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Generalized Hyperbolic Transformation

Purpose and expected result

Generalized Hyperbolic Transformation (GHT) is a permanent display stretch for normalized mono or RGB images. It combines generalized-hyperbolic, histogram, arcsinh, linear, inversion, and statistics-derived STF families in one window. Its symmetry point and shadow/highlight protection boundaries let an experienced processor concentrate nonlinear contrast around a chosen intensity while keeping the transfer continuous at both protection boundaries.

The usual input is a calibrated linear master after operations that require linear samples. Apply replaces the selected still image or sequence, preserves geometry and pixel type, optionally post-blends the active view mask, records an Image History step, and marks the result nonlinear. Two histograms and a full-image real-time preview provide diagnostics; no LUT, preset, report, or separate output file is created.

At a glance

Item Current behavior
Menu path Process > Intensity Transformations > Generalized Hyperbolic Transformation
Enabled when An image or sequence view is active. A second GHT window for the same target is rejected, as is launch while an exclusive process owns it. GHT itself is nonexclusive; Apply still requires the selected target's processing lock.
Inputs One intended one-channel grayscale or three-channel RGB still/sequence; normalized transform parameters; optional enabled view mask. RGB also exposes component and color-preserving modes.
Outputs Destructive target replacement with preserved dimensions, pixel type, and source metadata; nonlinear processing-state provenance and one history step. Channel count and pixel format are also preserved except when sequence CFA autodebayering converts one-channel mosaic frames to three-channel RGB before transformation. A sequence is rebuilt at a temporary path before replacement.
Recommended image state Normally a calibrated linear mono/RGB master after background/color calibration and any linear-only measurement, restoration, or denoising. Image Inversion and an analytical inverse are also available, but AfterNight still marks every successful GHT-process result nonlinear.
Preview support Full asynchronous real-time preview, which is the result Apply writes, plus a lower source histogram and upper predicted/processed histogram. A Preview area shows exactly what Apply writes there; an STF preview area uses the whole target's statistics, never the area's own. Histogram-only prediction is quantized and does not include the active mask.
Sequence support Supported by the generic replacement-sequence path with progress and cooperative cancellation. One UI parameter snapshot is captured for the run. STF statistics and its derived curve are recomputed from each frame, so STF is intentionally per-frame adaptive. The sequence reader may apply its configured CFA debayer request.
Mask support Supported as a final original/processed blend for stills and sequences, including mask inversion and the framework's grayscale/RGB mask-channel rules. The mask does not alter the transfer curve or immediate histogram prediction.
External dependencies None. The transform is the bundled engine's stretch, run on its threads. The cited GHS material is algorithm background, not a runtime dependency.

Before you start

  1. Finish calibration, integration, gradient correction, color calibration, and any measurement, deconvolution, or denoising step that requires linear data. Every successful mode in this process declares the result nonlinear.
  2. Activate the intended mono or RGB target. A one-channel CFA still is treated as grayscale and is not a substitute for debayering. A CFA sequence is different: if that view's automatic sequence debayer option is enabled, its frames are converted to RGB before the transform runs.
  3. Save a copy or confirm that Image History is available. Apply replaces the target and repeated stretches compound rounding and endpoint clipping.
  4. Inspect the active view mask. It is blended after the transform and is not represented in the transfer curve or histogram-only prediction.
  5. Start with Preview selected and Plot resolution at 8-bit (256). Plot resolution changes diagnostic binning only, never output precision.
  6. For GHT, Histogram, or Arcsinh, maintain LP <= SP <= HP. The spin controls and range handles enforce that order. For Linear Stretch, maintain Black point < White point; the UI enforces a minimum gap of 0.0001.

Procedure

  1. Open Process > Intensity Transformations > Generalized Hyperbolic Transformation. Confirm that Target Image names the intended view and that the lower histogram represents its source data.
  2. Choose Channel. Begin with RGB for a shared independent-channel transfer. Use one named channel for deliberate channel repair, or use Lightness, Saturation, or Colour only after reviewing their color models below.
  3. Choose Transformation type. For a conventional first GHT stretch, leave Generalized Hyperbolic, Invert cleared, and Local intensity b at 0. Set Stretch factor(In(D+1)) gradually; the displayed value is ln(D+1), not the internal strength D.
  4. Place Symmetry point SP at the intensity around which nonlinear contrast should be concentrated. Type a value or use one of the mutually exclusive point/area/histogram pickers. Pickers remain armed after a selection, so each subsequent point, rectangle, or histogram click updates SP until you toggle the picker off, select another picker, edit SP manually, or change Transformation type.
  5. Set Protect shadows LP no higher than SP and Protect highlights HP no lower than SP. Outside LP/HP the curve continues along boundary tangents; the controls do not hard-clip samples at those positions.
  6. Inspect the upper transfer curve and preview while changing one control at a time. Use the lower three-handle selector for LP/SP/HP. In Linear Stretch its outside handles control black/white points; the center handle is displayed but currently has no process effect.
  7. Check the target at 100% and inspect endpoints independently of the toolbar's Show clipping info overlay. That overlay is a coarse endpoint-occupancy diagnostic and has known component/prediction limits.
  8. Select Apply. A successful still-image run replaces the target and resets transform settings. For a sequence, wait for the progress dialog to finish; cancellation preserves the original sequence and removes the temporary replacement.
  9. Inspect Image History and the declared nonlinear state before continuing to Curves Transformation or other nonlinear tone and color work.

