The most obvious way to shrink an image is to copy only some of the pixels from only some of the scan lines. This sort of scaling is called “decimation,” “uniform sampling,” or “scaling without filtering.” For example, to make a thumbnail of a 601x601 pixel test image, which is six times the size of the desired output, every sixth pixel from every sixth scan line could be copied into a new image. Imago uses decimation to make thumbnails when its “none” filter option is specified.

Decimation is fast and may be adequate for some blurry input images, but thumbnails created this way usually look terrible.

When sampling theory is applied to digital images, it explains why decimation doesn't work well for making thumbnails. Patterns in the input image that alternate from light to dark at rates higher than half the sampling frequency will not be sampled at a high enough frequency and are likely to result in jagged artifacts as the high input frequencies alias to lower frequencies in the output. In the test image used here, aliasing artifacts are most noticeable in the text “601 pixels.”

Aliasing artifacts associated with uniform sampling can be minimized by expanding each sampling point to a weighted sum of pixel values in the neighborhood around the sample. Sampling theory indicates that neighboring pixel values should be weighted according to an infinite sync function, centered at the sample point. In practice, sync functions are approximated with finite functions. Many different finite functions have been proposed for approximating sync functions [Turkowski 90]. They are typically instantiated as a real-valued matrix, which is thought of as a filter “kernel.” One typical optimization is to use filter kernels that are separable so the two dimensions of the input image can be scaled in separate passes.

Sampling theory dictates using kernels that are large enough to sample at twice the rate of the highest possible input frequency. Large kernels can be accurate, but they can also make the process of shrinking images very slow, especially if the scaling factor is not known in advance and the filter kernel must be scaled at run time.

Imago's lanczos filter option uses a general image scaling algorithm that creates and scales filter kernels at run time based on a scale factor parameter [Schumacher 94]. This algorithm uses separable kernels and, as an additional optimization, pre-computes the kernel contributions for each row and column. Despite these optimizations, however, scaling images with the lanczos option may take five to ten times longer than decimation. Thumbnails created with the lanczos filter option look great, but they take too long to make.

To make great-looking thumbnails of arbitrarily-sized input images quickly, Imago uses a hybrid algorithm, which is a combination of successive invocations of a fast halving method, HDC, and a single invocation of the general image scaling algorithm with the Lanczos kernel. The possible slowness of the final pass is minimized because scale factors are guaranteed to be less than one half. Scaling images with the hybrid option typically takes only a few seconds longer than uniform sampling, but produces results that are difficult to distinguish from the slower lanczos option.