What frequency separation actually splits

Skin holds its colour and its surface in the same pixels. Every technique worth the name begins by pulling those apart, and the quality of the result is decided almost entirely by how the split is made rather than by what is done afterwards.

Look closely at a well-exposed cheek and two different things are happening at two different scales. There is the broad shape of the tone — a warm patch over the cheekbone, a cooler plane running to the jaw, a shadow under the eye that spans a couple of hundred pixels. And there is the surface: pores, fine hairs, the faint relief of skin, the grain the sensor added, all of it varying over two or three pixels.

Those are separable, and separating them is the whole of what frequency separation means. One band is built by smoothing the image; the other is what is left when the first is subtracted from the original. Add them back together and you have the photograph again, exactly, because nothing was discarded. Change one before adding them back and you have changed only that aspect of the picture.

Why the choice of smoother decides everything

The obvious way to build the low band is a Gaussian blur, and it is what most skin tools ship. It is also why most skin tools produce a portrait with a faint bright rim around every lash, nostril and lip.

A Gaussian does not know about edges. Run one over the boundary between a lip and the skin above it and the dark lip bleeds upward into the light skin, and the light skin bleeds down. The low band now shows a soft ramp where the photograph had a step. Subtract that ramp from the original and the detail band is left holding a strong bright-then-dark couplet along the whole edge — the edge itself, promoted from tone into texture. Reduce the detail band to smooth the skin and you reduce that couplet too, which leaves a visible halo. Everyone has seen it. Most people call it “looking retouched” without knowing which step produced it.

This tool builds the low band with a self-guided filter instead. The mechanism is local statistics: for every neighbourhood it computes a coefficient from the variance there, and that coefficient collapses toward zero only where variance is below a threshold. In a flat patch of cheek it collapses, and the filter smooths. Across a lip border the variance is large, the coefficient stays near one, and the filter passes the edge through untouched. So the edge stays in the low band where it belongs, the detail band holds pore texture and nothing else, and reducing it does not touch a single feature boundary.

The threshold here is 120 in squared eight-bit units — roughly four per cent local contrast. That is above pore and fine-noise scale and comfortably below the contrast of a lash, a nostril or the edge of a lip.

The radius, and why it is not a number of pixels

The split radius decides which scale of variation counts as texture. Too small and pores stay in the low band, so the smoothing control has almost nothing to act on. Too large and genuine structure — the shape of a nose, the modelling under a cheekbone — lands in the detail band, and reducing it flattens the face into a card.

The correct radius therefore depends on how many pixels a pore occupies, which depends entirely on how large the face is in the frame. A head filling a 6000-pixel portrait and the same head in a 900-pixel snapshot want radii six or seven times apart. Fixing the radius in pixels — which is what a tool does when it offers “radius: 4” as a setting — means the control behaves differently on every photograph and the user is left calibrating it by eye each time.

Here it is derived: the width of the working region divided by 220. On a face a thousand pixels across that comes to four and a half pixels. On a face three hundred across it comes to one and a half. In both cases the band being reduced is the band that holds pore texture, which is the property that lets a preview at 820 pixels, a preview at 2560 and an export at full size all agree about what the setting means.

Low band: self-guided filter, edge-preserving
High band: original minus low band
Radius: region width ÷ 220
Variance threshold: 120, squared 8-bit units
Texture control acts on: the high band only
Tone control acts on: the low band only
Recombination: low + high × (1 − amount)
Channels touched: luminance only

What the two sliders are actually doing

Texture removed scales the high band on the way back in. At 25 per cent the band is multiplied by 0.75, so three-quarters of the original pore structure returns to the picture. At 80 — the ceiling — a fifth returns, and the result reads as a surface rather than as skin. There is nothing past 80 because there is nothing worth reaching there.

Tone evened works on the low band, blurring it against a much wider version of itself and mixing the two. This is the control for a cheek that is blotchy or a forehead with a patch of shine. It is applied at 45 per cent of what the slider says, deliberately, because flattening the low band is how a face loses the look of having blood underneath it — and that failure is much harder to spot while you are making it than plastic texture is.

Where the technique runs out

Frequency separation cannot distinguish two things that occupy the same band, and sensor noise occupies exactly the band pore texture does. On a photograph taken indoors at high ISO there is no setting that removes the grain and keeps the pores, or the other way round, because at this scale they are the same signal. Working at a low setting and healing individual marks is the way through, and it is slower.

It also cannot help with anything structural. A shadow falling badly across a face, a strong colour cast, a face lit from the wrong side — those are properties of the low band across its whole extent, not variation within it, and no split makes them tractable. The same is true in the other direction: this is not a sharpening technique. Increasing the high band would amplify noise along with detail, which is why there is no control here that does it.