A team of Italian researchers led by Antonio Di Marino and Vincenzo Bevilacqua of the Institute for High-Performance Computing and Networking at Italy’s National Research Council, working with colleagues at the University of Naples Federico II and the University of Naples Parthenope, has now proposed a way out of this impasse. In a study published in Discover Artificial Intelligence, they introduce EDOKS, short for Earth mover’s Distance and Oklab Similarity, a full-reference image quality metric that is both perceptually grounded and fully transparent. Unlike the deep neural network metrics that currently dominate perceptual benchmarks, EDOKS contains no learned parameters at all. Every step of its computation can be inspected, and it hands users pixel-level maps showing exactly where two images differ in texture and in color.

The problem with the incumbents runs deeper than a single bad example. PSNR is built on the mean squared error between pixel values, a measure that Wang and colleagues famously dismantled by showing that images with identical MSE values can look wildly different to a human observer. Because PSNR is derived directly from MSE, it inherits every one of those failures. SSIM was designed as a perceptual alternative, comparing luminance, contrast and structure, but subsequent analyses have exposed its own quirks. Horé and Ziou demonstrated a direct mathematical relationship between PSNR and SSIM, showing that one can be derived from the other, while Nilsson and Akenine-Möller showed that SSIM can produce undefined and non-intuitive results, concluding that the metric is being used for far more than it was ever created for. Despite this, both remain de facto standards across the field.

At the other end of the spectrum sit the deep perceptual metrics, chief among them LPIPS, which measures distance between images in the feature space of a network pretrained on visual recognition tasks. These metrics correlate strongly with human judgment, but they are black boxes. When LPIPS assigns a score, no one can point to the specific regions or visual features that drove the number. That opacity has become more than an academic nuisance. Emerging artificial intelligence regulation, including transparency requirements in the European Union’s AI framework, increasingly demands that automated assessments be explainable. A similarity score that cannot be justified is a liability in any regulated pipeline, whether it certifies compressed medical imagery or audits the output of a generative model.

EDOKS attacks the problem by decomposing perceptual dissimilarity into two interpretable terms, one for texture and one for color. The texture term begins by converting the image to grayscale and dividing it into patches of 128 by 128 pixels. Each patch is passed through a dictionary of 24 Gabor filters, Gaussian-modulated sinusoids at four scales and six orientations spanning 0 to 150 degrees. Gabor filters are a natural choice because they closely model the receptive fields of simple cells in the visual cortex, offering optimal joint localization in space and frequency. The energy of each filter response is computed, producing a four-by-six matrix per patch that captures how strongly the patch responds at every scale and orientation combination.

Those per-patch energy matrices are then compressed into a compact signature using a Meng-Hee Heng clustering algorithm, a greedy max-min procedure that automatically determines the number of centroids rather than requiring the user to guess. Each centroid represents a texture pattern that appears frequently in the image, and each weight records how often it occurs. Comparing two images then reduces to computing the Earth Mover’s Distance between their signatures, a measure rooted in the Monge-Kantorovich optimal transport problem. Conceptually, one distribution is a pile of earth and the other a set of holes, and the distance is the minimum work needed to move the earth and fill the holes. Because the signatures are variable in size and the distance is cross-bin, matching similar texture prototypes across images while tolerating small shifts, the researchers argue it is ideally suited to texture comparison, and they note that EMD has not previously been used this way as a texture term in full-reference quality assessment.

The color term addresses a blind spot that trips up many luminance-only metrics. EDOKS converts both images into the Oklab perceptual color space, designed to be perceptually uniform and linear in hue, and then computes the average Euclidean distance between corresponding pixels. The choice of color space matters enormously. CIE XYZ is perceptually non-uniform, CIE Lab misrepresents hues in the blue region, and alternatives such as IPT or CAM16-USC sacrifice uniformity or numerical stability. Oklab, by contrast, offers closed-form analytic transforms requiring no lookup tables, perceptually orthogonal coordinates, and the best available approximation to the Munsell color system. Because the space is perceptually uniform, a fixed Euclidean step corresponds to an approximately constant perceived color difference, making the distance itself a perceptual feature rather than a mere numerical artifact.

The two terms are fused into a single index through a weighted combination controlled by an explicit parameter alpha, with the default set at 0.5 so that texture and color contribute equally. The result is converted to a similarity score by taking the reciprocal of the combined dissimilarity. Crucially, the two terms remain separately available as pixel-level heatmaps. The texture map highlights where the two images differ in shape and structure, while the color map highlights chromatic discrepancies. In validation experiments on the BAPPS dataset, which includes traditional distortions, artifacts generated by convolutional neural networks, and geometric warps, EDOKS outperformed all tested low-level full-reference competitors on both the JND and 2AFC subsets, achieving a ratio of 1.37 between its scores on pairs judged same versus not same by human juries, a separation comparable to that of deep metrics. On the JND subset it attained the best Spearman, Kendall and Pearson correlations among handcrafted metrics, well above PSNR and SSIM, and closest to PieAPP among the deep competitors.

