Non-Local Texture Analysis

• Non-local texture is defined by global patterns and long-range spatial dependencies, distinguishing it from locally repetitive textures.
• It is applied in diverse fields such as text-guided image editing, exemplar synthesis, CT interpolation, and adaptive denoising.
• Recent research addresses challenges like prompt entanglement, background preservation, and balancing macro-structure with fine local details.

Searching arXiv for recent and foundational papers on non-local texture. Non-local texture denotes texture whose appearance is governed by dependencies that span long spatial ranges or, in volumetric settings, long-range cross-view correspondences rather than only short-range repetition. In the literature, this term is used for large-scale motifs, spatially varying statistics, inhomogeneous patterns, globally coordinated material effects such as clouds, fire, smoke, and water, and high-frequency anatomical structures that recur across distant slices of a 3D scan. By contrast, local repetitive textures such as wood or gold are comparatively well described by stationary statistics, short correlation lengths, and local feature aggregation (Zhou et al., 2018, Su et al., 2024, Uhm et al., 24 Sep 2025).

1. Conceptual foundations and taxonomy

A central distinction is between local texture and non-local texture. Local texture is dominated by short-range neighborhoods, so its correlations decay quickly with distance and are often captured by small patches, local Markov assumptions, or standard convolutional operators. Non-local texture exhibits long-range dependencies, global motifs, or spatial organization; examples given in the literature include co-centric wood rings, leaf veins aligned at global orientations, cloud fields, flames, smoke plumes, water surfaces, edges, ridges, trabecular structures, vessel boundaries, and organ interfaces (Zhou et al., 2018, Uhm et al., 24 Sep 2025).

This distinction intersects with stationarity. For strict-sense stationarity, the joint distribution of a random field is invariant under translation, while second-order stationarity requires constant mean and translation-invariant autocovariance:

$$\mu = E[X(x)], \qquad C(r) = E[(X(x)-\mu)(X(x+r)-\mu)].$$

Non-stationary textures violate translation invariance because statistics such as mean, variance, orientation, or scale vary over space. In non-local, non-stationary textures, long correlation lengths coexist with position-dependent statistics, which is precisely why local stationary models are inadequate (Zhou et al., 2018).

In image editing, the taxonomy appears as a contrast between “simple, local, repetitive textures” such as wood and gold, and “complex, non-local textures” such as cloud, fire, smoke, and water. In medical imaging, non-local texture refers to high-frequency anatomical patterns that recur across spatially distant locations and, crucially, across orthogonal views within the same anisotropic CT volume. In denoising, the relevant non-local unit is often the repeated “texel,” or texture element, and the core problem is to group patches that share the same kinds of texels so that filtering does not average away genuine variation (Su et al., 2024, Uhm et al., 24 Sep 2025, Zhao et al., 2018).

Setting	Non-local mechanism	Representative work
Text-guided image editing	Texture-only prompting with self-attention and residual feature injection	"TextureDiffusion: Target Prompt Disentangled Editing for Various Texture Transfer" (Su et al., 2024)
Exemplar-based synthesis	Global patch matching, near permutations, or non-local patch flow	(Webster, 2018, Chatillon et al., 26 Sep 2025)
Learned texture synthesis	Adversarial expansion or self-similarity-driven transposed convolution	(Zhou et al., 2018, Liu et al., 2020)
CT interpolation	Cross-plane, multi-reference non-local attention	(Uhm et al., 24 Sep 2025)
Denoising	Non-local texel clustering with PCA-domain variation-adaptive filtering	(Zhao et al., 2018)

A common misconception is that non-local texture is merely “global style.” The cited works instead describe explicit long-range structure, explicit non-local matching, or explicit cross-view correspondence. This suggests that non-locality is not a vague aesthetic property but a modeling requirement: the best source of information for a target region may lie far away in the same image, in a different slice, or in an orthogonal view.

