Better Fixed-Point Filtering with Averaging Trees

Production imaging pipelines commonly operate using fixed-point arithmetic, and within these pipelines a core primitive is convolution by small filters - taking; convex combinations of fixed-point values in order to resample, interpolate, or denoise. We describe a new way to compute unbiased convex combinations of fixed-point values using sequences of averaging instructions, which exist on all popular CPU and DSP architectures but are seldom used. For a variety of popular kernels, our averaging; trees have higher performance and higher quality than existing standard practice.