Image Quality Assessment: From Error Visibility to Structural Similarity
1. Paper overview
In one sentence: SSIM compares local brightness, contrast and normalized structure to better track perceived compression quality, while retaining the need for an aligned reference and application-specific validation. e03e04e05e06e07e09e10
| At a glance | What to know |
|---|---|
| Research problem | Source description Full-reference quality assessment needs an inexpensive proxy for human judgment. Squared pixel error is convenient, but equally large errors can preserve or destroy very different amounts of visible structure. Traditional error-sensitivity pipelines weight differences using visual thresholds and masking. The authors question equating error visibility with objectionable quality loss, extrapolating near-threshold experiments to strong distortions, and pooling dependent natural-image components as though they were independent. e02e03 |
| Core mechanism | |
| A key reported result | Predict human quality rankings across JPEG and JPEG2000 images: MSSIM 0.963 Spearman rank-order correlation (higher is better). 344 compressed images from 29 references: 175 JPEG and 169 JPEG2000. No held-out partition is described. Luminance is locally averaged and downsampled before MSSIM. Sarnoff 0.947; PSNR 0.901; UQI 0.863. Best reported ranking agreement among these four methods on this database. Table I supplies no confidence intervals or significance test for these differences. e07e10 |
| Reading caution | Source description Subjective validation covers two compression families and mostly male college students. JPEG images have 13–20 raters each and JPEG2000 images 25; viewing distance was only moderately controlled. Color-channel findings are explicitly restricted to this dataset. e07 |
Core contributions
Figure 2. Equal reported pixel error leaves very different amounts of recognizable detail. Original paper, p. 4 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Use panel (a) as the reference. Panels (b) and (c) change contrast and mean luminance, while (d), (e) and (f) introduce JPEG compression, blur and impulsive noise. Compare the lettering, rigging and edges rather than only the overall brightness. The paper's caption assigns MSE=210 to the five distorted versions; the reference itself is not part of that equal-error claim. The authors argue that much of the upper-row information remains recoverable through a pointwise luminance transformation, except where saturation loses information. The lower row illustrates distortions that damage local detail in different ways. e03e02
What it supports. The inspected caption reports MSSIM 0.9168 for contrast stretching and 0.9900 for mean shifting, compared with 0.6949 for JPEG, 0.7052 for blur and 0.7748 for impulse noise. SSIM distinguishes these particular distortions even though their reported MSE is identical. This motivates separating structural change from pixel-error energy.
Where the evidence stops. These are selected examples from one reference, without separate human-rating statistics for the panels. The body describes nearly identical MSE, whereas the caption reports 210 for each distortion; that precision should not be expanded beyond the source.
2. Motivation
2.1 The problem and the proposed response
Full-reference quality assessment needs an inexpensive proxy for human judgment. Squared pixel error is convenient, but equally large errors can preserve or destroy very different amounts of visible structure. Traditional error-sensitivity pipelines weight differences using visual thresholds and masking. The authors question equating error visibility with objectionable quality loss, extrapolating near-threshold experiments to strong distortions, and pooling dependent natural-image components as though they were independent. e02e03
2.2 What this reading follows
A large pixel error need not destroy the recognizable structure of an image. This paper makes that observation operational: separate local brightness and contrast from the pattern remaining after normalization, compare each component, and average the resulting SSIM map. The illustrated route starts with equally strong pixel errors, follows the measurement diagram, and then asks what the score rewards under a fixed error budget. Finally, the human-rating plots and table test whether that preference helps across image content and compression types. Read those fitted evaluation results separately from the metric itself: SSIM needs no learned predictor, but evaluating score accuracy uses a fitted mapping to subjective ratings. e03e04e05e06e07e09e10
3. Research context
We place the paper in the collection through its world–action interface. The catalog labels and the reading’s assessment are shown separately.
| Catalog dimension | Recorded classification |
|---|---|
| Major category | Evaluation metrics |
| Architecture | Not applicable |
| Prediction paradigm | Not applicable |
| Quadrant | Not applicable |
3.1 Evidence-based assessment
Supports the recorded classification
The recorded evaluation-metric category is supported: SSIM is a fixed full-reference image-comparison function validated against human ratings. Architecture, prediction paradigm and world/action quadrant are not applicable because the source introduces neither a learned dynamics architecture nor an action-producing mechanism. e01e04e07
This is the collection’s architectural analysis, not a new related-work survey. Benchmark comparisons and their protocols appear in Section 6.