2. Diffusion-based editing of non-local material appearance

In text-guided editing, non-local texture becomes difficult when the target prompt must include both content tokens and a texture token. TextureDiffusion identifies this as “prompt entanglement”: the texture token competes with object and scene tokens in cross-attention, weakening material representation and often failing to replace the object’s material without distorting shape or layout. The problem is especially acute for non-local textures because adjectives analogous to “wooden” or “golden” do not exist for many targets such as “cloud” or “fire”; adding such nouns into a sentence tends to change semantics or scene composition rather than purely material (Su et al., 2024).

TextureDiffusion addresses this by setting the target prompt directly to "<texture>" and using a texture-only embedding

$u_{\textrm{tex}} = E(\texttt{"<texture>"}),$

rather than a mixed embedding

$$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$

Structure is then recovered not from content words but from source-image feature reuse inside the UNet of Stable Diffusion v1.4. The method injects source query features into self-attention and source residual-block features into designated layers. At attention layer $l$, it forms

$$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$

with the standard self-attention operator

$$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$

The edited branch therefore retains $Q_s^l$ from the source to preserve layout, while $K_t^l,V_t^l$ are driven by the texture-only prompt, so material appearance is governed by the target texture rather than by mixed scene semantics (Su et al., 2024).

Background preservation is handled through edit localization. A mask $M$ is derived automatically from 16×16 cross-attention maps aggregated across all heads and layers, then used to blend both attention outputs and intermediate latents:

$\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$

$u_{\textrm{tex}} = E(\texttt{"<texture>"}),$0

The end-to-end pipeline uses VAE encoding and DDIM inversion to obtain an initial latent $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$1, followed by DDIM sampling for $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$2 steps, conditioned on $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$3, with classifier-free guidance scale $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$4. Query feature insertion is applied during the first 40 steps at UNet layers 12–15, while residual block features are inserted at layer 7 for all steps. The method is tuning-free: it does not fine-tune the base UNet or VAE (Su et al., 2024).

Qualitative results report that baselines struggle on clouds and fire for distinct reasons: SDEdit distorts structure; P2P alters shape via cross-attention leakage; MasaCtrl over-preserves original content; and PnP, FPE, and InfEdit still entangle texture with content. On PIE-Bench material change, TextureDiffusion reports Structure Distance↓ 10.39, Background preservation PSNR↑ 31.22, LPIPS↓ $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$5, MSE↓ $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$6, SSIM↑ $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$7, and CLIP Similarity (Edited)↑ 16.88. The stated limitations are slight background alteration due to the reconstruction upper bound of the VAE, imperfect masks when the source prompt does not isolate the target object cleanly, and a trade-off between rigid structure preservation and allowing highly dynamic textures to flow naturally over the object (Su et al., 2024).

3. Non-parametric exemplar synthesis through global patch correspondence

A major line of work models non-local texture by letting any synthesized patch draw support from any location in the exemplar. "Innovative Non-parametric Texture Synthesis via Patch Permutations" formalizes this through global patch matching with either Bidirectional Similarity (BS) or entropy-regularized optimal transport (OT). The synthesis image $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$8 and exemplar $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$9 are patchified as

$$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$0

typically with stride 1 and, in practice, 35% patch subsampling for both match and update. Small patch size is central: innovation is obtained from recombining tiny pieces, while plausibility relies on global match quality rather than copying large tiles (Webster, 2018).

BS combines coherence and completeness through nearest-neighbor search in both directions, with Euclidean RGB patch distances. OT instead solves an entropy-regularized transport problem over the Birkhoff polytope

$$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$1

with cost matrix

$$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$2

and objective

$$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$3

As $$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$4, $$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$5 concentrates toward permutation matrices, so the method approaches hard near-permutation assignments. Soft transports are rounded to a high-cardinality assignment $$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$6 to avoid blur. The paper’s Innovation Capacity analysis reports that OT with $$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$7 and $$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$8 yields average IC around 0.79, compared with approximately 0.75 for BS and approximately 0.83 for the random convolutional baseline; in the “oil” exemplar, BS is reported at approximately 0.67, OT at approximately 0.79, and the statistical baseline at approximately 0.83 (Webster, 2018).

