In an illustrative embodiment, watermark decoding reliability is increased, for images of watermarked objects captured at close distances, by reducing influence of pixel noise (e.g., shot noise). In the same or different embodiment, watermark decoding reliability is increased, for images of watermarked objects captured from far distances, by reducing image under-sampling. A particular implementation down-samples input imagery twice—a first time by a fixed factor, preparatory to performing an FFT, and a second time by a variable factor, preparatory to submitting the image for decoding, where the variable factor is determined using results from the FFT. A number of other features and arrangements are also detailed.