New Transparent Metric EDOKS Judges Image Similarity the Way Human Eyes Do

For decades, two workhorse numbers have quietly governed how the digital world judges pictures: the peak signal-to-noise ratio, known as PSNR, and the structural similarity index measure, or SSIM. Every time an engineer evaluates a lossy compression algorithm, a super-resolution network, or an image-generating artificial intelligence, one of these scores usually decides whether the output counts as faithful. Yet a growing body of evidence shows that neither metric actually agrees with what human eyes consider similar. In one striking example from the Berkeley-Adobe Perceptual Patch Similarity dataset, PSNR and SSIM both declared that a reference photograph was more similar to a distorted image on the right, while a panel of five human judges unanimously chose the distorted image on the left. The machines, in other words, were confidently wrong.

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