4. Problem formulation
4.1 Inputs and outputs
| Inputs | Outputs |
|---|---|
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4.2 Equations and their role
5. Method in detail
5.1 Separate a changed appearance from a changed local pattern
The Boat examples motivate a precise decomposition. A mean shift changes brightness, and a contrast stretch changes the scale of local variation; neither necessarily destroys the arrangement of edges. SSIM therefore measures the mean first, subtracts it, measures the remaining contrast, and normalizes before comparing structure. However, only the structure branch receives this normalization. The separate luminance and contrast comparisons still affect the final product, which prevents the method from simply declaring every brightness-adjusted image identical. In the implemented equation, covariance and the two variances combine the contrast and structure information, while the means supply the luminance factor. Reader interpretation: the useful conceptual move is to ask what changed locally before aggregating its severity, rather than expecting raw error energy to encode that distinction by itself. e03e04
Figure 3. Normalization separates the structure comparison from brightness and contrast comparisons. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Trace each input independently from left to right. The luminance measurement branches toward the upper comparison and also enters the subtractive input marked minus at the summing circle. The remaining signal enters contrast measurement; its standard deviation is then the divisor at the division circle. Follow the crossing lines to their arrowheads: the two means meet at luminance comparison, the two standard deviations at contrast comparison, and the two normalized patterns at structure comparison. Equations (6), (9) and (10) define the stabilized comparisons. Equation (13) combines them with unit exponents and the specified relation between stabilizing constants. e04e05
What it supports. The diagram explains why normalized structure can remain similar after a brightness or contrast change while the total score still changes: luminance and contrast each retain their own comparison branch. SSIM is therefore more than a correlation coefficient, and its full score is not invariant to every illumination transformation.
Where the evidence stops. The subtraction, division and arrow directions agree with the adjacent formulation. This is a conceptual measurement diagram: the stabilizing constants, local Gaussian window and image-wide averaging must be taken from the equations and Section III.C, not inferred from the blocks alone.
5.2 Turn the local formula into the paper's actual image score
An implementation must go beyond copying Equation (13). The introductory derivation uses ordinary patch statistics, whereas the evaluated local method specifies Gaussian-weighted statistics in Equations (14)–(16). Its 11×11 window has standard deviation 1.5, and the image score is the uniform mean of local SSIM values. Stabilizers are tied to the pixel dynamic range through K1 and K2, so their meaning depends on the intensity convention. The compression experiment additionally averages luminance over 2×2 neighborhoods and downsamples before scoring. These operations change what fine detail enters the local comparisons. The source explicitly uses no specific training procedure for SSIM. Fitting a logistic curve to compare scores with human ratings is a later evaluation operation, and should not be confused with learning the similarity function. e04e05e07e09
5.3 Connect the diagnostic preference to the human-rating evidence
Figure 5 probes the metric from inside: holding MSE fixed while changing MSSIM reveals what it prefers. That can expose a useful bias, but maximizing a score does not independently prove perceptual validity. The compression database supplies the next test, comparing objective predictions with normalized ratings across reference images and two codecs. Table I separates monotonic agreement from errors after score calibration, and MSSIM leads the reported comparisons. Reader analysis: this supports the proposed metric for the studied setting without resolving every causal explanation. In particular, the UQI comparison changes both its window and stabilizers, and no held-out calibration protocol is described. A controlled implementation comparison and a content-separated evaluation would therefore test different remaining questions: why the method improves, and how far the calibrated relationship transfers. e06e07e09e10e11
