Azulejo Diffusion Reconstruction

Img2img Reconstruction (k = 0.35)

With sampling noise fixed at k = 0.35, we compare four model configurations on two symmetry types. The main focus is whether central / diagonal symmetry is preserved and whether seamless tiling is maintained at tile seams. Click any image to open it in a lightbox.

A. Central Symmetry

Input

Aligned and cropped reference tile used as img2img input.

1) SD1.5

Vanilla SD1.5, without Azulejo LoRA or structural guidance.

2) SD1.5 + LoRA

Azulejo-style LoRA injected to enhance brushwork, contours and blue–white palette.

3) + UNet Shrink

Kohya Deep Shrink: reduces structural drift and noise, improving stability.

4) + ControlNet

Structural/edge control (tile / lineart, etc.), strengthening geometry and boundary consistency.

Reading hint: under a fixed noise condition (k = 0.55), compare the four configurations from left to right in terms of (i) geometric consistency (symmetry mapping), (ii) topological continuity (seams and borders), and (iii) style consistency (blue–white gamut and brushwork). Pay particular attention to the central cross seam and the agreement between the four quadrants.

B. Diagonal Symmetry

Input

Aligned and cropped reference tile used as img2img input.

1) SD1.5

Baseline: no LoRA and no structural guidance.

2) SD1.5 + LoRA

Style enhancement: blue–white glaze, brushwork and motif contours become more concentrated.

3) + UNet Shrink

Expected effect: fewer structural drifts and more stable symmetry and seams.

4) + ControlNet

Explicit structural control: clearer borders and more regular tiling pattern.

Note: compared to central symmetry, diagonal symmetry is more sensitive to global geometric consistency and typically fails through “diagonal drift” and “seam discontinuity”. This setting is therefore useful to disentangle the effect of different modules: LoRA mainly improves style, whereas UNet Shrink / ControlNet mainly target structure and border regularity.

Quantitative Metrics (single reference, multi-sample)

Figure 3. Cultural Style Consistency Index (CSCI) for four methods on a single reference tile. Higher values indicate that generated samples are both close to the reference style and internally consistent.

Figure 4. Img2img quantitative metrics for the same four methods (single reference, multiple samples). Top row: structure similarity (SSIM), PSNR, diagonal symmetry index, Lab color difference ΔE*ab. Bottom row: mean seam error (MSE), texture style distance, color style distance, and aggregated style distance (StyleDist). Bars show the mean over samples; error bars (if present) show standard deviation.

Metric definitions (sketch): let x be the generated tile and x_ref the aligned reference.
• SSIM (structural similarity) is computed on luminance: SSIM(x,x_ref) = ((2 μ_x μ_r + C1)(2 σ_xr + C2))/((μ_x² + μ_r² + C1)(σ_x² + σ_r² + C2)).
• PSNR (dB) is derived from the mean squared error MSE = ‖x - x_ref‖₂² / N: PSNR = 10 log₁₀(MAX² / MSE), with MAX = 255.
• Diagonal symmetry index compares the tile to its diagonal-mirrored version inside a symmetric mask: roughly SymDiag = 1 − MSE(x, M(x)) / σ², where M denotes diagonal reflection.
• ΔE*ab is the average CIE76 color difference in Lab space: ΔE*ab = (1/N) Σ‖L*a*b*(x) − L*a*b*(x_ref)‖₂.
• Mean seam error measures MSE along vertical / horizontal seams after tiling the image in a 2×2 grid.
• Texture style distance is the L2 distance between normalized GLCM (gray-level co-occurrence matrix) feature vectors of x and x_ref.
• Color style distance is the L2 distance between normalized Lab color histograms.
• StyleDist aggregates normalized texture, color and CLIP-based semantic distances via a weighted sum.
• CSCI (Cultural Style Consistency Index) uses the style feature space: for each method, we compute the mean distance to the reference cluster D_ref and mean intra-cluster distance D_intra, map them into [0,1] scores C_ref, C_intra by exponential normalization, and take the geometric mean CSCI = √(C_ref · C_intra).

