Ghost Fills: Methods and Applications

• Ghost fills are domain-specific operations that recover missing strength or suppress spurious artifacts in fields such as QCD, discrete tomography, and finite-volume methods.
• They involve techniques ranging from nonperturbative corrections in the ghost Schwinger–Dyson kernel to exact deconvolution in Fourier inversion and biasing stencils in numerical schemes.
• The concept also extends to inducing hallucinations in multimodal models and masking optical or LiDAR artifacts, highlighting its versatile application in scientific measurements.

$A\to 1$8 “Ghost fills” is not a single standardized term. In the cited technical literature, it denotes several domain-specific operations centered on “ghost” entities: a nonperturbative correction that fills the missing strength of the ghost Schwinger–Dyson kernel in Landau-gauge QCD, deconvolution of finite ghost artifacts caused by missing DFT slices, assignment of values to ghost cells in boundary treatments for finite-volume schemes, induction of hallucinated objects in multimodal LLMs, masking of optical ghosting artifacts in astronomical survey images, and removal of multi-path ghost points in full-waveform LiDAR (Aguilar, 2014, Chandra et al., 2010, Semplice et al., 2021, Parast et al., 29 Sep 2025, Tanoglidis et al., 2021, Ikeda et al., 30 Mar 2026).

1. Terminological scope

In the cited works, the phrase refers less to a common mathematical object than to a recurring operational pattern: some “ghost” quantity is either introduced, compensated, detected, masked, or removed. A common misconception is that “ghost fill” always means interpolation of missing data. In fact, the surveyed uses range from boundary-condition bookkeeping to artifact deconvolution and hallucination induction.

Domain	“Ghost” entity	Meaning of “fill” or analogous operation
Landau-gauge QCD	Ghost–gluon vertex contribution	Fills the missing strength of the ghost SDE kernel
Discrete tomography / DFT	Finite ghost circulants from missing slices	Construct and deconvolve ghosts to recover missing slice contributions
Finite-volume numerics	Ghost cells outside the domain	Fill boundary-adjacent auxiliary cells from boundary data
Multimodal LLMs	Hallucinated object absent from the image	Make the model fill in a nonexistent object
Survey imaging / LiDAR	Optical ghosts or ghost points	Detect, mask, or remove spurious sensor artifacts

This distribution of meanings suggests that “ghost fills” is best read contextually. In some fields it names a remedy for missing information; in others it names the generation or suppression of spurious structure. The shared element is not ontology but workflow: a ghost object mediates between incomplete measurements, boundary constraints, or model failure modes (Aguilar, 2014, Chandra et al., 2010, Semplice et al., 2021, Parast et al., 29 Sep 2025, Tanoglidis et al., 2021, Ikeda et al., 30 Mar 2026).

2. Landau-gauge QCD: filling the ghost Schwinger–Dyson kernel

In the Schwinger–Dyson analysis of the ghost propagator in Landau gauge, the relevant “ghost fill” is the contribution of the nonperturbative ghost–gluon vertex form factor $A$ to the kernel of the ghost dressing equation. The full ghost propagator is written as $D(p^2)=F(p^2)/p^2$, where $F(p^2)$ is the ghost dressing function. The ghost–gluon vertex has the decomposition

$$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$

but Landau-gauge transversality removes the $B$-term from the ghost SDE, so only $A$ survives in the kernel. The dressing equation is therefore sensitive to the momentum dependence of this single scalar form factor, rather than merely to a tree-level vertex (Aguilar, 2014).

The central result is that a bare-vertex approximation, $A\to 1$, is insufficient when the lattice gluon propagator is used as input. For $SU(3)$, using the MOM coupling $\alpha_s(4.3\,\mathrm{GeV})=0.22$ produces a ghost dressing function that is systematically too small; matching the lattice curve requires an artificial increase to $\sim 0.29$. In the one-loop dressed truncation, however, the soft-ghost form factor $D(p^2)=F(p^2)/p^2$0 develops a peak around $D(p^2)=F(p^2)/p^2$1 GeV, reaching about $D(p^2)=F(p^2)/p^2$2, while the soft-gluon form $D(p^2)=F(p^2)/p^2$3 peaks around $D(p^2)=F(p^2)/p^2$4 GeV at roughly $D(p^2)=F(p^2)/p^2$5. Solving the coupled system for $D(p^2)=F(p^2)/p^2$6 and $D(p^2)=F(p^2)/p^2$7 with the physical $D(p^2)=F(p^2)/p^2$8 raises the saturation value from $D(p^2)=F(p^2)/p^2$9 to $F(p^2)$0, bringing the solution into very close agreement with lattice data without boosting the coupling. In this precise sense, the ghost–gluon vertex “fills in” the missing strength of the ghost equation’s kernel (Aguilar, 2014).