5.4 Training and inference
During training
No specific training procedure is used before applying SSIM to this database. Parameters are fixed; the authors describe the stabilizer settings as somewhat arbitrary and report qualitative insensitivity without a sweep table. Logistic score fitting belongs to performance evaluation, separate from computing SSIM. e05e07e09
During inference
Scoring deterministically extracts corresponding local statistics, evaluates the stabilized index and averages the map. It predicts no future state and executes no action. Interpreting the similarity as quality depends on having a suitable aligned reference; the symmetric formula alone cannot identify which image is better. e04e05e12
5.5 Implementation flow
- Separate brightness, contrast and structure
Measure each patch's mean luminance, subtract its own mean, and estimate contrast from its standard deviation. Compare the means and contrasts separately; compare structure through correlation after mean subtraction and contrast normalization. Figure 3's subtraction and division branches implement this ordering. e04
- Stabilize and combine
Use constants C1 and C2 in the luminance and contrast/structure ratios to avoid unstable nearly zero denominators. The implemented form sets all three comparison exponents to 1 and C3=C2/2. Its luminance and contrast terms still penalize changes even when normalized structure is preserved. e04e11
- Compute local statistics
Use an 11×11 circularly symmetric Gaussian window with standard deviation 1.5 samples and unit-sum weights. Equations (14)–(16) specify weighted means, variances and covariance. K1=0.01 and K2=0.03 set the stabilizers relative to pixel dynamic range; L=255 for 8-bit grayscale. e04e05
- Pool and respect the evaluation scale
Average local SSIM values uniformly. For the compression experiment, the luminance component is averaged over a 2×2 window and downsampled by two before scoring. This experimental preprocessing matters when comparing implementations; the paper does not establish it as optimal for every application. e05e07
6. Experiments & results
SSIM evaluates an aligned image against a reference by comparing local luminance, contrast and normalized structure, then averaging the local scores into MSSIM. It requires no learned predictor. On this paper's JPEG/JPEG2000 database, MSSIM tracks human quality ratings better than PSNR, Sarnoff and UQI under the reported criteria. The evidence supports perceptual assessment of compressed still images; it does not validate a general measure of semantic correctness, temporal dynamics or control performance.
The source supplies no controlled component-ablation table or quantitative stabilizer sweep. Figure 5 is a fixed-MSE diagnostic, and the UQI comparison jointly changes window configuration and constants. They are presented with those limits rather than treated as isolated ablations. The experiments concern still-image compression quality; there are no learned-model training curves, temporal-dynamics tests or action-execution results to illustrate. e05e06e07e10e11
6.1 Read the original evidence
Figure 7. Local similarity and pixel error highlight different image regions. Original paper, p. 11 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read down each column: (a–c) are original images, (d–f) compressed versions, (g–i) SSIM maps and (j–l) absolute-error maps. The paper squares SSIM for display, so brightness represents its displayed magnitude; the bottom row reverses contrast to make visual comparison easier. Neither row should be read as an untransformed numerical heatmap. In Stream, compare the blurred tree detail with the dark regions of (g). Across Caps and Bikes, compare how the bottom-row errors distribute around texture and edges with how well the compressed images retain recognizable structure. These displayed image excerpts were already cropped by the paper for visibility. e08e07
What it supports. The caption gives Caps PSNR 34.56 dB and MSSIM 0.9409, versus Bikes PSNR 33.47 dB and MSSIM 0.9747. The authors judge Bikes visually better despite its lower PSNR. This illustrates their cross-content argument and shows why inspecting a local map can reveal more than a single global score.
Where the evidence stops. Page 9 cross-references Figure 6(j) while discussing Figure 7(g). The corresponding-map reading here follows Figure 7's own panel labels and caption, pairing (g) with (j). Squaring also removes the sign of SSIM, so display brightness alone cannot establish a signed local value.
