Gram-MMD: A Texture-Aware Metric for Image Realism Assessment

Joé Napolitano; Pascal Nguyen

cs.CVApr 3, 2026

Gram-MMD: A Texture-Aware Metric for Image Realism Assessment

Authors: Joé Napolitano, Pascal Nguyen

Organizations: AMIAD

Abstract

Evaluating the realism of generated images remains a fundamental challenge in generative modeling. Existing distributional metrics such as the Frechet Inception Distance (FID) and CLIP-MMD (CMMD) compare feature distributions at a semantic level but may overlook fine-grained textural information that can be relevant for distinguishing real from generated images. We introduce Gram-MMD (GMMD), a realism metric that leverages Gram matrices computed from intermediate activations of pretrained backbone networks to capture correlations between feature maps. By extracting the upper-triangular part of these symmetric Gram matrices and measuring the Maximum Mean Discrepancy (MMD) between an anchor distribution of real images and an evaluation distribution, GMMD produces a representation that encodes textural and structural characteristics at a finer granularity than global embeddings. To select the hyperparameters of the metric, we employ a meta-metric protocol based on controlled degradations applied to MS-COCO images, measuring monotonicity via Spearman's rank correlation and Kendall's tau. We conduct experiments on both the KADID-10k database and the RAISE realness assessment dataset using various backbone architectures, including DINOv2, DC-AE, Stable Diffusion's VAE encoder, VGG19, and the AlexNet backbone from LPIPS, among others. We also demonstrate on a cross-domain driving scenario (KITTI / Virtual KITTI / Stanford Cars) that CMMD can incorrectly rank real images as less realistic than synthetic ones due to its semantic bias, while GMMD preserves the correct ordering. Our results suggest that GMMD captures complementary information to existing semantic-level metrics.

Figures & tables

Figure 1: Overview of the GMMD pipeline. Images from the anchor and evaluation sets are passed through a pretrained backbone. Per-pixel (CNN) or per-patch (Transformer) Gram matrices vectorized via the upper-triangular part, and compared using MMD.

Figure 6: Spearman’s $\rho$ vs. Kendall’s $\tau$ on KADID-10k for each configuration.

Figure 7: Spearman’s $\rho$ (top) and Kendall’s $\tau$ (bottom) on KADID-10k across our 13 configurations and CMMD [2].

Figure 8: Partitioning of the 480 AI-generated RAISE images into 24 groups of 20, sorted by ascending MOS.

Figure 9: Linear regression between group-averaged MOS and metric score for each GMMD configuration and for CMMD (with $\gamma_{\mathrm{med}}$ and $\gamma=0.005$ ). Spearman’s $\rho$ is reported for each fit.

Figure 10: Two examples illustrating MMD behaviour. Left: a tight evaluation cluster within the anchor yields a high MMD due to limited coverage. Right: a broader but shifted evaluation set achieves lower MMD by better matching the anchor’s spread.

Metric	$\boldsymbol{\gamma}$	VKITTI2	Stanford Cars	Ratio	Inv.?
		(synth.)	(real)
GMMD (DC-AE L12)	$\gamma_{\mathrm{med}}$	$2.57\times 10^{-9}$	$2.65\times 10^{-11}$	$96.7$	No
CMMD (CLIP ViT-L/14)	$\gamma=0.005$	$0.494$	$0.517$	$\mathbf{0.96}$	Yes

Table 1: GMMD (DC-AE L12) and CMMD evaluated on a KITTI anchor (1,000 images) against Virtual KITTI 2 (synthetic) and Stanford Cars (real). Ratio

<1

indicates inversion.

Figure 11: GMMD scores for Virtual KITTI 2 (synthetic) and Stanford Cars (real) against a KITTI anchor, across multiple $\gamma$ values. The correct ordering (synthetic $>$ real) is preserved for all $\gamma$ .

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 13: KADID-10k evaluation. Top: MS-COCO anchor images (left) and sample images from five degradation groups at ranks 0, 31, 62, 93, and 124 (increasing DMOS). Bottom: GMMD and CMMD scores as a function of degradation rank.

Figure 14: RAISE realism assessment. Top: AI-generated images from groups at ranks 1, 2, 3, …, 23, 24, sorted by ascending MOS (perceived realism). Bottom: squared MMD vs. group rank with linear regression for each GMMD configuration and CMMD.

Figure 15: Sample images from the three datasets used in the KITTI experiment: KITTI (real driving scenes), Virtual KITTI 2 (synthetic driving scenes), and Stanford Cars (real vehicle photographs).

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