Complete parameter and action reference

UI label/action Type and unit Runtime default Persisted-default exception Valid values, step, or constraints Effect of increasing, decreasing, or selecting Dependencies and enable/visibility rules Quality, artifact, runtime, memory, or disk trade-off Scope: preview/apply, channel, mask, still/sequence Persistence
Upper preview histogram Interactive plot Current transformed prediction/preview None Normalized horizontal intensity; vertical count scale Shows the selected channel/component after the current transform; the curve is always drawn Available with a valid target; recalculated after target/settings changes Image-derived recomputation is slower than remapping existing bins Diagnostic only; unmasked; still target shown while configuring a sequence Window lifetime
Lower source histogram Interactive plot Current target source None Normalized horizontal intensity; vertical count scale Shows untransformed source data and hosts the range selector Available with a valid target Higher plot resolution costs more histogram work and memory Diagnostic only; unmasked; target still/source view Window lifetime
Range selector handles Three normalized handles LP=0, SP=0, HP=1 None Enforces left <= center <= right In nonlinear modes sets LP/SP/HP; in Linear Stretch the outside handles set black/white points Center handle has no process effect in Linear Stretch; hidden behavior is reflected by fields Direct manipulation can move two constrained values when they meet Preview/apply parameters; all applicable channels; still/sequence Transform settings reset after success/Reset
Histogram mouse gestures Mouse/wheel actions No active gesture None Left click/drag, middle-drag pan, right-click reset, Ctrl+wheel zoom Left interaction moves a handle or supplies histogram SP when that picker is active Histogram-point picker uses the upper histogram; ordinary handles are on the lower histogram Display navigation only, except deliberate handle/picker edits Diagnostic and parameter input; mask-independent Window lifetime
Zoom in Toolbar action — None Repeated action, 1.30x per click Enlarges both histogram widgets inside their scroll areas Always available with histograms Diagnostic only Both plots only Not persisted
Zoom out Toolbar action — None Repeated action, 0.70x per click Shrinks both histogram widgets inside their scroll areas Always available with histograms Diagnostic only Both plots only Not persisted
Zoom reset Toolbar action — None Single action Fits both histogram widgets to their scroll areas Always available with histograms Diagnostic only Both plots only Not persisted
Show grid Checkable toolbar action Selected None On/off Shows or hides grid lines on both histograms Always available Display only Both plots only Window lifetime; Reset does not change it
Show transfer curve Checkable toolbar action Selected None On/off Shows or hides the curve on the lower source histogram The upper histogram's transfer curve remains enabled Display only; does not disable processing Lower plot only Window lifetime; Reset does not change it
Show clipping info Checkable toolbar action Selected None On/off Shows or hides clipped-low/high overlays on both histograms Values are each plot's endpoint counters; a bin-remapped prediction counts its end bins Coarse and potentially misleading in predicted/component cases; see limitations Both plots; unmasked diagnostic Window lifetime; Reset does not change it
Absolute scales Checkable toolbar action Selected UI-builder seed is cleared, but process construction selects it before use On/off Selected actually normalizes each displayed channel to its own peak; cleared preserves relative peak heights Disabled for grayscale Selected improves per-channel visibility but hides relative channel populations Both plots only Window lifetime; Reset does not change it
Draw histogram areas Checkable toolbar action Cleared None On/off Fills histogram areas instead of drawing outlines Always available Rendering preference only Both plots only Window lifetime; Reset does not change it
Plot resolution Combo box, bins 8-bit (256) None 6-bit (64), 7-bit (128), 8-bit (256), 9-bit (512), 10-bit (1024), 12-bit (4096), 14-bit (16K), 16-bit (64K), 100 levels, 1000 levels, 10000 levels More bins reveal finer diagnostic structure Recalculates both histograms More bins cost histogram time/memory; output samples are unchanged Diagnostics only Window lifetime; Reset does not change it
Channel Combo box RGB for RGB; disabled Grayscale for mono None RGB, Red, Green, Blue, Lightness, Saturation, Colour; mono Grayscale Chooses independent sample channels or a component/color-preserving model RGB-only choices on three-channel targets; controls below change with mode Single-channel edits can unbalance color; component conversions can introduce gamut/rounding effects Preview/apply, still/sequence; mask post-blend is unchanged Transform settings reset after success/Reset
