Multi-View Frequency Consistency

• Multi-view frequency consistency is a concept that enforces alignment of spatial-frequency representations across views using Fourier-based attention and correlated noise initialization.
• It enhances scene coherence by integrating low-frequency signals for global structure and high-frequency filters for local detail, even in non-overlapping regions.
• Spatial-domain methods such as feature and normal consistency serve as complementary analogues, achieving stable cross-view reconstruction without explicit Fourier modeling.

Searching arXiv for papers on multi-view consistency, frequency-aware methods, and related reconstruction/generation work. arxiv_search query: "multi-view frequency consistency Fourier attention multi-view diffusion reconstruction feature consistency arXiv" Multi-view frequency consistency denotes a family of mechanisms that seek to make multiple views of the same scene agree through frequency-structured representations rather than through pixel correspondence alone. In the most explicit current formulation, it means making generated views share coherent scene-level structure and appearance by coordinating them through frequency-aware latent initialization and Fourier-based cross-view attention, especially in non-overlapping regions (Theiss et al., 2024). In adjacent reconstruction literature, the same objective is often pursued without an explicit Fourier or wavelet term, through multi-view feature consistency, multi-view normal consistency, patch-level cross-view agreement, and suppression of view-inconsistent distractors (Li et al., 2024, Hou et al., 11 Mar 2025). The term therefore spans a narrow sense—explicit frequency-domain modeling across views—and a broader sense in which cross-view stable fine structure is preserved by frequency-analogous spatial-domain constraints.

1. Scope and conceptual definition

The literature does not present a single universal definition of multi-view frequency consistency. Instead, several lines of work instantiate closely related ideas. The most direct instance is a multi-view diffusion model in which low spatial frequency information is correlated across views at initialization and frequency-filtered features are used during denoising to align non-overlapping regions (Theiss et al., 2024). Reconstruction methods such as FD-NeuS and MVGSR use explicit multi-view consistency, but the cited descriptions state that they do not introduce an explicit frequency-domain, Fourier, spectral, wavelet, or band-limited consistency term (Li et al., 2024, Hou et al., 11 Mar 2025). A plausible implication is that the topic is best understood as a spectrum ranging from explicit spectral coordination to spatial-domain surrogates that target the same failure mode: loss of cross-view stable detail.

Work	Domain	Relation to multi-view frequency consistency
"Multi-view Image Diffusion via Coordinate Noise and Fourier Attention" (Theiss et al., 2024)	Multi-view image generation	Explicit frequency-aware multi-view consistency
"Fine-detailed Neural Indoor Scene Reconstruction using multi-level importance sampling and multi-view consistency" (Li et al., 2024)	Neural indoor reconstruction	Spatial-domain precursor; no explicit frequency-domain term
"MVGSR: Multi-View Consistency Gaussian Splatting for Robust Surface Reconstruction" (Hou et al., 11 Mar 2025)	Gaussian-splat reconstruction	Spatial-domain analogue; no Fourier formulation
"Exploring Spatial-Temporal Multi-Frequency Analysis for High-Fidelity and Temporal-Consistency Video Prediction" (Jin et al., 2020)	Video prediction	Multi-frequency decomposition relevant by analogy
"Multi-Frequency Phase Synchronization" (Gao et al., 2019)	Synchronization theory	Formal consistency across harmonic frequency channels

A recurrent motivation across these works is that different frequency bands play different semantic roles. The multi-view diffusion paper explicitly associates low spatial frequencies with global structure and coarse appearance, and high spatial frequencies with local detail and texture (Theiss et al., 2024). The reconstruction papers make an analogous claim indirectly: detail-rich small regions, thin structures, and local surface evidence are precisely the parts most vulnerable to cross-view inconsistency or oversmoothing (Li et al., 2024, Hou et al., 11 Mar 2025).

