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Previously, I had used triangulations along with other compuatational image manipulation techniques to perform actions such as creating face morphing animations here.
After doing this, I experimented with more cool applications of triangulations and discovered a more artistic use: creating "Low Poly" art, or art made from using a relatively low amount of polygons.
As a quick refresher, we first establish critical points in the image. We then use the points to create a Delaunay Triangulation.
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Instead of using the triangulation to create the morph, however, we now do something different. We now color all of the pixels that lie within the triangle the color of the middle pixel of the triangle. Of course, we could try other techniques such as coloring the triangle the mean or mode color but I found the center color to be the most visually satisfying and, of course, computationally efficient.
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As you may notice, in order for the poly-art images to have distinguishable features, we may need more points than our previous triangulations. Generally, there needs to be a higher concentration of points in the areas of small and important features. Using our knowledge of working with images in the frequency domain, I believe the point selection can possibly be automated by scattering a high concentration of points in areas of high frequency and low concentration of points in areas of low frequency. Furthermore, to keep the shapes close to the same, we could be sure to assign points to edges. Perhaps as a future project I will attempt to create a fully automatic Low Poly Art creator.