The interpretability of the metric is not an abstract virtue; it catches failures that would otherwise be invisible. In one test case, a red-bordered no-entry sign for bicycles was compared with a blue mandatory sign for cycle paths, two images whose opposite meanings would create a genuine road safety hazard. Metrics including SSIM, PSNR-HVSM, VIF and DSS assigned the pair a maximum similarity score, effectively declaring the signs identical. The reason is that these metrics convert color to grayscale using the ITU-R BT.601 standard, under which that particular shade of red and that shade of blue collapse to the same luminance. EDOKS, by contrast, detected no shape distortion but clearly flagged the color difference in its Oklab heatmap, producing a similarity score of 13.511 and visible evidence for why the images differ.

The computational cost of this transparency is modest. The Oklab conversion and per-pixel distances scale linearly with pixel count, the 24 Gabor convolutions are parallelized across cores, and the dominant cost is the clustering step, which grows cubically with the number of patches. At 1080p resolution, EDOKS runs faster than MS-SSIM and PieAPP and comparably to VIF and DISTS, while remaining slower than the cheapest luminance metrics such as PSNR and GMSD. The authors regard that overhead as the price of explainability: no GPU, no learned weights, no training, and two localized evidence maps that no fast luminance metric can provide. As generative AI systems proliferate and regulators demand verifiable evidence behind automated judgments, a metric that can show its work, rather than merely assert a number, may prove to be exactly what the field has been missing.

Subject of Research: A transparent full-reference image quality assessment metric combining Earth Mover's Distance texture signatures and Oklab color distances

Article Title: A new image similarity metric for a perceptual and transparent geometric and chromatic assessment

Article References: Marino, A. D., Bevilacqua, V., Nardo, E. D., Ciaramella, A., Falco, I. D., & Sannino, G. (2026). A new image similarity metric for a perceptual and transparent geometric and chromatic assessment. Discover Artificial Intelligence, 6(1), Article 1536. https://doi.org/10.1007/s44163-026-02424-4

Image Credits: AI Generated

DOI: 10.1007/s44163-026-02424-4

Keywords: image quality assessment, EDOKS, Earth Mover's Distance, Oklab color space, Gabor filters, perceptual similarity, PSNR, SSIM, LPIPS, explainable AI, BAPPS dataset, image processing

The core difficulty the researchers set out to address is client drift. In a standard federated training round, each client updates a shared model on its own local data before sending the updated parameters back to a server for aggregation. When those local datasets are skewed, for example when one phone contains mostly images of cats while another holds mostly images of cars, each client pulls the model in a different direction. The averaged global model ends up oscillating between incompatible preferences, converging slowly and often settling at a worse solution than a model trained on pooled data would reach. This non-independent-and-identically-distributed data problem has spawned an entire subfield of research, and knowledge distillation has emerged as one of its more promising remedies.

Knowledge distillation, in its classic form, asks a smaller or newer model to mimic the output probabilities of a teacher model, transferring not just the correct answers but the teacher’s nuanced confidence across all classes. In federated settings, the global model on the server typically acts as the teacher for local students. But Wang and Guan point out a subtle weakness in the conventional, coupled formulation of distillation when data are highly heterogeneous. The distillation loss blends two distinct signals: the knowledge about the target class, meaning the probability assigned to the correct label, and the knowledge about non-target classes, the relative ordering of all the wrong answers. Under skewed local distributions, a client can develop biased confidence in its dominant target classes, and that bias contaminates the coupled loss, misguiding the learning process rather than correcting it.

Their remedy builds on decoupled knowledge distillation, a technique introduced at the 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition, which separates the distillation objective into a target-class component, abbreviated TCKD, and a non-target-class component, abbreviated NCKD, each weighted independently. Decoupling alone, however, uses fixed weights that ignore how heterogeneous a given client’s data actually are. The key innovation of FedML-DKD is a heterogeneity-aware weighting mechanism that adjusts the balance between TCKD and NCKD dynamically for each client. The measure used to gauge heterogeneity is the Earth Mover’s Distance, a metric with roots in computer vision and transportation theory that quantifies the minimum work needed to transform one probability distribution into another, like measuring how much soil must be moved to reshape one pile of earth into the shape of another.