Text2img Generation (Symmetry Groups)

Here we show text2img results grouped by central symmetry and diagonal symmetry, comparing different model configurations under the same sampling setup. The current version includes SD1.5, SD1.5 + LoRA, and SD1.5 + LoRA + ControlNet. SD1.5 + LoRA + UNet Shrink will be added as a follow-up experiment (work in progress).

A. Central Symmetry

Original

Reference tile: used as a visual baseline for central symmetry and typical blue–white glaze style.

SD1.5

Baseline generation: produces blue–white motifs but with unstable central symmetry and border rules; local details tend to drift.

SD1.5 + LoRA

Style injection: blue–white glaze, brushwork and contours become more Azulejo-like, while global symmetry is still slightly imperfect.

+ ControlNet

Structural constraints: central symmetry becomes more consistent and borders cleaner, yielding a pattern closer to a “tileable” design.

What to compare: focus on the agreement along the central axes and between the four quadrants, as well as boundary continuity (tiling readiness), while checking that the blue–white style remains faithful.

B. Diagonal Symmetry

Original

Reference tile: used to illustrate diagonal symmetry (mirror/rotation along diagonals) and seam continuity rules.

SD1.5

Baseline generation: produces plausible blue–white floral elements, but behaves more like a free-form botanical illustration; diagonal symmetry and tileable border rules are largely missing.

SD1.5 + LoRA

Style improvement: the blue–white palette and brushwork are closer to Azulejo, but the model tends to produce a “wallpaper-like” repeating pattern. Periodicity emerges, yet the original scroll structure and diagonal correspondence are not fully recovered, especially near the central seam.

+ ControlNet

Structural reinforcement: the generation shows clear quadrant partition and diagonal correspondence, with cleaner borders and stronger tiling consistency; however, fine texture is over-smoothed and more abstract (low-frequency), and the detailed scroll structure of the reference is not fully reconstructed.

Work in progress: we plan to add SD1.5 + LoRA + UNet Shrink for text2img as well, to study how UNet shrink affects structural stability and style drift in free generation.

Framework (Data → Model → Evaluation)

Figure 1. Overall framework: data & annotations → structure-aware diffusion → metrics & style space.

Method Core (Structure-aware Diffusion)

Figure 2. Conditions injected at different UNet stages: encoder (edges), middle (global symmetry/layout), decoder (detail & seam refinement).

Text is deliberately compressed here: the main goal of this page is to show visual evidence. Full technical details are documented in the thesis PDF.

To-do & Future Work

This page is a snapshot of an ongoing project. Below is a non-exhaustive to-do list for experiments and extensions that are completed, in progress, or planned for the next stages.

Completed for this page

• Img2img quantitative metrics (Figures 3–4): CSCI bar chart and multi-metric plots for a single reference tile with multiple samples.

Ongoing

• Text2img: add SD1.5 + LoRA + UNet Shrink configuration and compare with existing baselines.
• User study: expand the subjective experiment, align human ratings with style-space distances, and refine the CSCI calibration.

Short-term experiments

• Img2img noise-level study: systematically compare reconstruction quality under multiple denoising strengths (e.g. k = 0.25, 0.35, 0.45, 0.55, 0.65), focusing on the trade-off between structure preservation, seam continuity and texture restoration.
• Text2img · cultural style consistency evaluation：Design a CSCI-based evaluation protocol that measures how well text2img generations preserve the cultural style of the reference tiles, using central / diagonal symmetry galleries with diverse prompts, seeds and annotated failure cases.
• Dataset: augment the training and evaluation set beyond street signs and floral tiles to include azulejo-style tiles depicting figures (human portraits), landscapes and architectural scenes, and test how well the current pipeline generalizes to these motifs.

Longer-term ideas

• Structure-aware diffusion backbone: move from “SD1.5 + add-on ControlNet” to a diffusion model with explicit symmetry / tiling priors built into the UNet itself.
• CSCI & style-space refinement: extend the cultural style consistency index (CSCI) family and learn a human-aligned style distance from larger-scale subjective experiments.
• Cross-domain cultural patterns: apply the same pipeline to other pattern-based cultural media such as Portuguese azulejo in Portugal, mosaics and textile patterns, and compare style spaces across domains.