摘要
目的针对太阳影子定位问题,建立一系列数学模型对视频中的数据进行研究,并通过太阳影子定位技术确定视频拍摄时间与地点。方法以一段时长30min拍摄时间与地点未知的直杆影长变化视频为研究对象,根据全国大学生数学建模网提供的数据,运用最小二乘拟合、构建方程组求解、画图分析以及图片灰度处理、锐化处理等方法,分别构建了影长变化模型、影子定位模型和影子定时模型等,并依据影子的坐标点,结合MATLAB、Excel等软件得出了影子长度的变化规律、目标物所在地的经纬度以及测量数据的时间。结果经画图分析得知2015年10月22日北京时间9∶00~15∶00之间天安门广场(北纬39度54分26秒,东经116度23分29秒)3m高直杆的太阳影子先随时间的推移而变短,在中午某一时刻达到最小值,后又随时间的变化而变长;在只知直杆在水平地面上的太阳影子顶点坐标的情况下,求得实例中直杆所在地点为(37.707 23°N,71.788 99°E),测量日期为11月10号;在只获取一段视频的情况下,经过对图片截取、灰度化以及锐化等处理读取出视频中直杆影子顶端坐标,并求得该视频的拍摄地点与时间分别为(40.16°N,122.70°E)、2015年7月26日。结论在视频中物体所投射的影子坐标可读取的情况下,运用合理的数学模型,可以通过太阳影子的变化对视频的拍摄时间及其地点进行精准的判断。
Objective The paper,according to the sun shadow positioning issue,establishes a series of mathematical models to study the data of the video,and determines the shooting time and site of the video through the sun shadow positioning technology.Methods Taking the video of 30-minute-long and unknown shooting site reflecting the length variation of the straight rod's shadow as the research object,this paper respectively constructed the shadow's length variation model,the shadow positioning model,the shadow timing model and other models by applying the least square fitting,the equation set,the graph drawing analysis,and the image processing of the gray scale and sharpening,based on the data provided by the contemporary undergraduate mathematical website in modeling.The paper also concluded the law of the shadow's length variation,the longitude and latitude of the site in the object,and the time of the data measurement by MATLAB,Excel and other software,based on the coordinates of the shadow.Results Through the graph drawing analysis,it was found that on October 22,2015,Beijing time between 9∶00-15∶00,the sun shadow of the 3-meter-high straight rod firstly got short with time passing by,reached the minimum in a certain moment of the noon,and got long as the time varied.Under the circumstance that only the coordinate of the shadow's vertex on the rod horizontal ground was known,it was calculated that in instance 1,the site of the straight rod was in the coordinate and the date of the measurement was November 10 th.Under the circumstance there was only one piece of the video,the coordinate of the shadow's vertex of the straight rod,the shooting site ofand the shooting date of October22,2015.Conclusion In the case that the coordinate of the shadow projected by the object can be read;the shooting time and site of the video can be judged concisely through analyzing the changes of the sun shadow by applying the reasonable mathematical models.
出处
《河北北方学院学报（自然科学版）》
2016年第11期35-42,49,共9页
Journal of Hebei North University:Natural Science Edition
基金
国家自然科学基金项目(11301001)
安徽财经大学教研项目(acjyzd201429)