2. Explicit frequency-domain formulation in multi-view diffusion

The clearest operational definition appears in "Multi-view Image Diffusion via Coordinate Noise and Fourier Attention" (Theiss et al., 2024). The method addresses the case in which multiple generated images should depict the same underlying scene from different viewpoints without contradictions in appearance, geometry, semantics, or global scene structure. Its central claim is that consistency should not be enforced only at explicitly corresponding pixels in overlapping regions, but also at the level of shared spatial-frequency structure across views, especially in non-overlapping regions.

The method is built on a latent diffusion model with a U-Net denoiser. It adds three components: coordinate-based noise initialization, Fourier-based attention, and a prompt cross-attention loss. During inference, it generates 8 views jointly. For each view $i$, the initial latent is not independent Gaussian noise alone; it is constructed from shared noise, a coordinate- or depth-derived low-frequency signal $\mathbf{c}^i$, and an independent view-specific noise term. The paper defines

$\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$

and then

$\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$

Here $\mathbf{c}^i$ is the normalized depth map in the depth-conditioned setting, or normalized pixel coordinates transformed into the coordinate space of the center view in the panoramic setting. The stated purpose is to inject low spatial frequency information that is correlated across views (Theiss et al., 2024).

The Fourier-based attention block is the core frequency-domain module. Let $\mathbf{G}^i_t$ denote feature maps obtained from coordinate-noise-driven latents at diffusion timestep $t$. The Fast Fourier Transform is applied over height and width: $$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$ A timestep-dependent radius

$r_t = 1 - \frac{t}{T}$

controls a high-pass mask

$\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$

and the filtered feature is

$\mathbf{c}^i$0

The paper’s preferred schedule is the time-dependent high-pass variant denoted HPF-$\mathbf{c}^i$1, which progressively shifts attention toward higher frequencies as denoising proceeds (Theiss et al., 2024).

The attention mechanism distinguishes overlapping and non-overlapping regions. Overlap masks $\mathbf{c}^i$2 are computed using homographies. For overlapping regions, the method uses correspondence-aware attention as in MVDiffusion. For non-overlapping regions, it replaces geometrically corresponded target features with the filtered Fourier features $\mathbf{c}^i$3. The fused target features are

$\mathbf{c}^i$4

followed by standard query-key-value attention

$\mathbf{c}^i$5

The paper is explicit that this is not a direct loss matching Fourier coefficients across views. Rather, consistency is enforced indirectly through attention design and correlated initialization (Theiss et al., 2024).

The third component is a prompt cross-attention loss computed on the $\mathbf{c}^i$6 resolution cross-attention modules. Clean latent views $\mathbf{c}^i$7 are passed through the U-Net to obtain noise-free attention maps $\mathbf{c}^i$8, which are then matched to noisy-time attention maps $\mathbf{c}^i$9: $\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$0 with total objective

$\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$1

where $\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$2. This term is not frequency-domain, but it regularizes prompt-to-scene alignment across views and timesteps (Theiss et al., 2024).

3. Spatial-domain reconstruction analogues

Two reconstruction methods are directly relevant because they pursue cross-view stability of fine detail, while explicitly not adopting a frequency-domain consistency loss. In FD-NeuS, the scene is represented by a geometry network $\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$3 and a color network $\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$4, with surface

$\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$5

The paper states that multi-view consistency is not the sole reconstruction signal: core geometry remains an SDF optimized through volume rendering with RGB and normal priors. Multi-view consistency enters after approximate surface localization through an interpolated ray-surface intersection $\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$6, and is used in two distinct ways: as direct supervision via multi-view feature consistency and as a confidence estimator via multi-view normal consistency or uncertainty (Li et al., 2024).