Colour clip Combo box Clip None Clip, Rescale Clip clamps scaled RGB independently; Rescale reduces a common scale when a channel would exceed 1 Visible only for Channel: Colour Clip can alter ratios at the upper boundary; Rescale preserves ratios but yields less luminance increase Colour mode, preview/apply, still/sequence Transform settings reset after success/Reset
Luminance coefficients source Combo box Default None Default, Image, Manual Selects pseudo-luminance weights for Colour mode Visible only for Colour; manual fields appear only for Manual Current Default and Image both use equal weights; Image does not read a profile Colour mode only Transform settings reset after success/Reset
R Numeric coefficient 1.0000 None 0–10, step 0.1, four decimals Raises/lowers red's share after all three values are normalized Visible only for Colour + Manual Biased weights change which colors drive the common scale; all-zero falls back to equal thirds Colour pseudo-luminance only Transform settings reset after success/Reset
G Numeric coefficient 1.0000 None 0–10, step 0.1, four decimals Raises/lowers green's normalized share Visible only for Colour + Manual Same as R Colour pseudo-luminance only Transform settings reset after success/Reset
B Numeric coefficient 1.0000 None 0–10, step 0.1, four decimals Raises/lowers blue's normalized share Visible only for Colour + Manual Same as R Colour pseudo-luminance only Transform settings reset after success/Reset
Transformation type Combo box Generalized Hyperbolic None Generalized Hyperbolic, Histogram Transformation, Arcsinh, Linear Stretch, Image Inversion, STF Transformation Selects the transfer family and its relevant controls Visibility/enabling rules are described in the dependent rows Families differ in contrast concentration, color behavior, and adaptation Preview/apply, still/sequence Transform settings reset after success/Reset
Invert Check box Cleared None On/off Uses the analytical inverse of Generalized Hyperbolic, Histogram, or Arcsinh Enabled only for those three families; switching to Linear, Image Inversion, or STF clears and disables it Useful for reversing a matching curve, but conversion/clipping/quantization prevent perfect image restoration Preview/apply, selected channel model, still/sequence Transform settings reset after success/Reset
Linked STF Check box Cleared None On/off Selected derives one RGB MTF; cleared derives one per RGB channel Visible only for STF; mono is effectively linked. In Lightness/Saturation/Colour, current unlinked execution uses STF slot 0 rather than component statistics Linked better preserves channel balance; unlinked neutralizes RGB backgrounds and can alter color STF preview/apply; each sequence frame derives its own values Transform settings reset after success/Reset
Stretch factor(In(D+1)) Numeric natural-log strength 0.0000 None 0–20, step 0.01, four decimals; internal D=exp(value)-1 More strength increases nonlinear separation; 0 is identity for GHT/Histogram/Arcsinh Visible for GHT, Histogram, and Arcsinh only High values can compress highlights and amplify noise/quantization Preview/apply, applicable channel model, still/sequence Transform settings reset after success/Reset
Local intensity b Numeric shape parameter 0.0000 None -5–15, step 0.01, four decimals Moves among logarithmic/integral/exponential/hyperbolic GHT shapes; positive values concentrate more locally around SP Visible only for Generalized Hyperbolic Strong positive localization can make transitions visually abrupt even though the curve remains continuous GHT only Transform settings reset after success/Reset
Symmetry point SP Normalized numeric intensity 0.0000 None 0–1, step 0.01, four decimals; LP <= SP <= HP Moves the maximum-slope center to darker or brighter source intensities GHT, Histogram, Arcsinh; synchronized with center handle/pickers Poor placement can emphasize noise or compress the intended subject Preview/apply, applicable channel model, still/sequence Transform settings reset after success/Reset
Protect shadows LP Normalized numeric intensity 0.0000 None 0–1, step 0.01, four decimals; LP <= SP Raises/lowers the point below which a tangent linear continuation replaces the nonlinear base curve GHT, Histogram, Arcsinh Larger LP protects a broader shadow range but reduces nonlinear shadow lift Preview/apply, applicable channel model, still/sequence Transform settings reset after success/Reset
Protect highlights HP Normalized numeric intensity 1.0000 None 0–1, step 0.01, four decimals; HP >= SP Lowers/raises the point above which a tangent linear continuation replaces the nonlinear base curve GHT, Histogram, Arcsinh Lower HP protects a broader highlight range but reduces nonlinear highlight separation Preview/apply, applicable channel model, still/sequence Transform settings reset after success/Reset
