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arxiv: 2601.19117 · v2 · pith:4LHCXK5Qnew · submitted 2026-01-27 · 📡 eess.IV · cs.CV· stat.AP

Optimized k-means color quantization of digital images in machine-based and human perception-based colorspaces

Ranjan Maitra This is my paper

Pith reviewed 2026-05-25 07:17 UTC · model grok-4.3

classification 📡 eess.IV cs.CVstat.AP
keywords color quantizationk-meansRGB colorspaceCIE-XYZCIE-LUVVisual Information Fidelityimage processingdigital images
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The pith

k-means color quantization yields highest visual fidelity in RGB for about half of images, with CIE-XYZ better at higher k and CIE-LUV at lower k in some cases.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies the k-means algorithm to reduce colors in 148 digital images at four different quantization levels, testing performance in the RGB, CIE-XYZ, and CIE-LUV or CIE-HCL colorspaces. Quality of the resulting images is measured numerically with the Visual Information Fidelity metric. The results show RGB produces the best scores in roughly half the cases, CIE-XYZ often wins especially when more colors are retained, and CIE-LUV can be preferable at smaller k values. The authors further examine how an image's hue, chromaticity, and luminance distributions relate to which colorspace works best.

Core claim

k-means color quantization produces the highest Visual Information Fidelity scores in the RGB colorspace for about half of the 148 tested images across quantization levels, while the CIE-XYZ colorspace yields better results in the remaining cases, particularly at higher k, and the CIE-LUV colorspace performs best in some instances at lower k. Distributions of hue, chromaticity, and luminance in the original images provide a way to characterize when each colorspace is preferable.

What carries the argument

Performance comparison of k-means clustering for color quantization across RGB, CIE-XYZ, and CIE-LUV/CIE-HCL spaces, scored by Visual Information Fidelity on 148 images at multiple k levels, plus analysis of hue, chromaticity, and luminance distributions.

If this is right

  • At higher quantization levels, using CIE-XYZ instead of RGB can improve the fidelity of the reduced-color image.
  • At lower k, testing CIE-LUV may give better results for images with particular hue or luminance properties.
  • No single colorspace is optimal for all images, so selection can depend on image content statistics.
  • Further breakdown by hue, chromaticity, and luminance distributions can guide practical choices of colorspace for quantization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • An adaptive algorithm could select the colorspace automatically based on quick statistics of an image's luminance and hue distribution.
  • The approach might extend to other clustering-based image processing tasks where color representation affects output quality.
  • Validation against actual human perception studies would clarify whether the VIF differences are noticeable to viewers.
  • These patterns could inform color quantization steps in image compression or web image optimization pipelines.

Load-bearing premise

The Visual Information Fidelity metric provides a reliable numerical proxy for human-perceived visual quality when comparing quantized images produced in different colorspaces.

What would settle it

Human viewer preference rankings on a sample of the quantized image pairs that contradict the VIF-based ordering of which colorspace performed best.

Figures

Figures reproduced from arXiv: 2601.19117 by Ranjan Maitra.