NIFTY recasts non-local patch matching as an explicit probability flow on the exemplar’s empirical patch distribution. For a synthesized patch $$u_{\textrm{mix}} = E(\textrm{content} + \texttt{"<texture>"}).$$9 and exemplar patches $l$0, it uses the affine conditional path

$l$1

with $l$2, and derives the patch velocity

$l$3

where

$l$4

Early in time, the weights are broad and average many plausible matches; as $l$5, the weight concentrates on the nearest neighbor, recovering the sharpness of hard assignment. Patch velocities are overlap-averaged back to the image and integrated with Euler updates. To reduce complexity, NIFTY restricts evaluation to top-$l$6 neighbors and searches only a random subset of exemplar patches augmented with a memory of previous matches (Chatillon et al., 26 Sep 2025).

The experimental comparison in NIFTY uses 12 reference images at 256 px and 10 syntheses at 512 px for each image. Reported metrics are Gram loss, SIFID, autocorrelation discrepancy, and time. NIFTY with $l$7 reports Gram 3,601; SIFID 0.28; Autocorr 85.9; Time approximately 0.70 s. Texture Optimization reports Gram 12,676; SIFID 0.76; Autocorr 431.8; Time approximately 1.92 s. The exemplar-trained U-Net flow-matching baseline reports Gram 17,034; SIFID 0.54; Autocorr 133.1; Training approximately 600 s; Eval approximately 0.13 s. The reported qualitative behavior is fewer seams and better global coherence than Texture Optimization, while still stitching together exemplar microstructures (Chatillon et al., 26 Sep 2025).

Taken together, these methods define non-local texture synthesis as explicit global correspondence rather than purely local filtering. A plausible implication is that patch-based non-locality remains competitive because it preserves the exemplar’s empirical microstructure instead of replacing it with a learned parametric prior.

4. Learned synthesis of non-stationary and long-range structure

"Non-Stationary Texture Synthesis by Adversarial Expansion" addresses exemplars with large-scale motifs, spatially varying statistics, and inhomogeneities. The generator $l$8 is trained per exemplar to map a $l$9 source block $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$0 to a $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$1 output consistent with an enclosing target block $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$2. The paper sets $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$3 and samples nested 128×128 and 256×256 blocks on the fly from an exemplar typically around 600×400 pixels. The generator is a fully convolutional Johnson-style residual encoder–decoder with three convolution layers, six residual blocks, and three strided deconvolution layers; the receptive field at the end of the residual chain is 109×109, close to the 128×128 source block size. The discriminator is a fully convolutional PatchGAN that judges overlapping patches of size 142×142. The total loss combines adversarial loss, $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$4, and Gram-based style loss with weights $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$5 and $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$6 (Zhou et al., 2018).

The method is explicitly designed for non-local, non-stationary textures rather than stationary ones. The residual block chain is reported as the stage where new large-scale structures are “invented,” for instance doubling the count of veins, bricks, or rings while preserving exemplar-specific geometry such as radial or directional organization. Training is self-supervised per exemplar for up to 100,000 iterations with Adam, learning rate 0.0002 for the first 50,000 iterations and linearly decayed to 0 over the next 50,000, on an NVIDIA Titan Xp GPU (12GB). Training takes approximately 5 hours; inference takes 4–5 ms to double a 600×400 exemplar. Quantitative metrics are not reported; the evaluation is qualitative and comparative, and limitations include border and corner artifacts, failure on scarce or singular macrostructures, and the requirement for per-exemplar training (Zhou et al., 2018).