The feature-consistency term in FD-NeuS compares deep image features extracted by a pre-trained convolutional neural network for supervised MVS at corresponding projections of the same reconstructed surface point across views. Correspondence is established geometrically by projecting $\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$7 into neighboring views using

$\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$8

The normal-consistency component compares monocular normal priors across views and converts their average angular disagreement into an uncertainty

$\mathbf{\hat{\epsilon}^{i} = w * \mathbf{c}^{i} + (1 - w) * \mathbf{\epsilon}_{\text{shared},$9

which is thresholded by $\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$0 into a binary reliability mask. The uncertainty is then used both to filter unreliable normal priors in the normal loss and to guide ray importance sampling toward unreliable areas (Li et al., 2024). The paper explicitly states that it does not use any frequency-domain, Fourier, spectral, wavelet, or band-limited consistency term. It identifies its own multi-view feature consistency, small-region ray sampling, and near-surface point sampling as the closest analogues.

MVGSR provides a second reconstruction analogue. It uses multi-view feature consistency to detect distractors, multi-view contribution pruning to reset transmittance, and a multi-view consistency loss based on patch-wise normalized cross-correlation. Correspondence is established through plane-induced homographies

$\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$1

DINOv2 features from a reference image $\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$2 and an initially rendered neighboring view $\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$3 are compared through

$\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$4

with $\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$5 used in the reported implementation. Pixels identified as clutter by at least two visible adjacent views are retained in the multi-view mask, which is then refined with SAM (Hou et al., 11 Mar 2025).

MVGSR’s cross-view loss is an $\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$6 patch-based NCC term,

$\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$7

weighted by

$\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$8

and combined as

$\mathbf{\hat{z}^{i}_T = \sqrt{\bar{\alpha}_T} \mathbf{\hat{\epsilon}^{i} + \sqrt{1 - \bar{\alpha}_T} \mathbf{\epsilon}^{i}.$9

with $\mathbf{c}^i$0 and $\mathbf{c}^i$1 (Hou et al., 11 Mar 2025). The paper states that it does not define or optimize frequency consistency in the Fourier sense, but that its feature consistency, NCC term, and pruning behavior are relevant to preserving cross-view stable structural detail while suppressing view-specific artifacts.

4. Frequency consistency as a broader analytical principle

Outside strictly multi-view generation and reconstruction, two additional works clarify the broader structure of the concept. "Exploring Spatial-Temporal Multi-Frequency Analysis for High-Fidelity and Temporal-Consistency Video Prediction" introduces STMFANet, which is not a multi-view system, but explicitly models multiple spatial and temporal frequency bands through wavelet decomposition (Jin et al., 2020). Spatially, S-WAM decomposes each frame into $\mathbf{c}^i$2, $\mathbf{c}^i$3, $\mathbf{c}^i$4, and $\mathbf{c}^i$5 bands, which the paper describes as one low-frequency sub-band and three high-frequency directional sub-bands. Temporally, T-WAM applies multi-level DWT on the time axis to separate motions at different temporal frequencies. The method does not use a dedicated wavelet-domain loss; the frequency structure is architectural rather than an explicit consistency penalty. A plausible implication is that multi-view frequency consistency could likewise benefit from separating coarse structure, directional detail, and motion frequencies before enforcing agreement across views.

"Multi-Frequency Phase Synchronization" provides a mathematically sharper but domain-different notion of consistency across frequency channels (Gao et al., 2019). There, a frequency $\mathbf{c}^i$6 corresponds to the $\mathbf{c}^i$7-th harmonic of a latent phase variable,

$\mathbf{c}^i$8

and multi-frequency consistency means that all channels must arise from one common latent vector $\mathbf{c}^i$9. The paper formalizes this through

$\mathbf{G}^i_t$0

Its key principle is that each channel is a different harmonic view of the same underlying quantity, and the channels are coupled algebraically through the shared latent variable. The work is not about camera viewpoints, but it supplies a rigorous template for what “consistency across frequency views” can mean: the different channels are not independent signals, but structured transforms of one scene variable (Gao et al., 2019).

These two works frame multi-view frequency consistency as part of a more general design pattern. One strand decomposes signals into multiple spatial or temporal bands and lets the network process them differently. The other enforces cross-channel coherence through an explicit shared latent variable. The multi-view diffusion paper sits between these extremes: it does not impose direct coefficient equality across views, but it does make all views attend to correlated, frequency-filtered features derived from a shared initialization process (Theiss et al., 2024).

