a limited number of cameras then propose possible additional security precautions KeyKeyKeyKey words words words words museum security video surveillance backward pass Team 0016Page 2 of 11 ContentsContentsContentsContents 1 Introduction 4 1 1 Backgrounds 4 1 2 Problems Restatement 4 2 Assumptions 5 3 Models 6 3 1 Backward Pass model 6 3 2 The Mona Lisa Model 10 3 3 GradeModel 10 4 Strength and Weakness 11 5 FutureWork 11 6 References 12 Team 0016Page 3 of 11 1 1 1 1 IntroductionIntroductionIntroductionIntroduction 1 1 Backgrounds Based on video surveillanceisthe perception of the environment powerful means in highway airport square community and soona large numberofuse Due to a single camera perception areaislimited people often use multiple camera monitoring to expand common perception scope or strengthen the effectofperception How to schedule multiple cameras to obtain the biggest benefit they form a variety of optimization problems For visual surveillance optimization research firstisAGP art galleryproblem problems requirements in a polygon in the museum to determine the number and locationofthe guard so that can monitor to every important place In 3 d reconstruction study more than the position of the camera for optimization in order to reduce the reconstruction Error In video monitoring system dispatching camera to avoid obstacles to ensure that the best monitoring effect The current camera network coverage model basically isthe camera and monitoring area as uniform in the view of the camera in the near and far no matter the target monitoring abilityisthe same In a given surveillance area the parts have the same monitoring requirements However in the practical application andisnot so the distance from the camera targetwillaffect imaging resolution the surveillance area also has the need to focus on position Museum security system should be a high definition multi function intelligence and linkage alarm high sensitive system combined with more comprehensive system The stateispay attention to the constructionofthe museum crack down on three stolen and smuggling crime security professionals to the attentionofthe security museum also not slack makefulluse of security technology ofhighreliability and practicability scalability compatibility advantage museum securitywillbe more mature perfect from the real meaning to ensure the safety of the cultural heritage museum 1 2 Problems Restatement Museum security have been a major concern of curator for many years Many security company has a contract with museum to provide video surveillance at several locations The cameras that theywilluseare toobigfor the tasteofmuseum curators who want to have as few cameras as possible interfering with theartexhibitions The camera resolutionisgoodupto 25 feet when still and up to about 8 feet when scanning horizontally Besides the angle covered by the camera lensisapproximately 50 degrees Team 0016Page 4 of 11 Most museums try to maximize the area available to display paintings and other exhibits so their floor plans are quite convoluted with several panes standing in the middleofa room at odd angles and corridors connecting exhibitions Although rooms can be long up to 100 feet opposite walls are never more than 30 feet apart so that visitors do not have to walk unnecessarily Allwalls and panes areflat Museum security have been a major concern of curator for many years Many security company has a contract with museum to provide video surveillance at several locations The cameras that theywilluseare toobigfor the tasteofmuseum curators who want to have as few cameras as possible interfering with theartexhibitions The camera resolutionisgoodupto 25 feet when still and up to about 8 feet when scanning horizontally Besides the angle covered by the camera lensisapproximately 50 degrees Most museums try to maximize the area available to display paintings and other exhibits so their floor plans are quite convoluted with several panes standing in the middleofa room at odd angles and corridors connecting exhibitions Although rooms can be long up to 100 feet opposite walls are never more than 30 feet apart so that visitors do not have to walk unnecessarily Allwalls and panes areflat So our goalispretty clear 1 Design a procedure to place cameras in choice locations around the museum in order to provide the best possible coverage 2 Proposed strategycanbe easily modified to accommodate some extra security concern 3 Discuss a strategy to place a limited numberofcameras inanoptimal way then propose possible additional security precautions 2 2 2 2 AssumptionsAssumptionsAssumptionsAssumptions 1 Inthis paperallthe exhibition halls are cube 2 Ignore the camera installation andwallangle 3 In the monitoring periodallthe