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Instead of perturbing each pixel in the input image at random, we can choose to dither by a predetermined amount depending on the pixel’s position in the image. This can be achieved using a threshold map; a small, fixed-size matrix where each entry tells us the amount by which to perturb the input value , producing the dithered value . This matrix is tiled across the input image and sampled for every pixel during the dithering process. The following describes a dithering function for a 4×4 matrix given the pixel raster coordinates :
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There's a tradeoff: a lower capacity means you can skip more space during queries (you zoom in faster), but the tree has more nodes and uses more memory. A higher capacity means fewer nodes but each node requires checking more points linearly. As a starting point, capacities between 4 and 16 are reasonable defaults, though the best value depends on your data distribution and query patterns.