Image Scaling Algorithms: Nearest, Bilinear, Bicubic, and Lanczos

A raster image is a finite array of samples. A 100 × 100 image enlarged to 200 × 200 needs four times as many output pixels, while a reduction must combine information from many source pixels.

• Upscaling: reconstruct values between existing samples.
• Downscaling: remove frequencies that the smaller grid cannot represent, then resample.

Treating the source as a sampled continuous signal explains why no single method is best for every image.

The sampling theorem associated with Harry Nyquist and Claude Shannon states that a band-limited signal must be sampled above twice its highest frequency for lossless reconstruction. Frequencies above the new Nyquist limit fold into lower frequencies when an image is reduced without sufficient filtering.

In pictures this appears as moiré, jagged diagonal edges, flickering detail, or a fine pattern changing into a different pattern. Conceptually, high-quality reduction is therefore:

low-pass filter → sample on the smaller grid

Nearest-neighbour chooses the source pixel closest to each output coordinate.

output(x, y) = input(round(x / scaleX), round(y / scaleY))

It is fast and never invents intermediate colours. That is exactly what pixel art, masks, and many diagrams need. On photographs it creates blocky enlargement, and careless reduction can alias badly.

Bilinear interpolation blends the four surrounding pixels. If fx and fy are the fractional distances within the source cell:

output = (1-fx)(1-fy) I00
       +    fx (1-fy) I10
       + (1-fx)   fy  I01
       +    fx    fy  I11

It is inexpensive and widely accelerated by graphics hardware. The trade-off is visible softening, especially after repeated transformations.

Bicubic interpolation normally uses a 4 × 4 neighbourhood and a separable cubic kernel. “Bicubic” is a family name rather than one universal filter: different parameters change sharpness, blur, and ringing.

Catmull and Rom described a local interpolating spline in 1974, Keys published a widely used cubic-convolution formulation in 1981, and Mitchell and Netravali described a two-parameter family in 1988. Their commonly used balanced choice is B = 1/3, C = 1/3.

The ideal band-limited reconstruction kernel is the sinc function, but its infinite support is impractical. A Lanczos kernel multiplies sinc by a second sinc window and limits it to a finite radius:

sinc(x) = sin(πx) / (πx)
L(x) = sinc(x) × sinc(x/a),  |x| < a

a = 2 and a = 3 are common practical choices. Lanczos often preserves fine detail well during reduction, but strong transitions can produce light and dark halos. More lobes increase work and do not guarantee a more pleasing result for every image.

Always inspect edges, thin lines, text, and repeating patterns. A filter that looks sharp on a portrait can create unacceptable halos on interface graphics.

img {
  image-rendering: auto;
  image-rendering: smooth;
  image-rendering: high-quality;
  image-rendering: pixelated;
  image-rendering: crisp-edges;
}

CSS Images defines these values as rendering preferences. It does not require every browser and device to use an identical mathematical kernel. Use pixelated when preserving hard pixel boundaries matters, then test the target browsers and scale factors.

Super-resolution models can generate plausible texture using patterns learned from training data. That can produce attractive results, but the extra detail is inferred rather than measured from the source.

For evidence, scientific measurement, medical work, or any task where fidelity matters more than appearance, retain the original and use a deterministic resampling method whose behaviour can be documented.

• Scaling reconstructs a signal and samples it on a new grid.
• Reduction needs low-pass filtering to limit aliasing.
• Nearest preserves discrete pixels; bilinear is fast but soft.
• Bicubic names a family of cubic filters with different trade-offs.
• Lanczos is a practical windowed-sinc filter that can be sharp but may ring.
• AI upscaling invents plausible detail and is not evidence recovery.