Recently, I worked with Ingrid Daubechies and her postdoc Shira Faigenbaum Golovin on repairing damaged data set. Mainly, the damaged data are tooth data. We used trivariate spline functions to find a smooth surface which interpolates the given partial data points and let the spline surface construction method to automatically fill in the region with missing points. Let me show you four examples. For convenience, I used the tooth data set from Shira Golovin and took partial data points off and then apply my trivariate spline method to find a smooth surface. The following are four examples. One is to take a circle data points off, one is to take a strip of data points off, one is to take data point off from a corner, and finally one is to take a squared data points off. All these cases, our method works beautifully. See examples below for yourself. There are two other webpages which may be interesting to you. One is Tooth Surface Construction and the other one is Tooth Surface Construction by 3D Splines. Example 1. I first show the data set with missing points, and then I show the spline surface with the given data. Finally, I show the smooth surface without data points. Example 2. In this example, I show the data points with a strip of points missing. One can think that the one tooth was broken and one has to piece them together. Example 3. Now I tested repairing the tooth surface with missing data points at one corner of the tooth. Example 4. Finally, I present an example of repairing a tooth from a given data set with missing points located over a square region. Reconstructed Tooth Surface