Figure 1
Figure 1. Figure 1: Distributions of the hue, chromaticity and luminance in each image used in our study. The distributions are displayed by means of grouped circular boxplots (for hue) and linear boxplots for chromaticity and luminance. The distributions, and the brightness of the colors in the display are ordered from inside out, and left-to-right in order of number of image pixels. The orange, green and purple palettes rep… view at source ↗
Figure 2
Figure 2. Figure 2: The mean, standard deviation, skewness and kurtosis of the distribution of the hue, chromaticity and luminance in each image. Since hue is an angular measure, its characteristics are in terms of the angle-derived quantities of mean direction µˆ ◦ H, circular standard deviation σˆ ◦ H, circular skewness ˆζ ◦ H, and circular kurtosis κˆ ◦ H while chromaticity and luminance are in terms of linear descriptions… view at source ↗
Figure 3
Figure 3. Figure 3: Our showcase images: a modestly-sized image (top left: statlab, of 930×1789 pixels), two moderate-sized images (top center: rosehibiscus, with 1536×2048 pixels, and top right: eclipse, having 2658×3547 pixels) and a fairly large image (bottom: congress containing 5433×7240 pixels) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Results from k-means color quantization of the statlab image. For each colorspace, the images are better resolved without increasing k. The optimized XYZ colorspace is the best for all k for this image [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The k-means color quantized rosehibiscus images in the RGB (top row), XYZ (middle row), and LUV (bottom row) spaces, for k ∈ {8, 16, 32, 64} (from left to right). does best in each of the colorspaces, for k = 8, 16, 32, 64. In general, it appears that RGB is the best in about half the cases for all k. For the other half, it appears that XYZ is better than LUV in more cases, with the gap increasing substant… view at source ↗
Figure 6
Figure 6. Figure 6: The four ultra-large images: Westerlund2, earth-HD, pluto and eso1208a. TABLE 1: VIF of k-means color quantized images with the true rosehibiscus, eclipse, stainedglass and congress images. The best performance for each setting is highlighted in bold. rosehibiscus eclipse stainedglass congress k RGB XYZ LUV RGB XYZ LUV RGB XYZ LUV RGB XYZ LUV 8 0.462 0.462 0.432 0.552 0.601 0.524 0.290 0.294 0.286 0.632 0.… view at source ↗
Figure 7
Figure 7. Figure 7: The distribution of the VIFs of the k-means color quantized images done on the three colorspaces for k = 8, 16, 32, 64. The lines in the linked boxplots indicate the individual VIFs and allow us to track the performance of the same image upon k-means color quantization across the different colorspaces and for a specified k. we explain performance in terms of the difference in logit VIFs between k-means col… view at source ↗
Figure 8
Figure 8. Figure 8: The MVRT upon fitting µˆC , µˆ ◦ H, ˆζL, σˆ ◦ H to the matrix-valued ((yi,ℓ,k))s as defined in (9). The leaves at each terminal node (labled 1–19 for ready reference) display the matrix-valued responses assigned to that node, with greens and oranges representing the yi,XYZ,k and yi,LUV,k values for the ith digital image, and darker shades indicate higher k ∈ {8, 16, 32, 64}. The vertical line through all t… view at source ↗
Figure 9
Figure 9. Figure 9: The smaller-sized images that are Set 1. In nondecreasing order of total number of pixels, they are snedecormural, BlueMarble, AlertTiger, owlet, Tiger, BabyGiraffe, LagunaVerde, peacock, dolphins, tortoise, MarchingPenguins, IceBed, traminterior, ugc12295, Bandhavgarh, 2023Pujatram, hybridbird, arches, bisons, blackpepper, bryce, ChengHoonTeng, cleopatra, edithcavill, elephantseal, Glacier, Jungfrau, notr… view at source ↗
Figure 10
Figure 10. Figure 10: The moderate-sized images that form Set 2: ocelot, ngc2264, kathakali, MangroveTree, MediterraneanRipples, CoastRange￾FenceLizzard, WaterLilies, snedecorhall, FallRiot, TurningLeaves, FallBeforeBlack, FallFrenzy, FallFiesta, AristocraticAutumn, StagesOfFall, StagesOfBloom, IndomitableTopkapiTree, KaunosTombsOfTheKings, CirclesInStPauls, SandDollar, LittleSmokeyBear, Azure, Blue, CannaIs￾land, HooghlyFerry… view at source ↗
Figure 11
Figure 11. Figure 11: The images in Set 3: FilteredRays, qutb, SanMarcoClockTower, GiraldaNight, Monsoon, GrainsOfTurtuk, macarena, Campanile￾OfKastelruth, dolomiti, cavalli, vernazza, monterosso-trees, vibrant-colors, olives, limes, 2limes, cactus-nochtli, valeriana, Vieques, Rathaus, lisbon, Algarve, fossil, flotilla, bologna, albarracin, sintratower, alcazar-shadows, alcazar-tower, alhambra-wall, plaza-espana, Giethoorn, mi… view at source ↗
read the original abstract

