2019APMCM亚太赛——A
- The position of silicon dioxide particles in the high-temperature molten pool during the melting process is changing constantly, and the first step to analyze the melting behavior of silicon dioxide is to track the target. Please establish a mathematical model to track the centroid position of silicon dioxide particles during the melting process, and present the motion trail of centroid of silicon dioxide.
- Establish indexes which represent the edge outline characteristics of silicon dioxide during the melting process of silicon dioxide (such as shape, perimeter, area, generalized radius, etc.); the participants can select by themselves, as long as they can represent the melting process of silicon dioxide.
- For the image given in the attachment is 2D, while the key parameter which represents the melting rate of silicon dioxide is mass, and the mass is in direct proportion to the 3D volume, estimate the actual melting rate of silicon dioxide based on edge outline characteristic indexes of silicon dioxide in the No. 2 question.
problem analysis
problem 1 analysis
For the first problem, in order to track the movement of the silica centroid, we
first perform a grayscale transformation on the image, then use the median filter to reduce noise and use the gamma curve to enhance the contrast of the image, then segment the image and intercept the silica The grainy area allows the picture to accurately identify the edges of the silica. Finally, according to the tracked particle edges, the silica edge set in the image is obtained. Based on the result of the edge set, the centroid position of the silica is obtained by the centroid method, and finally theequation of motion of the silica centroid is obtained
problem 2 analysis
For question two,in order to establish the edge contour feature index that can represent the silica melting process, we use the edge set calculated in question one to detect the edge contour shape of silica. Curve fitting was performed on the shape of the edge contour, and a relatively smooth curve was used to represent the edge contour of the silica to eliminate the influence of bubbles generated during the melting of the silica on the edge definition. According to the obtained curve integral, the perimeter and area of the edge contour and its change are obtained, and the silica melting process is finally expressed.
problem 3 analysis
For question three, in order to obtain the silica melting rate. We first think that the
melting rate represents the mass of melting in a unit time, and from the mass formula, we can know that the mass of the object is equal to the density of the object times the volume of the object. And because the fused silica in the title is pure particles, we get a proportional coefficient based on the formula of the mass of the substance as the density of the silica. According to the mass-volume relationship, it can be known that the rate of change in mass is equal to the rate of change in volume, that is, the melting rate of silica can be equivalent with the rate of change in volume. Finally, the rate of silica melting is calculated by calculating the rate of change in volume of silica.
As can be seen from the image,when the =2,the contrast between the silica
region and the corundum crucible in the image is most obvious.So, we take the value to 2.0, the rest of the picture also enhances the contrast - gamma transformation processing.