This paper summarizes several quality issues of an approach for high-quality filtering with arbitrary filter kernels on PC graphics hardware that has been presented previously. Since this method uses multiple rendering passes, it is prone to precision and range problems related to the limited precision and range of intermediate computations and the color buffer. This is especially crucial on consumer-level 3D graphics hardware, where usually only eight bits are stored per color component. We estimate the accumulated error of several error sources, such as filter kernel quantization and discretization, precision of intermediate computations, and precision and range of intermediate results stored in the color buffer. We also describe two approaches for improving precision at the expense of a higher number of rendering passes. The first approach preserves higher internal precision over multiple passes that are forced to store intermediate results in the less-precise color buffer. The second approach employs hierarchical summation for attaining higher overall precision by using the available number of bits in a hierarchical fashion. Additionally, we consider issues such as the order of rendering passes that is crucial for avoiding potential range problems, and a variant of hardware-accelerated high-quality filtering that is able to reduce the number of passes by four for filtering single-valued data, thus improving both performance and precision.

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