Black point Normalized numeric intensity 0.0000 None 0–1, step 0.01, four decimals; at least 0.0001 below White point Values at/below it become 0; raising it clips more shadows Visible only for Linear Stretch; synchronized with left handle Direct shadow clipping Linear preview/apply, applicable channels, still/sequence Transform settings reset after success/Reset
White point Normalized numeric intensity 1.0000 None 0–1, step 0.01, four decimals; at least 0.0001 above Black point Values at/above it become 1; lowering it clips more highlights Visible only for Linear Stretch; synchronized with right handle Direct highlight clipping Linear preview/apply, applicable channels, still/sequence Transform settings reset after success/Reset
Pick from image point Checkable icon action Cleared None One mutually exclusive picker Sets SP to the arithmetic mean of all source-channel samples at each selected image coordinate GHT/Histogram/Arcsinh only; selecting it clears other pickers; manual SP edit cancels it One hot/cold pixel is not representative; repeated clicks continue changing SP while armed SP input from source target; preview view routes coordinates Remains armed after completion; cleared by toggling it off, selecting another picker, manual SP edit/handle movement, changing Transformation type, Reset, or close
Pick from image area Checkable icon action Cleared None One mutually exclusive rectangular source-selection picker Sets SP to the arithmetic mean of the per-channel means in each completed source rectangle GHT/Histogram/Arcsinh only; selecting it clears other pickers; manual SP edit cancels it A representative area is more stable but can mix background and structure; repeated selections continue changing SP while armed SP input from source target; mask is not sampled Remains armed after completion; cleared by toggling it off, selecting another picker, manual SP edit/handle movement, changing Transformation type, Reset, or close
Pick from histogram point Checkable icon action Cleared None One mutually exclusive picker accepting repeated clicks on the upper histogram Sets SP to each clicked normalized x coordinate GHT/Histogram/Arcsinh only; selecting it clears other pickers; manual SP edit cancels it Quantized visual placement depends on plot/view scale; repeated clicks continue changing SP while armed SP input; upper preview histogram Remains armed after completion; cleared by toggling it off, selecting another picker, manual SP edit/handle movement, changing Transformation type, Reset, or close
Target Image View selector Active view at launch None Open supported still or sequence views Retargets controls, source statistics, histograms, and preview Apply later requires target processing lock Recalculation cost follows image size and plot resolution Source for preview/apply and picker sampling Window lifetime; Reset does not change it
Preview Check box Selected None On/off Enables/disables asynchronous full-image real-time preview updates Requires a valid target; a new generation supersedes stale work Full-image transforms and color conversions can be expensive Preview only; target is unchanged Window lifetime; Reset does not change it
Preview image pane Image display Current transformed preview None Zoom/pan through shared preview viewer behavior Displays the current full-image result Updated only while Preview is enabled and work completes Allocates a transformed image; special color modes add conversion buffers Mask-aware image preview; still target view while configuring sequence Window lifetime
Apply Button/action Enabled when settings update and target can be locked None Single action Captures typed settings and starts destructive still/sequence execution Fails if the target is unavailable or already processing Full-image/sequence CPU, memory, and temporary-disk cost Target replacement; active mask post-blend; still/sequence Successful run resets transform settings
Close Button/action Enabled None Single action Closes immediately when idle; requests cancellation and defers close while work is active Worker/preview lifecycle aware Cancellation is cooperative Window and active execution Not persisted
Reset Button/action Enabled None Single action Restores transform/channel settings, cancels pickers, resets histogram zoom, and refreshes the source preview Does not reset target, Preview, Plot resolution, Grid, transfer/clipping/scale/area toolbar states No image change Configuration only Restores execution defaults; listed display states survive
Sequence progress Progress dialog Appears only during sequence Apply None 0–frame count Reports replacement-sequence progress Sequence targets only Dialog updates add negligible cost; output uses temporary disk space Sequence Apply only Run lifetime
Cancel Sequence progress action Available while sequence work runs None Cooperative request Stops before replacement, removes the temporary sequence, and preserves the source Sequence progress dialog only The current frame may finish before cancellation is observed Sequence Apply only Run lifetime