Transposer attacks the same long-range dependency problem from a different direction. Instead of local convolutional filters, it treats the whole encoded feature map of the input texture as a bank of transposed-convolution filters and uses the features’ self-similarity map as the transposed-convolution input. At scales $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$7, the encoder produces

$$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$8

For a feature map $$R_s^l = \mathrm{Attention}(Q_s^l, K_s^l, V_s^l), \qquad R_t^l = \mathrm{Attention}(Q_s^l, K_t^l, V_t^l),$$9, self-similarity over shifts $$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$0 is computed by a normalized negative $$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$1 difference over the overlap region:

$$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$2

After a light learned transformation, the resulting map $$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$3 serves as the input to a transposed convolution whose filters are the channels of $$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$4, producing expanded feature maps that are decoded into a 2× larger texture (Liu et al., 2020).

The key technical claim is that assembling or stitching shifted copies of a source patch is algebraically equivalent to a transposed convolution. This compresses non-locality into a displacement-indexed auto-correlation map rather than a full pairwise attention matrix. Transposer is trained once on a dataset of 55,583 images and is therefore universal rather than per-exemplar. Its generator loss uses perceptual, Gram-style, and GAN terms with weights $$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$5, $$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$6, and $$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$7. On 5,000 test images for 128→256 synthesis, the reported performance is SSIM 0.386, FID 21.615, c-FID 0.4763, LPIPS 0.2709, and c-LPIPS 0.2653, outperforming Self-tuning, pix2pixHD, and WCT in all metrics. Runtime on one V100 is 43 ms for 256×256 and 260 ms for 512×512. The paper also reports that random maps can replace self-similarity maps for irregular textures to increase diversity and enable direct 2048×2048 synthesis from 128×128 inputs in one pass (Liu et al., 2020).

These two learned approaches differ sharply. Adversarial Expansion is exemplar-specific and explicitly targets non-stationary structure; Transposer is universal and uses displacement-indexed self-similarity to preserve regularity. This suggests that “non-local texture” can be modeled either by learning exemplar-specific macro-structure transformations or by learning a reusable mechanism that scatters globally correlated feature copies.

5. Cross-view non-local texture in anisotropic CT interpolation

In anisotropic CT volumes, non-local texture refers to high-frequency anatomical patterns that recur across distant locations and across orthogonal views of the same 3D scan. Clinical thick scans have high in-plane axial resolution, typically approximately 0.6–1.0 mm, but much larger inter-slice spacing, for example 5 mm, so coronal and sagittal views lose high-frequency detail. ACVTT exploits the anisotropic structure directly by treating high-resolution axial slices as intra-volume references for low-resolution through-plane reconstruction (Uhm et al., 24 Sep 2025).

The pipeline starts from a sparsely sampled CT volume

$$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$8

and reconstructs

$$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\!\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$9

where $Q_s^l$0. Coronal and sagittal slices are bilinearly upsampled along depth, and $Q_s^l$1 axial slices are selected as references. A shared encoder extracts through-plane features $Q_s^l$2, $Q_s^l$3 and axial reference features $Q_s^l$4. Multi-reference non-local attention (MRNLA) then performs cross-view transfer:

$Q_s^l$5

The coronal and sagittal volumes are stacked and fused as

$Q_s^l$6

with $Q_s^l$7 a slice-wise convolutional residual module (Uhm et al., 24 Sep 2025).

MRNLA is a cross-plane extension of the non-local operation. For through-plane feature $Q_s^l$8 and axial reference features $Q_s^l$9, the method computes

$K_t^l,V_t^l$0

then

$K_t^l,V_t^l$1

A per-query relevance estimate

$K_t^l,V_t^l$2

is normalized across references to produce the relevance map $K_t^l,V_t^l$3, and the final fused feature is

$K_t^l,V_t^l$4

The paper emphasizes that this is not spatial overlap matching: axial and through-plane slices are not co-registered, so semantic and textural consistency must replace spatial correspondence (Uhm et al., 24 Sep 2025).

