Shape Fitting for the Shape Control System of Silicon Single Crystal Growth


Form fitting, together with straight line and ellipse fitting, plays an necessary role in the (cylinder-) form management system of silicon single crystal growth, because the straight lines and ellipse in the crystal image contain the important horizontal circle center and diameter information. This data can be used as management variables thus that the grown crystal approximates to a good cylinder, and so can be used as high-quality supply materials. During this paper, we tend to develop new straight line and ellipse fitting algorithms. The key points are as follows. We have a tendency to formulate the two-dimensional (a pair of-D) binary image into one-snapshot array signal of a virtual sensor array, and casts the angle estimation drawback of straight lines into the direction finding one among virtual incoming sources. Based mostly on the virtual array manifold and potential incoming angles, the relevant over-complete dictionary is made, and so a sparse regression drawback is formed. To solve such a regression drawback, we have a tendency to introduce the weight vector sparsity term into the standard linear least-squares support vector regression framework to estimate the angles of these straight lines. Primarily based on the estimated angles and potential offsets, another over-complete dictionary is built, and therefore the image can be looked upon as the sparse illustration of these dictionary atoms. Since the created dictionary is of the identical size because the image, we tend to use the compressed sensing theory to reduce the relevant dimensionality and then apply the aforementioned sparse regression technique to obtain the relevant offsets of those straight lines. We tend to derive a replacement second-order polynomial of ellipse equation to obtain the ellipse parameters to avoid the trival answer from the standard polynomial model. Some simulation and experimental examples are given to illustrate the effectiveness of the proposed algorithms.

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