In practice, the framework computes the distributional divergence between each client’s local label distribution and a reference distribution, then uses that EMD value to set the relative contributions of the two distillation components. Clients whose data deviate sharply from the global distribution receive a rebalanced distillation signal that prevents them from overfitting to their biased local samples, while clients with more representative data can lean more heavily on the standard knowledge transfer pathway. This adaptive decoupling improves the reliability of the knowledge flowing between server and clients, because the teacher’s guidance is no longer distorted by the statistical quirks of any single participant. The result, according to the authors, is a training process that remains stable even as the degree of heterogeneity across clients increases.

The second pillar of FedML-DKD concerns what happens on the server after clients upload their updates. Conventional federated learning aggregates those parameters, typically through weighted averaging, to produce the next global model. Wang and Guan instead replace this aggregation step with a meta-learning objective. Meta-learning, often described as learning to learn, seeks an initialization from which a model can rapidly adapt to new tasks with only a few gradient steps. In the federated context, the uploaded client parameters are treated as a shared initialization that must generalize across the diverse local tasks represented by the participating devices. Rather than simply averaging away the differences between clients, the meta-learning objective explicitly optimizes for a starting point that can be fine-tuned quickly and effectively on each client’s particular distribution.

This design choice addresses a persistent tension in federated systems between personalization and generalization. A single global model must serve clients with very different data profiles, and pure averaging can wash out the specialized competence each client develops locally. By framing the global model as a meta-learned initialization, the framework preserves the ability of each client to adapt rapidly while ensuring that the shared foundation remains broadly capable. The approach connects to a growing literature on federated meta-learning, including model-agnostic meta-learning formulations with theoretical guarantees and group-based personalization methods, but the integration with adaptive decoupled distillation guided by EMD is what distinguishes the new framework from its predecessors.

The empirical evidence presented in the paper is substantial. The authors evaluated FedML-DKD on three widely used image classification benchmarks: CIFAR-10, CIFAR-100, and EMNIST-Letters. These datasets were partitioned across simulated clients under different levels of data heterogeneity, replicating the skewed, non-IID conditions that plague real deployments. Across these experiments, FedML-DKD consistently outperformed six representative baseline methods drawn from the federated learning and distillation literature. The reported gains are striking: accuracy improvements of up to 10.87 percentage points on the more challenging classification tasks, alongside stable convergence behavior, meaning the training did not exhibit the erratic oscillations that often accompany heterogeneous federated optimization.

The significance of a ten-percentage-point improvement in this domain should not be understated. Benchmarks like CIFAR-100, with one hundred fine-grained classes, are notoriously sensitive to distributional skew, and many published federated methods report gains of only one or two points over baselines. A framework that maintains both accuracy and convergence stability under severe heterogeneity could matter for applications where data cannot be centralized for legal or practical reasons, such as healthcare systems that must protect patient privacy, intrusion detection in resource-constrained networks, and mobile-edge computing scenarios where devices learn collaboratively over limited bandwidth. The paper’s reference list itself maps this landscape, citing recent work on privacy-preserving federated learning for smart healthcare, green federated learning, and data-free distillation techniques that avoid sharing even synthetic data.

Like any study, the work has boundaries worth noting. The experiments were conducted on standard computer vision benchmarks rather than production-scale deployments, and the authors state that no new datasets were generated or analyzed during the study. The computational cost of computing Earth Mover’s Distance between distributions at each round, while modest compared with model training itself, is a factor that future deployments will need to characterize. Nevertheless, the conceptual contribution is clear and elegant: by measuring how far each client’s data distribution sits from the collective norm and using that measurement to recalibrate what kind of knowledge gets distilled, FedML-DKD turns heterogeneity from a silent saboteur into an explicit signal that the training algorithm can respond to. As federated learning moves from research prototypes toward the infrastructure of privacy-conscious AI, techniques that make collaborative learning robust to the messy reality of uneven data will only grow in importance, and this study offers a concrete, empirically validated step in that direction.

Subject of Research: Adaptive decoupled knowledge distillation and meta-learning for federated learning under data heterogeneity

Article Title: EMD-guided adaptive decoupled knowledge distillation for federated meta-learning under data heterogeneity

Article References: Wang, D., & Guan, S. (2026). EMD-guided adaptive decoupled knowledge distillation for federated meta-learning under data heterogeneity. Cluster Computing, 29(14), Article 786. https://doi.org/10.1007/s10586-026-06617-5

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06617-5

Keywords: federated learning, knowledge distillation, meta-learning, data heterogeneity, Earth Mover's Distance, client drift, non-IID data, CIFAR-100, decoupled knowledge distillation, distributed machine learning, privacy-preserving AI, model aggregation