Function: ABE - setiastro/setiastrosuitepro GitHub Wiki

Function: Automatic Background Extraction (ABE)

Polynomial background modeling with optional RBF refinement, smart sampling, exclusion polygons, non-destructive preview, and apply-with-undo. Works with mono or RGB float images in ([0,1]).

What ABE Does

  • Estimates a smooth background (B) (gradients, vignetting, LP glow).
  • Subtracts (B) while preserving the global median of the working domain.
  • Optionally refines with RBF for complex/curvy gradients.
  • Respects masks and user-drawn exclusion polygons in image space.

Model (math)

1) Polynomial stage (degree (d\in{0,\dots,6}))

We fit a 2-D polynomial to per-sample patch medians by least squares. For sample locations ((x_i,y_i)) with measured values (z_i), build a design matrix (A) of monomials up to degree (d) and solve:

\min_{\boldsymbol{\beta}}\;\|A\boldsymbol{\beta}-\mathbf{z}\|_2^2
\quad\Rightarrow\quad
\boldsymbol{\beta}=(A^{\top}A)^{-1}A^{\top}\mathbf{z}.

Evaluate the fitted surface over the (downsampled) image to get (B_{\mathrm{poly}}).

2) RBF refinement (optional)

Multiquadric RBF on the polynomial-corrected image (same sampling), with smoothness (\lambda):

\phi(r)=\sqrt{1 + (\epsilon r)^2},\quad
B_{\mathrm{rbf}}(x,y)=\sum_{i} w_i\,\phi\!\left(\sqrt{(x-x_i)^2+(y-y_i)^2}\right).

Weights (w_i) come from solving the regularized system ((\Phi+\lambda I)\mathbf{w}=\mathbf{z}). The final background is (B = B_{\mathrm{poly}} + B_{\mathrm{rbf}}) (if RBF is enabled; otherwise (B=B_{\mathrm{poly}})).

3) Median re-centering

After subtraction we restore the original working-domain median (m_0) so overall brightness stays stable:

I_{\mathrm{corr}} = \text{clip}\!\Big( I - B + (m_0 - \text{median}(I-B)) ,\, 0,\, 1 \Big).

(Here (\text{clip}(x,0,1)) clamps to ([0,1]) and (\text{median}(\cdot)) is the scalar median.)

Sampling & Exclusions

  • Smart points: corners, borders, and quartile tiles.
  • Bright-region avoidance: ignore top quantiles in luminance; prefer dim/neutral areas.
  • Local patch median: each sample’s value is the median of a ((\text{patch size})) neighborhood.
  • User polygons: draw exclusion polygons (right-click to close); excluded pixels are never sampled.
  • Masks (if present): processing is blended as (m\cdot \text{ABE} + (1-m)\cdot \text{source}).

Parameters (UI)

  • Polynomial degree: (0) (skip poly, RBF-only) … (6).
  • # Sample points: count of background probes.
  • Downsample: integer factor for fitting speed; full-res background is reconstructed by high-quality resize.
  • Patch size (px): spatial window for per-sample medians.
  • RBF refinement: enable/disable; Smooth controls (\lambda) (higher = smoother).
  • Preview background: toggle between corrected image and background view.
  • Create background doc: export (B) as a separate image.

Defaults (suggested): degree (=2), samples (=120), downsample (=4), patch (=15), RBF on, smooth (\approx 0.10).

Preview & Navigation

Because images are linear, use the built-in display helpers (preview only):

  • Autostretch (Siril-style MAD) toggle for visualization.
  • Zoom In/Out buttons; Ctrl+Wheel to zoom at cursor.
  • Pan: middle-drag (or Ctrl+left-drag).
  • Fit: scale to fit the preview viewport.
  • Polygons: left-click to add vertices, right-click to close; Clear Exclusions removes all.

Workflow

  1. Add exclusions around nebulosity/galaxies and bright stars (optional).
  2. Pick a degree (start at 2) and enable RBF for complex gradients.
  3. Set samples, patch size, and smooth to taste.
  4. Preview → inspect corrected image (or background) with Autostretch as needed.
  5. Apply to commit (with undo). Optionally Create background doc.

Color vs Mono

  • Internally ABE runs per-channel for RGB (on float ([0,1])).
  • Mono inputs are treated as single-channel throughout; outputs match the input shape.
  • Median re-centering is computed in the working domain (after any optional modeling pre-stretch—see below).

Notes on Parity with SASv2 (optional)

For 1:1 compatibility with legacy projects, ABE can run in the same modeling domain as SASv2:

  • A lightweight pre-stretch (per-channel min shift + rational midtone lift to target median) is applied only for modeling, then analytically inverted after ABE so results return to the source domain.

Performance Tips

  • Degree 0 + RBF: fast, good for mild gradients with local wiggles.
  • Higher degree: captures broad vignetting/tilt; avoid overfitting—use RBF for the rest.
  • Downsample aggressively for large frames; increase samples if the field is uneven.
  • Increase patch size in noisy data to stabilize medians.

Output

  • Corrected image (applied to the active document, undoable).
  • Background image (optional extra document).
  • Metadata: degree, samples, downsample, patch size, RBF on/off, smooth value, and mask usage.

Troubleshooting

  • Residual gradient: raise samples, enable RBF, or bump degree by 1.
  • Over-correction in bright structures: expand exclusion polygons and/or increase smoothness.
  • Banding after subtraction: lower degree and rely more on RBF; ensure downsample isn’t too coarse.