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Sub-pixel BSP images

We propose new image representations that saves sub-pixel borders between objects. This provides a number of benefits in 4 scenarios: (1) anti-aliasing, (2) up-sampling, (3) de-noising, (4) differentiable rendering. For pixels containing borders, we store information about these borders using a small BSP tree. This allows us to restore the geometric shape of an object inside a pixel with high accuracy if is a need, for example, to significantly increase the image resolution (8-16 times). We demonstrate that the proposed method allows to save edge information with high accuracy and to make a qualitative increase in resolution with a slight increase in memory consumption relative to the original image by an average of (+1%) in typical scenarios. The scope of the proposed method is the synthesis of images in copmuter graphics.