How the algorithm works

Conceptual pipeline

  1. A still target is converted to 32-bit float working data, 64-bit for a Float64 or 32-bit integer image. A sequence frame is decoded first, including optional CFA-to-RGB autodebayering, and that decoded frame is converted the same way. Every processed input sample is clamped to [0,1]; unselected RGB channels and an alpha channel are held aside and copied back exactly as they were. A non-finite sample in a processed channel of a pixel the image's validity admits makes the engine refuse the run.
  2. GHT, Histogram, and Arcsinh build a continuous normalized transfer around SP and extend it linearly below LP and above HP. Linear, Image Inversion, and STF use their dedicated transfers. Invert selects an analytical inverse for the first three families.
  3. RGB/Red/Green/Blue apply transfers independently. Lightness uses CIELAB L, converted back through the exact inverse of the XYZ matrix; Saturation transforms HSV saturation and then restores the original CIELAB L; Colour transforms a weighted pseudo-luminance and applies a common RGB scale.
  4. The float result is converted back to the source pixel type, rounding to the nearest code. The framework then blends the active mask, commits the still or temporary sequence, and adds history; the result keeps the source's cards, acquisition record, and solution and is marked nonlinear.

Model and equations

Let source intensity be x in [0,1], strength be D = exp(displayed stretch factor) - 1, symmetry point be SP, and protection points be LP and HP. For the nonlinear families, define a positive-offset base g(u) for u >= 0 and construct

\[ q(x)= \begin{cases} -g(SP-LP)+g'(SP-LP)(x-LP), & x<LP,\\ -g(SP-x), & LP\le x<SP,\\ g(x-SP), & SP\le x\le HP,\\ g(HP-SP)+g'(HP-SP)(x-HP), & x>HP. \end{cases} \]

The final forward transfer is F(x) = (q(x)-q(0))/(q(1)-q(0)). This forces F(0)=0 and F(1)=1, places maximum slope at SP, and joins the protected tangent regions continuously. LP and HP are therefore protection boundaries, not clipping thresholds. The complete inverse construction is given below.

For Generalized Hyperbolic, the base family selected by b is:

\[ g(u)= \begin{cases} \ln(1+Du), & b=-1,\\ \dfrac{1-(1-bDu)^{(b+1)/b}}{D(b+1)}, & b<0,\ b\ne-1,\\ 1-e^{-Du}, & b=0,\\ 1-(1+Du)^{-1}, & b=1,\\ 1-(1+bDu)^{-1/b}, & b>0,\ b\ne1. \end{cases} \]

The limiting/special cases are implemented separately for numerical stability. At b=0 the family is exponential; negative values move through gentler, broader integral/logarithmic shapes, while positive values increasingly concentrate the response around SP. D=0 is identity.

For Histogram Transformation, m=1/(2(D+1)) and

\[ g(u)=\frac{(m-1)u}{(2m-1)u-m}. \]

It then uses the same symmetry/protection construction. This is not the same control convention as the dedicated Histogram Transformation window. Arcsinh instead uses g(u)=asinh(Du)=ln(Du+sqrt(D^2u^2+1)), again with the same construction.

Analytical inverse equations

For inverse input y in [0,1], let q0=q(0), q1=q(1), and undo the forward normalization with z=q0+y(q1-q0). Define the transformed boundaries LPT=F(LP), SPT=F(SP), and HPT=F(HP). The inverse bases h(v)=g^{-1}(v) are:

\[ h(v)= \begin{cases} \dfrac{e^v-1}{D}, & \text{GHT},\ b=-1,\\ \dfrac{1-(1-(b+1)Dv)^{b/(b+1)}}{Db}, & \text{GHT},\ b<0,\ b\ne-1,\\ -\dfrac{\ln(1-v)}{D}, & \text{GHT},\ b=0,\\ \dfrac{v}{D(1-v)}, & \text{GHT},\ b=1,\\ \dfrac{(1-v)^{-b}-1}{bD}, & \text{GHT},\ b>0,\ b\ne1,\\ \dfrac{mv}{(2m-1)v-(m-1)}, & \text{Histogram},\\ \dfrac{\sinh(v)}{D}, & \text{Arcsinh}. \end{cases} \]

Using the same tangent slopes as the forward construction, the implemented piecewise inverse is:

\[ F^{-1}(y)= \begin{cases} LP+\dfrac{z+g(SP-LP)}{g'(SP-LP)}, & 0\le y<LPT,\\ SP-h(-z), & LPT\le y<SPT,\\ SP+h(z), & SPT\le y<HPT,\\ HP+\dfrac{z-g(HP-SP)}{g'(HP-SP)}, & HPT\le y\le1. \end{cases} \]

At D=0, forward and inverse are identity. The implementation evaluates the GHT limiting cases separately and precomputes the transformed breakpoints and branch coefficients before processing samples. At exactly b=-1 the engine inverts the logarithmic branch directly and holds it to the family's definition.

Linear, Image Inversion, and STF

Linear Stretch uses 0 at/below BP, (x-BP)/(WP-BP) between the points, and 1 at/above WP. Image Inversion is 1-clamp(x,0,1); it is distinct from the Invert checkbox.

STF Transformation applies the rational midtones function

\[ M(x;m,\ell,r)= \begin{cases} 0, & x\le\ell,\\ 1, & x\ge r,\\ \dfrac{(m-1)t}{(2m-1)t-m}, & \ell<x<r, \end{cases} \qquad t=\dfrac{x-\ell}{r-\ell}. \]

For channel c, let p_c be its median and let s_c=1.4826* MAD_c; an exactly zero s_c is replaced by 0.001. If at least one channel median is at or below 0.5, the normal branch derives

\[ \ell_c=\max(0,p_c-2.8s_c),\quad r_c=1,\quad m_c=M(p_c-\ell_c;0.25,0,1) \]

for unlinked STF. Linked STF instead uses p=mean(p_c), ell=max(0,mean(p_c-2.8s_c)), r=1, and m=M(p-ell;0.25,0,1). When every channel median exceeds 0.5, the inverted branch uses

\[ \ell_c=0,\quad r_c=\min(1,p_c+2.8s_c),\quad m_c=1-M(r_c-p_c;0.25,0,1) \]

for unlinked STF. Its linked counterpart uses p=mean(p_c), ell=0, r=min(1,mean(p_c+2.8s_c)), and m=1-M(r-p;0.25,0,1). The resulting curve is M(x;m_c,ell_c,r_c) per channel or M(x;m,ell,r) when linked.