Figure 8. Human-score agreement must be assessed across content and codec, with score direction and calibration visible. Original paper, p. 12 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Each point is one compressed image; stars identify JPEG and plus signs JPEG2000. The vertical axis is subjective mean opinion score, while each panel has its own objective-score scale. Higher PSNR, UQI and MSSIM trend toward higher opinion scores; Sarnoff runs in the opposite direction. The curves are fitted logistic mappings, not identity lines. Compare dispersion around each curve and whether the two codec populations follow similar trends. The tight, strongly curved MSSIM relationship explains why rank correlation and post-regression prediction error answer different questions. The source's caption also identifies different windows and stabilizer settings for UQI and MSSIM. e07e09e10e11
What it supports. MSSIM organizes the two compression families into a comparatively tight relationship with subjective quality. Table I quantifies that visual impression with rank correlation 0.963, compared with UQI 0.863. The plot also makes clear that an increment in raw MSSIM does not correspond to a constant increment in subjective quality.
Where the evidence stops. The paper describes no held-out calibration split. UQI and MSSIM also differ in both window configuration and constants, so this plot cannot attribute their separation solely to stabilization. The source states that no specific SSIM training was used; logistic evaluation fitting is a separate step.
Table I. MSSIM leads the reported comparison under both score-fitting and ranking criteria. Original paper, p. 12 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. First separate the column groups. Nonlinear Regression reports correlation coefficient (CC), mean absolute error (MAE), root mean squared prediction error (RMS) and outlier ratio (OR). Variance-weighted Regression reports CC, weighted MAE (WMAE), weighted RMS (WRMS) and OR. Rank-order reports Spearman correlation (SROCC). Higher correlations are better; lower errors and outlier ratios are better. The error columns measure disagreement with subjective scores after regression, rather than squared image-pixel differences. Read horizontally within a model and compare vertically within the same column. Keep the two regression groups distinct: they use different fitting procedures, even where a rounded number happens to coincide. e07e09e10
What it supports. MSSIM's nonlinear-regression CC is 0.967 and RMS error 5.06, versus Sarnoff's 0.956 and 5.81. Its rank correlation is 0.963 versus 0.947 for Sarnoff and 0.901 for PSNR. All reported columns favor MSSIM among these four models on the evaluated 344-image database.
Where the evidence stops. The table gives point estimates without confidence intervals or significance tests for the differences. OR is a ratio, with an outlier defined using twice the subjective standard deviation; its printed value should not be read directly as a percentage number.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| Predict human quality rankings across JPEG and JPEG2000 images 344 compressed images from 29 references: 175 JPEG and 169 JPEG2000. No held-out partition is described. Luminance is locally averaged and downsampled before MSSIM. | MSSIM 0.963 Spearman rank-order correlation (higher is better) | Sarnoff 0.947; PSNR 0.901; UQI 0.863. Best reported ranking agreement among these four methods on this database. Table I supplies no confidence intervals or significance test for these differences. e07e10 |
| Predict subjective scores after nonlinear calibration Same 344-image database; logistic mapping between objective scores and subjective mean opinion scores, following the described VQEG procedure. | MSSIM 0.967 / 3.95 / 5.06 / 0.041 Correlation / MAE / RMS prediction error / outlier ratio | Sarnoff 0.956 / 4.66 / 5.81 / 0.064; PSNR 0.905 / 6.53 / 8.45 / 0.157; UQI 0.866 / 7.76 / 9.90 / 0.189. Errors are on the rescaled subjective-score scale after fitting, not raw pixel errors. Outlier ratio counts predictions beyond twice the subjective standard deviation; these are fitted-database results, not documented held-out calibration results. e07e09e10 |
| Distinguish equal-MSE distortions of Boat Figure 2 reports MSE=210 for five distorted versions of one reference. | Contrast stretch 0.9168; mean shift 0.9900; JPEG 0.6949; blur 0.7052; salt-and-pepper noise 0.7748. MSSIM (higher is better) | MSE assigns the same reported error to all five. A concrete illustration of cross-distortion discrimination, with no separate subjective-rating study reported for these panels. e03 |
