NITES: A Non-Parametric Interpretable Texture Synthesis Method

• Patch-based synthesis generally yields higher quality, but whole-image search is slow and stitching small patches limits diversity.Source: §1 · p. 1
• Deep-learning texture methods produce visually pleasant results but lack mathematical transparency and have higher training and inference complexity.Source: §1 · p. 1
• NITES analyzes joint spatial-spectral representations, characterizes sample distributions, and generates textures by mimicking source-image probabilities.It uses the data-driven channel-wise Saab transform, derived from successive subspace learning.Source: §1 · p. 2

• Adjacent subspaces are linked by affine combinations, linearized by appending 1 to vectors, with dimensions decreasing from D0 to Dn.Source: §2 · p. 2
• Texture patches form a high-dimensional source space, so the framework builds lower-dimensional embedded subspaces and designates the first and last as source and core.Source: §2 · p. 2
• Embedding decomposes each input space, while retaining the probabilistic relationship between its parts for reverse generation with diversity and fidelity.Source: §2 · p. 2
• Generation begins from statistics in the core subspace, then conditionally generates samples in successively larger subspaces; the subspaces can be chosen flexibly.Source: §2 · p. 2

3.1 System Overview

• Randomly cropped 32 × 32 exemplar patches form the input; NITES generates visually similar patches and quilts them into larger images.The process uses successive embedding and generation paths.Source: §3.1 · p. 3

3.2 Successive Subspace Embedding (SSE)

• The c/w Saab transform embeds patches using blockwise DC and PCA-derived AC components, discarding high-frequency channels for dimension reduction.Its successive hops capture short-, mid-, and long-range neighborhood information; the channel-wise version exploits weak inter-channel correlation and reduces model size.Source: §3.2 · pp. 3–4
• 83.3% and 67.5% are the successive dimension ratios from the source space to S1 and from S1 to S2, respectively.Users can flexibly choose channel counts in Hop-1 and Hop-2, making NITES non-parametric.Source: §3.2 · p. 4

3.3 Core Subspace Generation (CSG)

• In core space, NITES clusters coefficient vectors, applies PCA and ICA, and fits component CDFs to characterize cluster-conditional distributions.The method uses FastICA and stores quantized CDFs to reduce model size.Source: §3.3 · pp. 4–5
• Core-space sampling selects clusters in proportion to their sample share, matches Gaussian samples to the chosen cluster’s inverse CDFs, then reverses ICA and PCA.It repeats sampling when a generated sample has no value above a preset threshold.Source: §3.3 · pp. 4–5

3.4 Successive Subspace Generation (SSG)

• Successive subspace generation applies inverse c/w Saab transforms to generated coefficients, reconstructing each higher-dimensional sample with local detail.The transforms are lossy when high-frequency channels have been removed; the inverse is deterministic once the forward transform is set.Source: §3.4 · p. 5
• Generated examples progress from low-resolution DC patterns in core and intermediate spaces to texture patches in the source space.The paper reports that NITES can generate samples containing more local detail gradually.Source: §3.4 · p. 5

4.1 Experimental Setup

• The experiments use texture-dependent channel counts chosen at the near-flat PCA-energy knee, with matching, non-overlapping analysis and generation windows.The listed Hop-2 channel range is 20–30.Source: §4.1 · pp. 5–6

4.2 An Example: Brick Wall Texture Generation

• Generated brick-wall patches retain brick shape and texture diversity, and include unseen patterns; 64 × 64 patches can sometimes look blurry compared with 32 × 32 patches.The reported blur is attributed to the higher source dimension.Source: §4.2 · p. 6
• NITES’ four settings vary channel numbers in the intermediate and core subspaces; smaller dimensions yield poorer generated quality.Dimensions decrease faster from setting (a) to (d).Source: §4.2 · p. 6, Table 1 · p. 6
• For larger images, 5,000 generated patches are quilted into 256 × 256 images; 64 × 64 patches preserve global brick structure better, but can blur local detail.The eight stitched images use different initial quilting patches.Source: §4.2 · p. 7

4.3 Performance Benchmarking with CNN-based Methods

• NITES generates high-quality, visually pleasant textures in side-by-side examples, while the brown fog artifact reported for the CNN methods is absent from its results.The comparison uses methods by Gatys et al. and Ustyuzhaninov et al.Source: §4.3 · p. 7
• 213.04 seconds for one 256 × 256 image, versus 513.98 seconds for Gatys’ method and 949.64 seconds for Ustyuzhaninov’s method; NITES also produces visually pleasant textures.The timing comparison uses the same machine; the visual comparison reports a brown fog artifact for the CNN methods on texture meshed that does not appear in NITES.Source: §4.3 · p. 7
• For NITES, successive subspace embedding takes 24.24 seconds, reverse generation 108.03 seconds, and quilting 8.08 seconds; repeat synthesis takes 116 seconds for the latter two stages.The embedding stage runs once when generating multiple textures from the same exemplar.Source: §4.3 · p. 8

5 Conclusion and Future Work

• NITES uses multi-stage channel-wise Saab transforms for joint spatial-spectral representations and models sample distributions in the core subspace.Its successive subspace generation model builds higher-dimensional spaces from lower-dimensional ones and generates samples by mimicking source-patch probabilities and/or conditional probabilities.Source: §5 · pp. 8–9
• Experiments show NITES can generate visually pleasant texture images effectively, including some unseen patterns.Source: §5 · p. 9
• Future work includes controlling dimension growth, testing more intermediate subspaces, extending the model to other image types or inpainting, and comparing it with GANs.Source: §5 · p. 9