Derived STF values are not exposed in the UI. They are derived from the exact median and MAD of the whole image a run changes: the target's for a preview, a preview area, and Apply, measured once for each change of the image, and each frame's own for a sequence. For Lightness, Saturation, or Colour, the current component path evaluates STF slot 0; with Linked STF cleared that is the curve derived from the red input channel, not a curve derived from the selected component.

In Colour mode, normalized nonnegative weights form L = wR*R + wG*G + wB*B, then L'=F(L) and the nominal common scale is L'/L. Clip clamps each scaled channel. Rescale divides the common scale by max(1, L'*max(R,G,B)/L), preserving RGB ratios when possible. Zero luminance uses a guarded neutral/black result. Current Default and Image coefficient sources both resolve to equal thirds; only Manual changes the weights.

Histograms, masks, precision, and metadata

The lower plot is the source histogram. The upper plot is either an immediate bin-remapped prediction or a histogram of a transformed image. Lightness, Saturation, and Colour add a computed component as an auxiliary histogram and display that component; STF also requires image/statistics-derived work. Plot bin count changes only these diagnostics. A whole code on a bin boundary lands in its own bin, by exact interval arithmetic; a 12-bit or finer histogram is redrawn to fill its plot when the dialog is resized; and the transfer curve is drawn so that it stays visible in the light theme.

The clipping overlay sums the clipped counters of every channel a plot holds, an auxiliary component included, and divides by the samples those channels admitted. On the lower plot, and on an upper plot recounted from a stretched target, a clipped sample is one at or beyond 0 or 1; on a bin-remapped upper plot it is a count that lands in the first or last bin after the remap, so that figure is a binned forecast. Treat the overlay as orientation only.

Samples are held in a 32-bit float working image, 64-bit for a Float64 or 32-bit integer source; color-space intermediates and the curves are evaluated in double (a one-channel or independent row may use the engine's compiled Float32 evaluation within its stated accuracy) and stored at the working image's precision. Conversion back preserves the original pixel type, rounding an integer output to the nearest code. The active mask is a later original/result blend and is absent from the histogram-only prediction.

The source's header cards, acquisition record, and astrometric solution are kept; the result states no transfer function and its processing history records the stretch. The processing state becomes nonlinear with ght-stretch provenance for every mode. History records the process/transform, channel, displayed strength, b, LP/SP/HP, and BP/WP. It does not record the mask, Colour clip, luminance coefficient source/values, linked STF state or derived values, or histogram/display settings. Even an inverse, Linear Stretch, Image Inversion, or identity-strength Apply is marked nonlinear.

Boundary and failure behavior

  • The intended input is one-channel grayscale or three-channel RGB. The menu gate requires only an active image/sequence, so other channel counts are not proactively rejected even though the UI and color paths are designed for mono/RGB.
  • Nonlinear sample inputs are clamped to [0,1]; Linear Stretch and Image Inversion also clamp their outputs. A Lightness or Saturation conversion back to RGB can leave a value outside [0,1]: a floating image keeps it and an integer image saturates at its range.
  • The UI constrains LP/SP/HP and BP/WP. The engine still has a defensive WP <= BP step response for programmatic callers.
  • STF statistics are measured from the whole image a run changes. When they cannot be measured, or the engine refuses the derivation (no valid sample, a non-finite admitted sample, or a channel median outside [0,1]), the preview or Apply fails with an "Error executing the process" message and nothing is published.
  • Apply cannot acquire a busy target. Preview generations discard stale results. Sequence cancellation is cooperative, deletes its temporary output, and does not replace the source. A failed still transform does not commit a result.
  • No transform-specific preset or parameter persistence exists. Successful Apply and Reset restore execution defaults; several toolbar/preview/target states deliberately survive Reset for the current window only.

Parameter interactions and starting points

Combination Conservative starting point Too weak looks like Too strong looks like Adjustment order
GHT strength + SP b=0, LP=0, HP=1; set SP from a representative subject/background boundary, then raise strength from 0 Histogram/preview stays near the source Important regions crowd toward an endpoint; noise/contrast becomes overemphasized SP, strength, then protection points
LP/SP/HP Begin with full protection range 0 <= SP <= 1; move LP upward or HP downward only to reduce curvature outside the subject range Protected region is not visibly distinct from the central nonlinear response Broad tonal ranges become nearly linear and lose desired separation SP first, LP second, HP third, recheck strength
Local intensity b Start at 0 and compare nearby values with the same D/SP/LP/HP Desired local contrast remains broad Contrast becomes overconcentrated near SP Strength/SP first, then b, then protection
RGB vs Lightness/Colour Begin with RGB; compare Lightness or Colour only when channel balance/gamut requires it Color behavior remains unchanged from independent channels Saturated colors clip, rescale, or shift through component conversion Choose channel model, then transfer, then inspect all channels/endpoints
Colour Clip vs Rescale Start with Rescale when ratio preservation matters; compare Clip at identical settings Bright colors receive less luminance lift under Rescale Clip drives one or more channels to 1 and changes ratios Coefficients, transfer, then clip policy
STF linked/unlinked Start linked for a color-balanced RGB image; unlinked is a deliberate background-neutralizing choice Linked curve leaves channel backgrounds separated Unlinked curves alter intended color balance Inspect medians/MAD, choose linked state, then apply; do not tune hidden values
Linear BP/WP Start at 0/1, move one endpoint at a time using fields or outer handles Dynamic range is barely expanded Shadows/highlights become exactly 0/1 BP, WP, then inspect endpoint counts independently

These are source-backed adjustment orders, not measured recommendations. No approved real master was executed.

