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Demo Math SGI research projects

How to Comb a Tapir

By Erick Jimenez Berumen, Shreya Hegde, and Olga Guțan


For the past 2 weeks, our team has been hard at work, learning how to comb a tapir! Under the skilled and very patient guidance of Edward Chien and Mikhail Bessmeltsev, we extracted (in)contractible cycles, computed a vector field, and got closer to having a singularity-free frame field aligned to the drawing.

For context: Line drawings are commonplace in animation, CAD design, and other areas. They are mostly drawn in raster format. To do any geometry processing, the lines need to be vectorized—that is, converted to curves. State-of-the-art vectorization methods do the conversion using a frame field.

We explored how to design these frame fields. To be more precise, we tried to improve vectorization via designing a singularity-free frame field aligned to the drawing. The work has taken our (newly-acquired) knowledge of Discrete Trivial Connections and applied it to a real-world question, adapting the idea of Discrete Trivial Connections to pixelated planar domains with boundaries.

It was great fun and a very rewarding educational experience.

Figure 1. An image with one interior boundary and three exterior boundaries, with randomly-generated rotation angles.
Figure 2. An image with one interior boundary and three exterior boundaries.
Figure 3. An image with one interior boundary and one exterior boundary.

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