Intensity Filter

When two fluorophores are active at once inside a single diffraction-limited spot, the fitter sees one blob and returns a single localization with a corrupted position and an abnormally high photon count. The intensity filter rejects these multi-emitter events with a statistical test on brightness. It is a step native to SMLMAnalysis, selected by an IntensityFilterConfig.

analyze(smld, IntensityFilterConfig(cutoff = 0.01))   # → (filtered_smld, StepInfo)

When to use / prerequisites

Run on a fitted BasicSMLD whose emitters carry photons (i.e. after Detection & Fitting).
Most valuable on denser data, where simultaneous activations within one PSF are common (e.g. high-density dSTORM/PAINT). On very sparse data it has little to reject.
It needs enough localizations to estimate the excitation field — see min_bin_count below.

Inputs, returns & artifacts

Input — the current smld.
Returns — (filtered_smld, StepInfo); the StepInfo.info is an IntensityFilterInfo.
Artifacts (when outdir is set) — diagnostic figures of the fitted excitation field and the per-localization p-value distribution, plus the usual config.toml / info.toml.

Concept

A single emitter does not emit a fixed number of photons — the count is Poisson, and its mean varies across the field of view with the excitation intensity. The filter accounts for both:

Estimate the expected single-emitter rate, spatially. The field of view is binned (n_bins per axis); in each bin the rate_percentile (default 95th) of the photon distribution is taken as the upper bound of single-emitter emission there — high enough to sit above typical single-emitter counts but below true doubles. A smooth field model is then fit across bins: a spatially-varying Gaussian beam (field_mode = :gaussian) or a single global rate (:uniform).
Test each localization. Given its position's expected rate λ, a Poisson upper-tail test asks how improbable the observed photon count is under single-emitter emission. Localizations with p-value below cutoff are rejected as multi-emitter events.

Optionally (estimate_p2), the filter also estimates p₂, the fraction of localizations that are really two overlapping emitters — a diagnostic of how crowded the data is (it does not change what is filtered). The default p2_method = :mixture fits the field-normalized photon distribution as a two-component mixture, $h = (1-p)\,f_\text{single} + p\,f_\text{double}$ with $f_\text{double} = f_\text{single} \ast f_\text{single}$, and reads $p$ off directly; because it uses the whole distribution rather than a threshold it is unbiased. The legacy :tail method takes the ratio of bright-tail mass above p2_tail_threshold and is biased high (it attributes the whole single-emitter tail to doubles); it is kept for comparison.

Configuration

field	default	meaning
`cutoff`	`0.01`	p-value cutoff; localizations with p < cutoff are rejected
`field_mode`	`:gaussian`	excitation-field model: `:gaussian` (spatially-varying beam) or `:uniform` (one global rate)
`n_bins`	`10`	spatial grid bins per axis for field estimation
`min_bin_count`	`30`	minimum localizations per bin to estimate its rate
`rate_percentile`	`0.95`	per-bin percentile taken as the single-emitter rate; higher = more permissive
`estimate_p2`	`true`	also estimate the double-emitter fraction p₂ (info only)
`p2_method`	`:mixture`	p₂ estimator: `:mixture` (threshold-free mixture fit, default) or `:tail` (legacy tail ratio, biased high)
`p2_tail_threshold`, `p2_n_bins`	`1.0`, `200`	tail threshold τ (units of λ) for `:tail` and the tail diagnostics; histogram bins for the estimators

(filtered, info) = analyze(smld,
    IntensityFilterConfig(cutoff = 0.01, field_mode = :gaussian, rate_percentile = 0.95))

info.info.p2_estimate    # estimated double-emitter fraction (or nothing)

Output & interpretation

IntensityFilterInfo reports:

field	meaning
`n_before`, `n_after`	localizations in and surviving
`field_mode`	the field model actually used
`lambda_max_global`	peak expected single-emitter rate (photons)
`field_fit_r2`	goodness of the field fit
`p2_estimate`	estimated fraction of double-emitter events (or `nothing`)
`p2_tail_obs`, `p2_tail_f2`	observed vs. modeled bright-tail mass

Sanity checks: field_fit_r2 should be high for a clean :gaussian fit — if it is poor, the beam assumption may not hold and :uniform is the safer choice. A large p2_estimate signals crowded data where multi-emitter rejection matters most; if it is near zero, the filter is mostly a no-op and can be dropped.

Notes & caveats

Native, in-house method — the per-bin-percentile + smooth-field + Poisson-tail approach is implemented in SMLMAnalysis; there is no separate upstream package for it.
Field estimation needs data. With too few localizations per bin (below min_bin_count) the field estimate is unreliable; reduce n_bins or fall back to field_mode = :uniform.
Repeatable. Like the other filters, it can appear more than once in a pipeline, though once is typical.

References

This is a method native to SMLMAnalysis; there is no separate primary publication. See the API Reference for the full IntensityFilterConfig and IntensityFilterInfo field lists.