2020 China Postgraduate Mathematical Modeling Contest E Question
Explore the evolution of fog and predict the trend of fog.
Visibility is a common indicator in weather, highway driving, and airplane flight. The unit is usually meters. The main factors affecting visibility are fog and haze. As we all know, visibility is very important to highway safety. When the visibility is very low, for the sake of driving safety, highway managers usually close the road. In the aviation field, runway visibility is used to reflect the size of the fog and haze near the airport, which is defined as the maximum distance at one end of the runway that can identify the runway or targets close to the runway (runway side lights at night). Under normal circumstances, when the visibility of the airport is only about 400 meters, the flight will be prohibited from taking off and landing. When the airport visibility is only about 600-800 meters, although the flight can take off and land normally. However, for safety reasons, the airport will take measures to temporarily control the flow of flights to increase the interval between flight departures and easily cause flight delays. Therefore, visibility prediction is a matter of great concern to highway management departments and airlines.
Laser visibility meter is a commonly used instrument to detect visibility. At present, my country's highway network has gradually formed. If a large number of laser visibility meters are used to cover the national highway network, it will cost a lot of money. At the same time, laser visibility meters still have low accuracy in detecting cluster fog, small detection ranges, and maintenance costs. Not high enough. In recent years, the video-based road condition (runway) visibility detection method has attracted people's attention. It overcomes the deficiencies of laser visibility meters to some extent. The video visibility detection method is to combine atmospheric optical analysis with image processing and artificial intelligence technology. Through the analysis and processing of the video image, the relationship between the video image and the real scene is established, and then the visibility value is indirectly calculated according to the changes in image characteristics. However, the existing visibility detection method based on video images is difficult to accurately estimate the visibility due to indirect calculation. In particular, most of these methods only select a small number of videos and intercept certain inherent features in the image [1,2], and estimate based on Koschmieder's law [3, 4], and do not make full use of the continuous information of the video, so the estimated The accuracy is not high, and there is more room for improvement.
Under normal circumstances, whether the visibility is 2000 meters or 3000 meters has almost no impact on road traffic and aircraft flight. It is only necessary to accurately estimate current and especially forecast future visibility in severe weather, especially in heavy fog. Therefore, this project only focuses on the evolution of the fog.
In fact, the formation and dissipation of heavy fog has its own laws, which are usually related to meteorological factors near the ground. The video data contains a wealth of information, especially covering the changing process of the fog. Making full use of this information can not only improve the accuracy of visibility estimation, but also predict the dissipation of heavy fog.
In order to estimate the corresponding visibility under different heavy fog conditions and predict the dissipation of heavy fog, please answer the following questions:
One. As we all know, fog is related to meteorological factors near the ground. Establish a model to describe the relationship between visibility and ground meteorological observations (temperature, humidity, wind speed, etc.), and derive specific relationships based on the data provided by the subject (airport AMOS observation.zip);
2. According to the video data of a certain airport (airport video.zip) and visibility data (airport AMOS observation.zip) provided by the title, establish a visibility estimation deep learning model based on video data, and evaluate the accuracy of the estimated visibility;
three. A certain section of the expressway has only surveillance video data, and a visibility estimation algorithm that does not rely on the observation data of the visibility meter is established (hint: in fact, the depth of field of the object in the video can be estimated in a foggy situation [1]. Conversely, it can also be used in theory Objects in different depths of field in the video, the brightness difference under different visibility estimates the visibility), discuss the implementation process of related algorithms, and plot the highway visibility over time for this period of time in a video provided by the subject (highway video screenshot.zip) Change curve;
four. Using the law of visibility obtained in question 3 over time, establish a mathematical model to predict the changing trend of the fog (increasing or weakening) and when will it disperse (reach the specified visibility, such as MOR=150m)?
Explanation of related terms
1. Visibility refers to the maximum distance that a person with normal vision can recognize a target from the background. The so-called "visible" refers to the ability to see and recognize the outline and shape of the target during the day, and to clearly see the luminous point of the target lamp at night.
2. Fog: In the case of sufficient water vapor, breeze and stable atmosphere, when the relative humidity reaches 100%, the water vapor in the air will condense into tiny water droplets suspended in the air, reducing the visibility at the ground level. This weather phenomenon is called For fog.
3. Mass fog: Affected by the microclimate environment in a local area, a thicker fog with lower visibility appears in a local area ranging from tens of meters to hundreds of meters in heavy fog. The line of sight outside the mist is good, and the inside of the mist is hazy.
4. The brightness contrast between the target and the background. Whether the target can be seen in the atmosphere depends on its own brightness and the difference in brightness between it and the background. For example, a dark target is clearly visible against a bright background. Or the bright target is also clearly visible in the dark background. The indicator of this difference is the contrast value K of brightness. Set as the inherent brightness of the target object and the inherent brightness of the background, the contrast value of the brightness is defined as:
5. Basic equation of visibility measurement:
Here F and F0 represent the observed and incident light intensity respectively. The parameter is called the attenuation coefficient, which is related to the thickness of the fog: the larger the fog, the thicker the fog. Meteorological Optical Visual Range (MOR)
6. Runway visual range (RVR): refers to the distance at which the pilot on the aircraft on the centerline of the runway can see the signs or runway boundary lights or centerline lights on the runway.
参考文献
1.S. K. Nayar, S. G. Narasimhan, Vision in bad weather, ICCV’99
2.R. T. Tan, Visibility in bad weather from a single image, CVPR, 2008
3. N. Hautiere, J-P Tarel, J Lavenant D. Aubert, Automatic fog detection and estimation of visibility distance through use of onboard camera, Machine Vision and Application, 2006, 17（1）：8-20
4. C. Sakaridis, D. Dai, L. V. Gool, Semantic foggy scene understanding with synthetic data, International J. Computer Vision, 2018, 3
Relevant data and instructions
1. Highway video images (in order to reduce the amount of data, we will intercept the video into 100 frames of BMP pictures: highway video screenshots.zip);
2. An airport runway surveillance video (airport video.zip)
3. The airport's visibility meter observation data, ground temperature, humidity, air pressure, and wind speed corresponding to the above time period (airport AMOS observation.zip).
(To be continued...)