Inputs, outputs, and metadata

  • Input count and compatibility: one open still image or sequence target. Intended formats are mono and RGB; normalized access is provided for all supported source pixel types.
  • Output: the same target is replaced after success. Width, height, pixel type, and source metadata are preserved. Channel count and pixel format are normally preserved too. If automatic sequence CFA debayer is enabled, each one-channel mosaic frame is decoded as three-channel RGB before processing, so the successful replacement sequence is RGB rather than CFA. A sequence is written to a SEQ_SWAP file in the session's temporary directory, and the view shows it in place of the original only after full success; the original file is not modified.
  • Precision: processing is through a 32-bit float working image, 64-bit for a Float64 or 32-bit integer source. The output is converted to the original integer/float/double type.
  • Masks: the active mask is blended after transformation. Its inversion and channel mapping follow the shared process framework. The mask does not change the stored history parameters or histogram prediction.
  • State/history: output is marked nonlinear (ght-stretch). History records the transform name (including inverse), channel and primary numeric points, but omits the secondary color/STF/mask/display details listed above.
  • Auxiliary artifacts: none. Preview images and sequence temporary data are transient. No output filename, overwrite prompt, LUT, preset, or report is exposed.

Performance

The main independent-channel loop is linear in pixels × processed channels and uses oneTBB. GHT/Histogram/Arcsinh scalar evaluation is constant work per sample. Lightness and Saturation add full-image RGB↔CIELAB and/or HSV conversions; Colour adds weighted-luminance and per-pixel scaling; STF adds median/MAD statistics, measured once per revision of the target and kept for later previews and Apply, and once for each sequence frame. All paths allocate at least one float working image, and component modes allocate additional full-image buffers.

Real-time preview transforms the full target. Disable Preview while making a series of control edits on a large image, then re-enable it for a checkpoint. Use 8-bit (256) plot resolution unless finer diagnostic bins are necessary. Higher bin counts increase histogram time and memory but cannot improve output precision. A sequence additionally requires temporary disk space approximately comparable to its rewritten content. No network or external process is used. No production timing was measured.

Worked example

  • Evidence mode: Source-and-test-derived; no project-owned linear master was executed.
  • Input condition and settings: normalized grayscale samples with Generalized Hyperbolic, displayed strength ln(D+1)=1.252763 (D=2.5), b=0, LP=0.10, SP=0.35, HP=0.90, and Invert cleared. This is the exponential branch and matches the focused parity test's representative D/LP/SP/HP settings.
  • Expected checkpoint: the exact forward transfer gives 0→0, 0.05→0.047488, 0.10→0.094977, 0.20→0.202880, 0.35→0.424830, 0.50→0.646780, 0.90→0.955136, 0.95→0.977568, and 1→1. LP and HP are smooth tangent boundaries; neither clips to an endpoint.
  • Inspect at 100%/statistics/history: for a real run, verify endpoint counts independently, confirm that intended detail remains separated, and confirm a nonlinear ght-stretch state/history entry. Do not treat the toolbar clipping overlay as an exact prediction.
  • Limitations: the values verify equations and boundaries only. They do not establish visual quality, noise behavior, mask appearance, sequence consistency, or production runtime on an astronomical image.