| Probe MSSIM preferences at fixed MSE Figure 5: a 100×100 Boat crop, Gaussian-noise initialization, gradient ascent/descent constrained to MSE=2500. | Initial 0.3021; maximized 0.9337; minimized −0.5411. MSSIM at initialization and local extrema | Distorted images retain the same stated MSE while their visible structure differs. The diagnostic reveals the metric's preferences and negative values; it is neither a denoising benchmark nor proof of globally optimal extrema. e06 |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Figure 5. Optimizing similarity under a fixed error budget exposes what the metric rewards. Original paper, p. 8 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start at the left-hand original (a), follow the add-noise arrow to initialization (b), and then read the two vertical search branches. The upward arrow increases MSSIM to produce (c); the downward arrow decreases it to produce (d). Section IV.A describes projected gradient steps followed by rescaling to maintain the stated MSE constraint. The diagnostic asks how the spatial arrangement of an error can change while its strength remains fixed. Inspect the boat's outline and rigging in the upper endpoint, then the changed or reversed local contrasts below. The source's arrows match these ascent and descent roles. e06
What it supports. For the 100×100 example, the caption reports MSE=2500 for the distorted images, with MSSIM moving from 0.3021 to 0.9337 under ascent or −0.5411 under descent. The resulting images make the score's structural preference visible and demonstrate that negative MSSIM values occur in this paper.
Where the evidence stops. This is a diagnostic optimization, not a component ablation or measured human preference experiment. The procedure searches for local extrema from one initialization; the labels maximum and minimum do not establish global optimality or a general restoration capability.
7. Analysis & limitations
7.1 What the evidence leaves open
Subjective validation covers two compression families and mostly male college students. JPEG images have 13–20 raters each and JPEG2000 images 25; viewing distance was only moderately controlled. Color-channel findings are explicitly restricted to this dataset. e07
UQI versus MSSIM changes both square/Gaussian windowing and the stabilizers. The authors attribute much of UQI's weakness to flat-region instability, but the reported comparison does not isolate that mechanism. Parameter insensitivity is asserted without quantitative ablation results. e05e11
Strong still-image compression correlations do not establish sensitivity to temporal inconsistency, physically impossible futures or incorrect actions. Those properties require separate evaluation when SSIM is used around a world or action model. e04e07e10
The authors leave optimization of image-processing algorithms under SSIM for further study and describe SSIM as one implementation of structural similarity. Their broader extension to arbitrary signals is a proposed scope, not an experimentally validated result here. e12
7.2 Questions for discussion
- How much of the UQI-to-MSSIM gain remains when only the stabilizers change?
- Does logistic calibration learned on some reference images transfer to entirely unseen content?
- Which downstream errors could preserve local image similarity while still invalidating a predicted future?
8. Reproducibility audit
8.1 Requirements and known gaps
Reproduce the local weighted estimators, stabilizers, uniform pooling and compression-test downsampling before comparing scores. The prose does not specify the boundary-padding convention, exact luminance conversion or regression function parameters, so these must be documented rather than silently assumed. e04e05e07e09
Matching Table I needs the original images, normalized subjective scores and per-image standard deviations, plus comparable baseline implementations and regression procedures. The source points to MATLAB code, LIVE data, Sarnoff JNDmetrix and VQEG routines; these mentions establish requirements, not present-day availability or successful reproduction. e13e09e10
Reader-proposed checks: factorially vary windowing and stabilizers to isolate flat-region behavior, then test calibration on held-out reference images with all their distortions grouped together. Report rank agreement separately from fitted score errors. Neither check was run for this reading. e05e07e09e11
8.2 Proposed reproduction checks
The following checks are proposals motivated by the paper. They have not been run as part of this reading.