Training uses only slice-wise $K_t^l,V_t^l$5 losses,

$K_t^l,V_t^l$6

with no perceptual, adversarial, or TV terms. The implementation uses PyTorch, a single RTX 3090 (24 GB), Adam with learning rate $K_t^l,V_t^l$7, 20,000 training epochs, and default $K_t^l,V_t^l$8 references. The reported computational cost is 1.70 days for training and approximately 31 s per volume for inference at $K_t^l,V_t^l$9, with GPU memory approximately 2.8 GB and batch size 1 (Uhm et al., 24 Sep 2025).

Reported results are strong on multiple datasets. On RPLHR-CT, ACVTT reports 39.07 dB PSNR and SSIM 0.9401 in the axial view, with 0.9276 and 0.9272 in coronal and sagittal views. On MSD, the reported values are 42.26 dB, 0.9700, 0.9576, and 0.9574; on KiTS23, 41.84 dB, 0.9688, 0.9563, and 0.9562. The method remains robust across anisotropy factors on KiTS23, with 50.23 dB and 0.9922 at ×2, 47.35 dB and 0.9825 at ×3, and 44.69 dB and 0.9742 at ×4. Downstream segmentation on KiTS23 using nnUNet/3D-UNet reports Kidney Dice/NSD 0.9438/0.8763 and Tumor Dice/NSD 0.6584/0.4559. Ablation indicates that $M$0 provides the best balance, while gains saturate beyond $M$1 and inference time increases linearly, from 11.19 s at $M$2 to 31.00 s at $M$3 and 42.67 s at $M$4 (Uhm et al., 24 Sep 2025).

6. Non-local texture preservation in denoising

In denoising, non-local texture is not only a matter of long-range redundancy but of preserving genuine variation after grouping repeated texture elements. ACVA models both additive white Gaussian noise and signal-dependent Poisson–Gaussian noise. For AWGN, the observation model is

$M$5

For raw data, Poisson–Gaussian noise is stabilized using the generalized Anscombe transform before denoising and inverted with an exact unbiased inverse afterward (Zhao et al., 2018).

The first stage is adaptive clustering of non-local patches. Patches of size $M$6 are vectorized, with full overlap, so for an image $M$7 the patch count is

$M$8

The method over-clusters with K-means and then iteratively merges clusters. For two clusters $M$9 and $\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$0 with centers $\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$1 and $\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$2, the between-cluster distance is

$\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$3

With $\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$4 and merging probability $\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$5, the resulting threshold is

$\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$6

Clusters are merged if $\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$7. When the minimum cluster size exceeds $\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$8, the distance is amplified as

$\bar R^l = R_s^l \odot M + R_t^l \odot (1-M),$9

to avoid under-segmentation of large clusters. The rationale is that texel-consistent grouping concentrates signal energy into a few PCA dimensions; if dissimilar patches are mixed, texture variation cannot be preserved (Zhao et al., 2018).

The second stage is nonlocal PCA with variation-adaptive filtering. For centralized noisy cluster $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$00, the SVD is

$u_{\textrm{tex}} = E(\texttt{"<texture>"}),$01

The retained rank is determined by a spiked-model boundary

$u_{\textrm{tex}} = E(\texttt{"<texture>"}),$02

and

$u_{\textrm{tex}} = E(\texttt{"<texture>"}),$03

Within the selected dimensions, coefficient sequences are processed by LPA–ICI adaptive parameter estimation and a suboptimal Wiener filter. The local estimate at position $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$04 and window width $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$05 is

$u_{\textrm{tex}} = E(\texttt{"<texture>"}),$06

and the suboptimal Wiener filter is

$u_{\textrm{tex}} = E(\texttt{"<texture>"}),$07

with $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$08 selected to balance noise reduction and signal distortion. This is explicitly contrasted with hard and soft thresholding, which depend only on coefficient magnitudes (Zhao et al., 2018).