cameraisnormal work don t consider appear outside of the camera monitoringisinvalid Team 0016Page 5 of 11 3 3 3 3 ModelsModelsModelsModels 3 1 Backward Pass model In order to provide the best possible coverage design a procedure to place cameras in choice locations around the museum According to the design standard of the exhibition hall and the camera specifications this question using inverse inverse calculation model the detailed steps are as follows 500 X YZ O 25 X YZ O Fig 1 Fig 1 Fig 1 Fig 1 Left Left Left Left thethethethe rangerangerangerange ofofofof c c c cameraameraameraameraRight Right Right Right thethethethe volumevolumevolumevolume ofofofofc c c cameraameraameraamera Left Line YO 25 sin250 10 5654 feet Line XO 25 sin650 22 6576 feet Right V 1 3 Line YO 2 Line XO Team 0016Page 6 of 11 A CD B Fig 2Fig 2Fig 2Fig 2TwoTwoTwoTwocamerascamerascamerascameras forforforfor a a a a roomroomroomroom Line BC 25 cos500 16 0696 feet Line CD 25 sin500 19 1511feet So the room s areais S Line BC Line CD 307 7507 feet2 AB DC E Fig 3Fig 3Fig 3Fig 3ThreeThreeThreeThree camerascamerascamerascamerasforforforfora a a a roomroomroomroom Team 0016Page 7 of 11 Line CD Line YO 2 feet So the room s areais S Line BD Line CD 405 5233 feet2 AB C E Fig 4Fig 4Fig 4Fig 4FourFourFourFour camerascamerascamerascamerasforforforfora a a a roomroomroomroom Line ED 25 cos 400 Line CD Line CE Line ED 57 6371 feet So the room s areais S Line BD Line CD 1440 2350 feet2 Team 0016Page 8 of 11 AB CD Fig 5Fig 5Fig 5Fig 5FiveFiveFiveFive camerascamerascamerascameras forforforfor a a a a roomroomroomroom Line ED 25 cos 400 Line EF 21 2 cos 250 Line CD Line CE Line ED Line EF 75 3279 feet So the room s areais S Line BD Line CD 1581 8854 feet2 the restcanbe done in the same manner A B CD Fig 6Fig 6Fig 6Fig 6NineNineNineNine camerascamerascamerascameras forforforfor a a a a roomroomroomroom Team 0016Page 9 of 11 So the room s areais S Line BD Line CD 3000 0253 feet2 Witha number of cameras in increasing as the base design the most reasonable arrangement calculate the critical value of the visible range using the inverse method to establish a corresponding number of different range cameras The conclusions are as follows when the exhibitionhallarea belongs to the interval isfrom 0 to 307 7507 with 2 cameras when the intervalisfrom 307 7507 to 405 5233 with3 cameras when the intervalisfrom 405 52331 to 440 2350 with 4 cameras when the intervalisfrom 1440 2350 to 1581 8854 with 5 cameras when the areaisthe largest 3000 use 9 cameras the above data units are square feet 3 2 The Mona Lisa Model Some museums have a particularitemthat requires extra attention during the day to protectitfrom possible vandals Explain whether my proposed strategy can be easily modified to accommodate this extra security concern In order to ensure that the important items without any damage so must consider the monitoring of the exhibitionhallceiling Need to add a cameraonthe ground put in important exhibitions Basedonthe question one special protection object in some museum exhibition on camera number and position adjusted slightly 3 3 Grade Model Some museums have a limited budget that may not suffice to install maintainallthe necessary cameras Discuss a strategy to place a limited number of cameras inan optimal way then propose possible additional security precautions According to the important degree of exhibits of the exhibition hallisdivided into A B C three due to the limited number of camera take priority to install a showroom ensure no blind area secondly install theBhall finally ifthereisa surplusis Team 0016Page 10 of 11 installed at the C exhibition hall or gallery Weplace a limited number of cameras then propose possible additional security precautions 4 4 4 4 StrengthStrengthStrengthStrength andandandand WeaknessWeaknessWeaknessWeakness Strength Strength Strength Strength Installation scheme deduced backward exhibitionhalluse first asked in the area and the corresponding camera and number applicable to any rectangular hall versatility Weakness Weakness Weakness Weakness This modelisonlysuitable for cuboid hall And did notfullytake into account the camera in the corridors of the installation ignoring the camera installation position and the angle of the wall 5 5 5 5 FutureFutureFutureFutureWorkWorkWorkWork As everyone knows the realityoflifein the museum has various forms such as cylinder three pyramid This model applies only to the cuboid ifapplied to the cylindrical Museum do the following improvement stilluseinversion modelwillhave its areaisdivided into different areas onlyneed to change camera installation scheme the installation of a fixed camera in the center of the top then according to the extentofarea then the diameter of t