5. Mechanisms, evaluation, and empirical evidence

The empirical record is strongest where the frequency-domain mechanism is explicit. In panoramic generation, the Fourier-attention method reports FID $\mathbf{G}^i_t$1 versus $\mathbf{G}^i_t$2 for MVDiffusion, CLIP $\mathbf{G}^i_t$3 versus $\mathbf{G}^i_t$4, PSNR $\mathbf{G}^i_t$5 versus $\mathbf{G}^i_t$6, Ratio $\mathbf{G}^i_t$7 versus $\mathbf{G}^i_t$8, and I-LPIPS $\mathbf{G}^i_t$9 versus $t$0. In the depth-conditioned setting, it reports PSNR $t$1 versus $t$2, Ratio $t$3 versus $t$4, and Intra-LPIPS $t$5 versus $t$6, while FID is worse than MVDiffusion at $t$7 versus $t$8. The paper therefore presents its strongest gains as gains in consistency metrics rather than universally better single-image realism (Theiss et al., 2024).

The supplementary ablations in that work tie the gains specifically to the frequency design. Shared Noise alone improves some consistency, Coordinate Noise improves further, FBA Blocks also improve consistency, and the Full Model gives the best overall multi-view performance. For panorama ablation, the reported Ratio values are $t$9 for Shared Noise, $$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$0 for Coord. Noise, $$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$1 for FBA Blocks, and $$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$2 for the Full Model. Fourier-filter ablations further report Ratio $$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$3 for HPF-$$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$4, compared to $$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$5 with no filter, $$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$6 for LPF-$$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$7, $$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$8 for LPF-$$\mathcal{F}(m, n) = \sum_{h, w}\mathbf{x}(h, w)\exp{-j 2 \pi \left(\frac{h}{H} m + \frac{w}{W} n \right)}.$$9, and $r_t = 1 - \frac{t}{T}$0 for HPF-$r_t = 1 - \frac{t}{T}$1. These numbers are presented as evidence that the timestep-dependent frequency schedule itself matters (Theiss et al., 2024).

Reconstruction papers support the same overall objective through non-spectral mechanisms. FD-NeuS reports a progression in F-score from $r_t = 1 - \frac{t}{T}$2 for the Base model to $r_t = 1 - \frac{t}{T}$3 with region-based ray importance sampling, $r_t = 1 - \frac{t}{T}$4 with additional weight-based point importance sampling, $r_t = 1 - \frac{t}{T}$5 after adding multi-view feature consistency, and $r_t = 1 - \frac{t}{T}$6 for the full model with multi-view normal uncertainty. The same ablation gives Precision/Recall/F-score $r_t = 1 - \frac{t}{T}$7 for Model-B, $r_t = 1 - \frac{t}{T}$8 for Model-C, and $r_t = 1 - \frac{t}{T}$9 for the full method. The paper states that the multi-view terms provide a measurable final boost after sampling has already improved near-surface localization (Li et al., 2024).

MVGSR reports average F1 $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$0 on TnT-Robust, compared with $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$1 for PGSR, $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$2 for SLS, and $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$3 for NeRF-on-the-Go. On DTU-Robust it reports average Chamfer Distance $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$4, compared with $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$5 for PGSR and $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$6 for 2DGS, and average PSNR $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$7, compared with $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$8 for PGSR and $\mathbf{M}^{r_t}_{\mathcal{F} = \left( 1 - \mathbbm{1}_{(h, w) \in [-r_t H: r_t H, - r_t W: r_t W]} \right),$9 for 2DGS. Its ablation on DTU-Robust scan24 shows PSNR/CD $\mathbf{c}^i$00 with masks only, $\mathbf{c}^i$01 with $\mathbf{c}^i$02 and $\mathbf{c}^i$03, $\mathbf{c}^i$04 with $\mathbf{c}^i$05, $\mathbf{c}^i$06, and $\mathbf{c}^i$07, and $\mathbf{c}^i$08 with all components including MV-Prune. The paper interprets $\mathbf{c}^i$09 as the main geometry-improving consistency term, with pruning recovering rendering quality and further improving geometry (Hou et al., 11 Mar 2025).