The full algorithm is applied in 128×128 sliding windows and aggregates denoised patches by averaging overlaps. The reported runtime in MATLAB on a Core i5-4460 CPU is about 4.0 s to 16.0 s per window, depending on noise level. On 16 USC-SIPI textured images at $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$09, ACVA reports 23.87 dB PSNR, SSIM 0.6848, and FSIM 0.9103, compared with BM3D at 23.59, 0.6469, and 0.8925, and DnCNN-S at 23.73, 0.6659, and 0.8903. On six standard images at $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$10, ACVA reports 27.12 dB, SSIM 0.7227, and FSIM 0.8990. In camera raw simulation with $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$11, the reported average is 36.15 dB, 0.9508, and 0.9788; with $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$12, 31.61 dB, 0.8893, and 0.9492. The paper attributes its advantage especially to stochastic and high-frequency textures, where over-smoothing is a common failure mode of competing methods (Zhao et al., 2018).

7. Limitations, misconceptions, and open directions

Across the cited literature, non-local texture is repeatedly shown to be constrained by a trade-off between preserving global structure and allowing flexible local realization. In TextureDiffusion, aggressive structure injection can over-constrain highly dynamic textures; imperfect masks and VAE reconstruction limits can still slightly alter the background; and fine-grained local materials may require later-stage injections at the cost of texture richness (Su et al., 2024). In ACVTT, compute and memory grow with the number of references, performance saturates beyond $u_{\textrm{tex}} = E(\texttt{"<texture>"}),$13, and separate models are trained per upsampling factor; the method also uses no explicit positional encoding, relying instead on global correlations and plane-specific design (Uhm et al., 24 Sep 2025).

In exemplar synthesis, the limitations differ but are structurally similar. Adversarial Expansion can fail on exemplars with scarce or singular macrostructures and suffers border artifacts because borders receive fewer training samples (Zhou et al., 2018). Transposer can blur sparse thin structures or highly non-stationary directional textures, and self-similarity-based enlargement is constrained to approximately 3×3 expansion unless random maps are introduced, which then weakens structural preservation (Liu et al., 2020). Patch-permutation methods remain sensitive to the choice of patch size and entropy: low entropy favors near permutations and plausibility, whereas high entropy yields blur (Webster, 2018). NIFTY reduces seam artifacts but still inherits ambiguity when many patches are equally plausible matches, and highly non-stationary or semantic scenes remain difficult because the exemplar itself may not contain enough unambiguous non-local correspondences (Chatillon et al., 26 Sep 2025).

These limitations help dispel a second misconception: non-locality does not eliminate the need for locality. All successful methods in the cited corpus preserve some local mechanism—residual feature injection, overlap averaging, residual addition, decoder-level refinement, or coefficient-wise filtering—while adding a non-local mechanism that coordinates texture over larger extents. A plausible implication is that non-local texture should be understood as a hierarchical property: local detail remains essential, but it must be organized by global correspondence, global self-similarity, or cross-view relevance.

The open directions named in the literature are correspondingly pragmatic. TextureDiffusion identifies improving mask accuracy, controlling the balance between strict structure preservation and expressive texture dynamics, and simultaneous multi-texture transfer as open problems (Su et al., 2024). ACVTT points to unified models for variable slice thickness and factors, content-aware or anatomy-guided reference selection, sparse attention or patchwise matching for efficiency, and possible integration with diffusion priors while preserving intra-volume consistency (Uhm et al., 24 Sep 2025). Adversarial Expansion suggests attention or non-local blocks, multi-scale discriminators, global structural constraints, and volumetric or video extensions (Zhou et al., 2018). Transposer suggests mixing self-similarity and random maps to trade structure for diversity, as well as directional emphasis for anisotropic textures (Liu et al., 2020). NIFTY already proposes latent variants and remains compatible with approximate nearest-neighbor backends and patchwise accelerations (Chatillon et al., 26 Sep 2025).

Taken together, these works define non-local texture not as a narrow subtopic of texture synthesis but as a broader modeling principle. Whether the task is material editing, exemplar synthesis, CT interpolation, or denoising, the recurring requirement is to represent and transfer dependencies that cannot be reduced to local repetition alone.