Check 1: Isolate stabilization from the window configuration
Reader-proposed experiment: evaluate a two-factor comparison using the earlier 8×8 uniform window versus the paper's 11×11 Gaussian window, each with zero stabilizers versus K1=0.01 and K2=0.03. Hold luminance preprocessing, dynamic range, image pairs and pooling fixed. Inspect constant and nearly constant patches alongside the compression database; report undefined scores rather than hiding them with an undocumented fallback. Compare finite-score coverage and rank agreement within each window configuration. If positive constants remove flat-patch failures and improve agreement under both windows, that supports the stabilization explanation. Improvement only when windowing also changes would weaken a constants-only explanation. This check has not been run. e04e05e07e11
Check 2: Test whether calibration transfers to unseen reference content
Reader-proposed experiment: partition the 29 reference images, keeping every compressed version of a reference in the same partition. Keep SSIM fixed and fit the logistic mapping only on the training references; evaluate rank correlation and mapped-score errors on held-out references, separately for each codec and pooled. Use the same partitions and calibration rule for PSNR and Sarnoff, and compare with an explicitly labeled fit-on-all diagnostic. Obtain subjective scores and standard deviations using the documented normalization protocol, and quantify uncertainty by resampling reference groups. A stable held-out MSSIM advantage would support transfer across content; a large collapse confined to calibrated errors would indicate that fitting explains part of the apparent accuracy. This check has not been run. e07e09e10e13
8.3 Reading coverage
Visual audit: All 14 supplied PDF pages were rendered and visually inspected, including the title and affiliation block, Figures 1–8, the complete Table I, equations, evaluation protocol, discussion, resource references and biographies. All six final original crops were separately viewed. Figure 3's subtraction/division markers and arrow endpoints were checked against Sections III.B–C; Figure 5's ascent/descent directions were checked against Section IV.A. Figure 7's display transformations and the page-9 cross-reference mismatch are explained locally. Text reading covered all six supplied chunks. No appendix is present; no external implementation, data or supplement was inspected. Page references identify this supplied 1–14 artifact, not the catalog's publisher pagination.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. Appendix coverage: not present.
Original figures and tables remain the work of the source’s authors. Extractions preserve their scientific content; any HTML wrapper layout is disclosed with each figure. The surrounding reading notes are our own.
Text reading scope & known omissions
- Title, author affiliations, abstract and I. Introduction (PDF p. 1)
- II. Image Quality Assessment Based on Error Sensitivity, A. Framework and B. Limitations (PDF pp. 2–3)
- III. Structural Similarity Based Image Quality Assessment, A. New Philosophy, B. The Structural SIMilarity (SSIM) Index, C. Image Quality Assessment using SSIM index (PDF pp. 3–8)
- IV. Experimental Results, A. Best-case/worst-case Validation, B. Test on JPEG and JPEG2000 Image Database (PDF pp. 8–10, figures and table through p. 12)
- V. Discussion and VI. Acknowledgement (PDF pp. 10–12)
- References and author biographies (PDF pp. 13–14)
Outside the original text pass
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout.
- Separate supplemental material availability has not been fully verified.
- The extraction-only visual gap was addressed by inspecting every supplied PDF page and all six final crops. No supplement was supplied.
- Identity/version note: the title and all four authors match the catalog. The PDF header identifies IEEE Transactions on Image Processing, volume 13, number 4, April 2004, but this artifact uses pages 1–14, whereas the catalog bibliography gives 600–612. No explicit revision identifier or revision date is shown. The publisher-paginated edition was not supplied or compared; textual equivalence is not asserted.
- No linked implementation, dataset, external reference or website was inspected, and no experiment was reproduced.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e01PDF p. 1, title, author line, affiliation footnote, journal header and abstract
Title and authors are Zhou Wang, Alan C. Bovik, Hamid R. Sheikh and Eero P. Simoncelli; header states volume 13, number 4, April 2004. Affiliations identify NYU/HHMI and the University of Texas at Austin.