Color quantization represents an image using a fraction of its original number of colors while only minimally losing its visual quality. The $k$-means algorithm is commonly used in this context, but has mostly been applied in the machine-based RGB colorspace composed of the three primary colors. However, some recent studies have indicated its improved performance in human perception-based colorspaces. We investigated the performance of $k$-means color quantization at four quantization levels in the RGB, CIE-XYZ, and CIE-LUV/CIE-HCL colorspaces, on 148 varied digital images spanning a wide range of scenes, subjects and settings. The Visual Information Fidelity (VIF) measure numerically assessed the quality of the quantized images, and showed that in about half of the cases, $k$-means color quantization is best in the RGB space, while at other times, and especially for higher quantization levels ($k$), the CIE-XYZ colorspace is where it usually does better. There are also some cases, especially at lower $k$, where the best performance is obtained in the CIE-LUV colorspace. Further analysis of the performances in terms of the distributions of the hue, chromaticity and luminance in an image presents a nuanced perspective and characterization of the images for which each colorspace is better for $k$-means color quantization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript empirically compares k-means color quantization performance in RGB, CIE-XYZ, and CIE-LUV (and CIE-HCL) colorspaces across 148 varied images at four quantization levels. Quality is assessed via the Visual Information Fidelity (VIF) metric, leading to the claim that RGB performs best in roughly half the cases, CIE-XYZ is often superior at higher k, and CIE-LUV at lower k; additional analysis examines image hue, chromaticity, and luminance distributions to characterize when each space is preferable.

Significance. If the VIF-based rankings are reliable across colorspaces, the work supplies practical empirical guidance on colorspace choice for k-means quantization, which could inform compression, display, and machine-vision pipelines. The study is strengthened by its use of a sizable, diverse image corpus rather than synthetic or narrow test sets.

major comments (1)
  1. [Abstract] Abstract: The central empirical claim (RGB best in ~half the cases, XYZ at higher k, LUV at lower k) rests solely on VIF scores. VIF was formulated for luminance-channel distortions; the manuscript provides no validation (e.g., cross-check against CIEDE2000 on the same quantized images or subjective ratings) that VIF rankings remain consistent when the same results are produced in XYZ versus LUV and then converted to a common space for scoring. Systematic bias is possible because quantization error distributions affect chromatic channels differently across spaces.
minor comments (2)
  1. [Abstract] Abstract: The four specific quantization levels (k values) are not stated.
  2. [Abstract] Abstract: No information is given on statistical testing, exact image-selection criteria, or potential confounds such as content category balance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for highlighting a methodological point regarding the VIF metric. We address the concern directly below and indicate the revisions we are prepared to make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central empirical claim (RGB best in ~half the cases, XYZ at higher k, LUV at lower k) rests solely on VIF scores. VIF was formulated for luminance-channel distortions; the manuscript provides no validation (e.g., cross-check against CIEDE2000 on the same quantized images or subjective ratings) that VIF rankings remain consistent when the same results are produced in XYZ versus LUV and then converted to a common space for scoring. Systematic bias is possible because quantization error distributions affect chromatic channels differently across spaces.

    Authors: We agree that VIF was originally derived for luminance distortions and that its behavior when applied to full-color images quantized in different spaces merits explicit checking. In the manuscript we convert all quantized results to sRGB before computing VIF, which places the final images in a common coordinate system; however, we did not report a secondary metric such as CIEDE2000 or any subjective validation. We will therefore add a supplementary section that recomputes the per-image, per-k rankings using CIEDE2000 on the same set of quantized images and reports the agreement rate between VIF and CIEDE2000 orderings. This addition will quantify any systematic discrepancy introduced by the choice of VIF. We view the requested check as a useful strengthening of the evidence rather than a refutation of the current conclusions. revision: partial

Circularity Check

0 steps flagged

No circularity: purely empirical comparison of k-means in colorspaces via VIF

full rationale

The paper reports direct experimental results from running k-means quantization on 148 images in RGB, CIE-XYZ, and CIE-LUV/HCL spaces, then ranking the outputs by VIF scores. No equations, fitted parameters, predictions, or self-citations are used to derive the central claims (RGB best in ~half the cases, XYZ at higher k, LUV at lower k). The VIF application is a fixed external metric, not redefined or fitted within the paper. No load-bearing steps reduce to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that VIF is a valid quality metric across colorspaces and that the 148 images adequately sample the space of digital photographs; both are standard but unproven domain assumptions in the abstract.

axioms (1)
  • domain assumption VIF is an appropriate metric for assessing quantized image quality in different color spaces
    The paper relies on VIF to numerically assess quality without discussing its limitations in this context.

pith-pipeline@v0.9.0 · 5768 in / 1237 out tokens · 35250 ms · 2026-05-25T07:17:38.742612+00:00 · methodology

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