3. Discrete tomography and Fourier inversion: finite ghosts and deconvolution

In discrete tomography, “ghost fills” refers to the inversion of cyclic artifacts generated by missing slices of the 2-D DFT. The underlying geometry is the projective Discrete Radon Transform, where discrete lines on an $F(p^2)$1 lattice satisfy

$F(p^2)$2

and, for prime $F(p^2)$3, the $F(p^2)$4 associated projections tile DFT space exactly once through the discrete Fourier slice theorem. If some projections are absent, the backprojected image acquires systematic cyclic artifacts called Finite Ghosts (Chandra et al., 2010).

The key structural statement is that each missing projection $F(p^2)$5 at slope $F(p^2)$6 forms artifacts superimposed on the reconstruction in the form of a circulant matrix whose unique row is $F(p^2)$7. Thus the missing data do not produce arbitrary corruption; they generate a highly structured superposition of circulants. The corresponding 2-point structuring elements are $F(p^2)$8 for each missing projection, and the associated kernel projections along direction $F(p^2)$9 place a positive impulse at $$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$0 and a negative impulse at

$$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$1

Using the Projection Convolution Theorem, the paper replaces expensive 2-D cyclic convolutions by 1-D cyclic convolutions in projection space. It further replaces complex DFT arithmetic by a Number Theoretic Transform to avoid numerical overflow and round-off. The resulting de-ghosting pipeline remains $$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$2 with $$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$3 and supports exact, non-iterative reconstruction from incomplete slice data. In the reported application, a $$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$4 Lena image embedded in $$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$5 space is reconstructed exactly from 101 rational projections, with de-ghosting taking roughly $$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$6 s on a 1.6 GHz laptop. Here the “fill” is not interpolation of arbitrary Fourier coefficients; it is exact deconvolution of finite ghost circulants induced by the missing slices (Chandra et al., 2010).

4. Finite-volume boundary treatment: ghost-cell fills and ghost-free reconstruction

In high-order finite-volume and finite-difference schemes, ghost fills are the standard boundary mechanism: one creates ghost cells outside the physical domain and fills them using the boundary conditions so that an interior reconstruction stencil can be applied unchanged near the boundary. For third-order schemes, this is especially common because interior CWENO or WENO reconstructions typically require symmetric stencils extending beyond the domain. The cited paper treats this practice as a baseline and develops an alternative that avoids ghost cells entirely (Semplice et al., 2021).

The motivation is both analytical and practical. With time-dependent Dirichlet data and multi-stage Runge–Kutta time integration, naive stage-wise ghost filling can cap the global accuracy at second order. Boundary conditions at network nodes are also difficult to encode as ghost-cell averages. The proposed alternative, $$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$7, uses standard symmetric $$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$8 in interior cells but biased stencils at the boundaries. In one dimension, the first cell uses

$$\Gamma_{\nu}(-k,-p,r)=A(-k,-p,r)\,p_{\nu}+B(-k,-p,r)\,k_{\nu},$$9

where $B$0 is a quadratic built from $B$1, $B$2 is a linear polynomial on $B$3, and $B$4 is a constant polynomial with infinitesimal linear weight. To recover the desired $B$5 global smoothness indicator at the boundary, the method sets $B$6 and symmetrically $B$7. The two-dimensional Cartesian extension uses analogous inward-biased stencils at edges and corners, again with infinitesimal weights for very low-degree polynomials.

The significance of this construction is that it removes the ghost-fill step without sacrificing third-order accuracy or non-oscillatory behavior. The reported tests show third-order convergence in one and two dimensions, errors comparable to or slightly smaller than those of ghosted $B$8, and robust performance when shocks interact with boundaries and corners. In this literature, then, “ghost fill” names the conventional strategy, while the main technical contribution is a reconstruction framework designed to make such fills unnecessary (Semplice et al., 2021).

5. Multimodal LLMs: inducing ghost object fills

In multimodal LLMs, “ghost fills” denotes hallucinated object presence: the model fills an image with an object that humans and detectors agree is absent. GHOST, “Generating Hallucinations via Optimizing Stealth Tokens,” formalizes this as an optimization problem in CLIP embedding space. Starting from an original image $B$9 without target object $A$0, the method learns an embedding $A$1 that remains close to the original embedding $A$2, avoids directly encoding the semantics of $A$3, and nevertheless maximizes the probability that the model answers “Yes” to a prompt such as “Do you see a $A$4 in the image?” The total objective is

$A$5

where $A$6 increases the probability of the target answer token, $A$7 penalizes alignment with the target-object text embedding, and $A$8 keeps $A$9 near $A\to 1$0. The optimized embedding is then used to guide Stable Diffusion unCLIP from a partially noised latent of the original image, and OWLv2 filters out samples that actually contain the target object (Parast et al., 29 Sep 2025).