Warnings and limitations

  • Apply is destructive and every mode marks the result nonlinear. The inverse checkbox does not restore a linear declaration or guarantee a pixel-perfect round trip after clipping, color conversion, or quantization.
  • Image Inversion is a separate 1-x operation. Invert means the analytical inverse of GHT/Histogram/Arcsinh.
  • The UI label Stretch factor(In(D+1)) uses a capital I; the implemented quantity is natural logarithm ln(D+1).
  • Current Luminance coefficients source: Image does not read image/profile coefficients; it behaves like Default with equal RGB weights.
  • STF is recomputed per frame in sequences. This can normalize frames differently, as Histogram Transformation's Auto-stretch also does; use a manual curve here, or Histogram Transformation's manual values, for one fixed transfer across frames.
  • In Lightness, Saturation, and Colour modes, unlinked STF uses the red-derived STF slot for the transformed component. Use linked STF when a shared RGB statistic is more appropriate; no component-statistics STF is exposed.
  • Lightness/Saturation/Colour use float color conversions and can encounter gamut/rounding effects. Colour Clip can change RGB ratios; Rescale preserves a common ratio by reducing the requested luminance increase.
  • The upper/lower clipping overlays are histogram endpoint diagnostics. A bin-remapped prediction counts its first and last bins, and every percentage is a share of all the channels a plot holds, the auxiliary component included, so neither is an acceptance measurement.
  • Absolute scales is selected by default but actually enables per-channel local peak normalization. Clear it to compare relative channel populations.
  • In Linear Stretch, the center histogram handle remains visible but does not change any processing parameter.
  • The point/area SP pickers average all source channels regardless of the selected processing channel. The histogram picker uses the upper plot. All three remain armed after a selection and continue replacing SP until explicitly cancelled by the actions described in the parameter table.
  • A sequence with automatic CFA debayer enabled is transformed and replaced as RGB. Disable automatic sequence debayer when preserving the one-channel CFA representation is required; a CFA still is not automatically debayered here.
  • The analytical inverse at exactly b=-1 is held to the logarithmic branch's definition by the engine's tests.
  • Reset does not restore the target, Preview, Plot resolution, or most histogram toolbar choices. No process setting is persisted across windows.
  • A Float64 or 32-bit integer image is evaluated through a 64-bit working image, every other representation through 32-bit float. Plot resolution never changes this processing precision.
  • The primary GHS reference describes its upstream implementation and theory; current AfterNight source/tests are authoritative where controls, precision, metadata, defaults, or behavior differ.

Troubleshooting

Symptom or exact error Verified cause/validation path Recovery Evidence source
GHT is disabled in the menu No active image/sequence view exists Activate the intended view, then reopen Process > Intensity Transformations Registry/launcher/action-state source
A second window will not open The same process is already open for the target, or an exclusive process owns it Use/close the existing process or finish the exclusive operation ProcessLauncher source
Apply cannot start The selected target is closed or its processing lock is busy Re-select an open idle target and retry ImageProcessControl execution source
Strength changes do nothing Displayed strength is 0, or a special combination is effectively identity; an STF whose statistics cannot be derived fails with an error instead Raise strength for GHT/Histogram/Arcsinh; for STF verify a valid nonempty mono/RGB target and statistics Engine GHT/STF source
LP or HP seems to clip data LP/HP are tangent boundaries, while actual endpoint clipping may come from input clamping, Linear BP/WP, color conversion, or output conversion Inspect the transfer and real output statistics; do not infer clipping from protection-point location GHT equations/parity tests
Colour mode shifts bright color Clip clamps channels independently, or chosen luminance weights drive a large common scale Compare Rescale and check manual coefficients; inspect channels at 100% Colour model source/parity test
Image coefficients look identical to Default Both currently resolve to equal RGB weights Use Manual for explicit weights; record this limitation in the workflow Parameter mapping/engine source
Histogram clipping reads zero or an implausible percentage A bin-remapped prediction counts its first and last bins after the remap, and every figure is a share of all the channels a plot holds, an auxiliary component included Measure the applied/preview image independently; use the overlay only for orientation HistogramWidget::updateClippingInfo; remapHistogramThroughStretch
Sequence frames receive different STF curves STF statistics are recomputed for every input frame Use a manual GHT/Histogram/Arcsinh curve when a fixed transfer across frames is required Engine sequence execution source
A CFA sequence becomes RGB after Apply Automatic sequence CFA debayer was enabled, so frames were decoded to three channels before transformation Disable automatic sequence debayer before Apply when the output must remain a one-channel CFA sequence RT-preview, ImageViewControl, demosaic, and concrete sequence sources
Unlinked STF in a component mode follows red statistics Lightness/Saturation/Colour evaluate STF slot 0 after RGB statistics are prepared Select Linked STF for one shared RGB curve, or choose RGB/a named channel for true per-channel behavior Engine special-component and STF source
Linear center handle has no effect Linear mode maps only the outside handles to Black/White point Use the numeric BP/WP fields or outside handles Process range-handler source
Preview and Apply differ Active mask, target, picker source, stale preview generation, or sequence per-frame STF adaptation differs Confirm target/mask, wait for current preview, and remember that sequence STF is per frame RT-preview/process/engine source
Inverse does not restore original state Float conversion, clipping, quantization, component conversion, or prior unmatched settings prevent exact reversal; state is always marked nonlinear Apply inverse only with matching parameters to a suitable copy and compare numerically Parity/state tests and engine source

References and provenance

  • Mike Cranfield, Generalized Hyperbolic Stretch tool documentation: primary background for the five-parameter GHS construction, transfer families, inverse, protection points, and color models. The document credits David Payne's 2021 proposal and his collaboration with Mike Cranfield. Checked 2026-07-13.
  • GHS Astro, Generalized Hyperbolic Stretch information and publication history: authorship and algorithm-publication context. Checked 2026-07-13.
  • Current AfterNight process, engine, histogram, framework, and focused test sources are authoritative for the shipped UI, float precision, defaults, metadata, masks, previews, and sequence behavior.