Go to primary source ↓e02PDF pp. 1–4, Sections I, II.A–B and III.A; Figure 1
Full-reference scope; conventional error-sensitivity stages; quality-definition, suprathreshold, complexity, dependency and cognition limitations; structural preservation motivates an alternative.
Go to primary source ↓e03PDF p. 4, Figure 2(a–f), caption and Section III.A
Caption reports distorted-image MSE 210 and MSSIM values 0.9168, 0.9900, 0.6949, 0.7052 and 0.7748 for contrast, mean, JPEG, blur and impulse-noise changes respectively.
Go to primary source ↓e04PDF pp. 5–6, Section III.B, Figure 3 and Eqs. (2)–(7), (9)–(13)
Aligned signals are compared by luminance, contrast and normalized structure; stabilizers depend on dynamic range. Unit exponents and C3=C2/2 yield Eq. (13); negative structural similarity is possible.
Go to primary source ↓e05PDF pp. 7–8, Section III.C, Eqs. (14)–(17)
11×11 Gaussian weights with standard deviation 1.5 define local statistics; K1=0.01, K2=0.03; uniform mean pooling. Parameter insensitivity is described without a quantitative sweep.
Go to primary source ↓e06PDF pp. 8–9, Section IV.A, two-step search procedure and Figure 5 caption
Projected gradient ascent/descent and rescaling probe local extrema at fixed MSE; the Boat example reports MSE 2500 and MSSIM 0.3021, 0.9337 and −0.5411.
Go to primary source ↓e07PDF p. 9, Section IV.B, dataset, subjective-score and preprocessing paragraphs
29 references produce 175 JPEG and 169 JPEG2000 images. Rater counts, mostly male student sample, Z-score normalization, 1–100 rescaling, outlier removal and luminance downsampling are described; no SSIM training is used.
Go to primary source ↓e08PDF p. 9, Section IV.B image-map discussion; pp. 10–11, Figures 6–7 and captions
Original/compressed images are paired with squared-for-visibility SSIM maps and contrast-inverted absolute-error maps. Figure 7 reports Caps/Bikes PSNR 34.56/33.47 dB and MSSIM 0.9409/0.9747.
Go to primary source ↓e09PDF pp. 9–10, Section IV.B, evaluation-metric definitions
Logistic regression maps objective to subjective scores. Evaluation includes ordinary and variance-weighted correlations/errors, rank correlation and an outlier ratio based on twice subjective standard deviation.
Go to primary source ↓e10PDF p. 12, Table I, all model rows and regression/rank-order columns; Figure 8
MSSIM has SROCC 0.963 versus Sarnoff 0.947, PSNR 0.901 and UQI 0.863; nonlinear CC/MAE/RMS/OR are 0.967/3.95/5.06/0.041. No confidence intervals are tabulated.
Go to primary source ↓e11PDF p. 6, text after Eq. (13); p. 7, Section III.C; p. 9, UQI discussion; p. 12, Figure 8 caption
UQI uses zero stabilizers and square windows; MSSIM uses positive stabilizers and Gaussian windows. The authors associate UQI instability with nearly flat regions, while the comparison changes both factors.
Go to primary source ↓e12PDF pp. 11–12, Section V. Discussion
SSIM is presented as complementary to traditional approaches; optimization and extension beyond images are future directions, and other implementations of structural similarity may differ.
Go to primary source ↓e13PDF p. 8, implementation pointer; p. 9, data pointer and Sarnoff footnote; p. 12, Section VI; p. 14, references [53], [55], [58]
The source names MATLAB SSIM code, LIVE subjective data, Sarnoff JNDmetrix and VQEG regression routines as resources associated with the evaluation.
Go to primary source ↓8.5 Primary sources
Image Quality Assessment: From Error Visibility to Structural Similarity ↗
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