The resulting images are designed to be visually natural and object-free while inducing object hallucination. The reported hallucination success rates are 29.9% for Qwen2.5-VL, 28.1% for LLaVA-v1.6, and 32.4% for GLM-4.1V-Thinking, compared with about 0.1% for the prior data-driven DASH baseline on COCO. Transferability is strong: images optimized for Qwen2.5-VL induce hallucinations in GPT-4o at 66.5%. Human evaluation also separates these images from genuine insertions: control images that do contain the object receive 91.2% “Yes,” while GHOST-LLaVA and GHOST-Qwen images receive only 11.0% and 13.7% “Yes,” respectively. The same framework is then used for mitigation: LoRA fine-tuning of Qwen2.5-VL on GHOST-generated negatives and synthetic positives reduces transferred hallucination success from 52.6% to 7.0% on LLaVA-generated samples and from 63.1% to 7.3% on GLM-generated samples, while POPE F1 improves from 88.5 to 90.7 and VQAv2 accuracy and COCO-caption BERTScore remain essentially unchanged. In this setting, a ghost fill is neither a mask nor an auxiliary boundary value; it is a model-internal completion of absent visual content (Parast et al., 29 Sep 2025).

6. Instrumental sensing: optical survey ghosts and LiDAR ghost points

In observational astronomy, ghost fills are closely related to masking rather than inpainting. Wide-field optical surveys such as DES are affected by reflections and scattered-light artifacts arising from bright sources in the telescope and camera optics. The cited work distinguishes three classes derived from the DECam optical model: Rays, Bright ghosts, and Faint ghosts. Rays are long radial scattered-light streaks that can span up to $A\to 1$1 CCDs; Bright ghosts are relatively compact circular or elliptical patches of order 1–3 CCDs; Faint ghosts are much larger diffuse structures, often 10–30 CCDs in area. DeepGhostBusters uses a Mask R-CNN with ResNet-101 and FPN to detect and localize these artifacts on downsampled $A\to 1$2 grayscale focal-plane images, producing instance masks, bounding boxes, and three-way labels. The method is explicitly framed as a precursor to masking: it does not fill or inpaint pixels. At a 0% CCD area threshold, Mask R-CNN achieves 84.3% precision, 63.6% recall, and 72.5% F1 for Rays+Bright, compared with 64.7%, 48.4%, and 55.4% for the DES Ray-Tracing baseline; for Rays+Bright+Faint, the corresponding values are 68.7%, 82.5%, and 75.0%, versus 89.9%, 23.5%, and 37.3% for Ray-Tracing. The combined CNN+Mask R-CNN image-level pipeline yields 83.1% accuracy, 87.3% precision, and 75.6% recall, with inference time of about 0.34 s per focal-plane image (Tanoglidis et al., 2021).

In mobile LiDAR, practitioners may colloquially describe ghost points as structures that “fill” free space with false geometry. These points arise from multi-path returns on glass and reflective surfaces and are particularly difficult to remove from sparse, dynamic mobile scans. Ghost-FWL addresses this at the waveform level rather than the point-cloud level. The dataset comprises 24,412 annotated frames across 10 scenes with 7.5 billion peak-level annotations, which the paper states is 100× larger than existing annotated FWL datasets. Peaks are labeled as Object, Glass, Ghost, or Noise. The baseline task is volumetric four-class classification on preprocessed $A\to 1$3 full-waveform volumes using focal loss, and the paper introduces FWL-MAE, a masked autoencoder that masks 70% of spatial patches and jointly reconstructs masked waveforms and peak statistics. The best reported model reaches ghost recall 0.751 and ghost removal rate 0.918. Downstream improvements are substantial: in SLAM, absolute trajectory error drops from $A\to 1$4 m for Dual-Peak and $A\to 1$5 m for Multi-Peak to $A\to 1$6 m after ghost removal; in 3D pedestrian detection, the ghost false-positive rate falls from 75.8% and 67.9% to 1.34%, a reduction the paper summarizes as about $A\to 1$7. Here the relevant operation is removal, not filling in a missing quantity: the system suppresses ghost structure that would otherwise populate free space with nonphysical points (Ikeda et al., 30 Mar 2026).

These sensing examples sharpen the contextual nature of the term. In astronomy, the practical task is to localize ghost-contaminated pixels for exclusion from analysis. In LiDAR, the task is to classify and remove multi-path peaks before they become spurious map geometry. This suggests that, across instrumentation literatures, “ghost fills” often functions as shorthand for how false structure occupies measurement space, even when the corrective action is masking or removal rather than literal filling.