The evidence from STMFANet is not multi-view evidence, but it supports the broader frequency-consistency thesis. On KTH, the full model reports PSNR/SSIM $\mathbf{c}^i$10 for 10$\mathbf{c}^i$1120 prediction and $\mathbf{c}^i$12 for 10$\mathbf{c}^i$1340; removing T-WAM reduces these to $\mathbf{c}^i$14 and $\mathbf{c}^i$15, respectively, while removing both wavelet modules reduces them further to $\mathbf{c}^i$16 and $\mathbf{c}^i$17. The paper uses these results to argue that explicit frequency decomposition improves fidelity and temporal consistency (Jin et al., 2020).

6. Limitations, misconceptions, and likely directions

A common misconception is to treat all multi-view consistency as frequency consistency. The cited reconstruction works explicitly contradict this equivalence. FD-NeuS states that its method uses spatial or geometric consistency, feature consistency, and normal consistency, but not frequency-domain consistency (Li et al., 2024). MVGSR likewise states that it has no FFT, no frequency decomposition, and no spectral regularizer, even though it is relevant to preserving cross-view stable structural detail (Hou et al., 11 Mar 2025). The term should therefore be reserved, in its strict sense, for methods such as Fourier-attention diffusion that manipulate frequency-aware representations directly.

A second misconception is that the explicit frequency-domain approach already defines a direct cross-view spectral matching loss. The multi-view diffusion paper states the opposite: its method does not define an explicit loss saying that a given frequency band must match across views. Consistency is induced indirectly through shared or correlated coordinate noise, frequency-filtered target features, and attention routing in non-overlapping regions (Theiss et al., 2024). This distinction matters because indirect frequency-aware aggregation can improve scene coherence without requiring exact bandwise equality under viewpoint change.

Current limitations are also consistent across the literature. The Fourier-attention method depends on camera information and, in one setting, depth maps; it is not always best on image-quality metrics such as FID; and its quantitative evaluation still relies largely on overlap-based PSNR ratio and pairwise perceptual measures even though it targets non-overlapping regions (Theiss et al., 2024). FD-NeuS does not describe visibility-aware masking or occlusion handling for its feature consistency term, and its consistency losses depend on the accuracy of the interpolated surface point $\mathbf{c}^i$18 (Li et al., 2024). MVGSR depends on rough initial geometry after 7,000 iterations, uses SAM refinement as an external dependency, and leaves some pruning and reset mechanics under-specified in the cited description (Hou et al., 11 Mar 2025). STMFANet does not provide explicit wavelet-domain supervision, and its spatial-temporal band interactions remain implicit rather than formally coupled (Jin et al., 2020). Multi-Frequency Phase Synchronization, while mathematically clean, relies on an exact harmonic relation across channels that does not automatically transfer to camera views (Gao et al., 2019).

Several directions follow directly from the cited material. FD-NeuS explicitly identifies multi-view feature consistency as the cleanest precursor to a future multi-view frequency-consistency method and suggests replacing spatial feature agreement with spectral correspondence between local patches, wavelet features, or learned frequency-decomposed features (Li et al., 2024). The wavelet-based video-prediction literature suggests separating low-frequency structure, directional high-frequency detail, and temporal-frequency motion before applying cross-view alignment (Jin et al., 2020). The synchronization literature suggests that stronger future formulations may define a shared latent representation from which multiple frequency channels are derived, rather than treating frequency bands as independent descriptors (Gao et al., 2019). Together, these works suggest that multi-view frequency consistency is evolving from an implicit design intuition into an explicit modeling principle: low-frequency agreement can stabilize scene identity, while controlled high-frequency coordination can preserve detail without collapsing viewpoint diversity.