Extra Polynymous
In a previous post, I deformed a grid of lines to halftone an image. I wanted to do the same thing with a checkerboard, but I figured that it would be similarly difficult and would require optimization. So I used the same optimization framework with a checkerboard, applied it to a brightness ramp, and found: […]
Imagine that we have a screen door, and we want to push around the wires to make an image. It’s not a simple problem! There’s a fixed number of wires in each direction, so how do we properly distribute them? Let’s define a pair of phase maps for x and y, and . We’ll draw […]
Sometimes you want one picture to have the color scheme of another. This is called color mapping or transfer. When I was making the rearranged images, I was concerned that I would get bad matches if I didn’t make sure the images were similar enough. It was helpful to ensure that their brightness histograms matched, […]
Let’s halftone an image with some overlapping wiggly spirals! I want to draw N lines, spiraling out from the center of the image, and have them each slightly offset. With the proper offset, this will create the (approximately) proper darkness. With image darkness k, line width w, and line spacing L, we can get a […]
I want to have the ink on a photo clump together, leading to a black and white image. This is a sort of flow, so my first thought is to take a look at the advection-diffusion equation. Let’s say that the ink distribution across an image is , the diffusion factor is , and the […]
Previously, I took one photo and rearranged its squares to make a version of another photo. How about a sillier version, where you use one image to re-make itself? The simple answer is to just keep every square in its original place, but that’s no fun at all. Instead, we can add the requirement that […]
Previously, I recreated an image by rearranging squares of another image. Typical photomosaics allow for repeated use of tiles, so I’ll try that for comparison. I’ll still allow rotation, as it helps the edges so much. The image on the left is the result: It works, but isn’t great. The repeated use of certain tiles […]
I want to take one image, chop it into square tiles, and use those to make an approximation of another image. When the images are the same size, the simplest version is identical to the assignment problem. This is a classical optimization problem that has been well studied. In those terms, there is a “cost” […]
I want to approximate images using constant-color shapes. Given a shape, how do we choose where to put it? We have the original image, , and the approximate image, . I want to place a shape, , with area on such that it improves the approximation. First, define the average color under the shape (which […]