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Structural Similarity (SSIM)

Key: ssim · Family: signal fidelity · Better: higher ↑ · Per-lead: yes

SSIM asks: do two signals have the same level, the same variation and the same shape? Instead of summing raw differences it compares three statistics, which makes it closer to how a person judges similarity. ECGEN-Eval uses a global (whole-signal) 1-D version.

Try it

The two extra cards split SSIM into a luminance term (are the means equal?) and a contrast × structure term (are the variations equal and correlated?).

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What to notice:

  • Amplitude changes lower only the contrast part, and only a little: a beat at 80 % amplitude still has SSIM near 1, while PRD calls it a 20 % error.
  • Baseline drift affects the luminance term.
  • Inverted T wave and 20 ms late reduce the correlation (structure), which is the part that matters most.

How it works

  1. For each real recording, find the nearest synthetic recording.
  2. Per lead, compute the means, variances and covariance over the whole signal, and the stabilising constants from the real signal's dynamic range \(L\).
  3. Combine them into SSIM and average; the score is the mean over leads.

The math

\[ \mathrm{SSIM}(x,y) = \underbrace{\frac{2\mu_x\mu_y + C_1}{\mu_x^2 + \mu_y^2 + C_1}}_{\text{luminance}}\cdot \underbrace{\frac{2\sigma_{xy} + C_2}{\sigma_x^2 + \sigma_y^2 + C_2}}_{\text{contrast}\times\text{structure}} \]

with \(C_1 = (0.01L)^2\), \(C_2 = (0.03L)^2\) and \(L\) the range of the real signal. The second factor equals \(c\cdot s\) when \(C_3 = C_2/2\), with \(c\) the contrast and \(s\) the Pearson correlation.

Reading the score

  • Range [−1, 1]; 1 means identical. Negative values mean anti-correlated signals.
  • This is the global form: one value per signal, not a sliding-window average as in image SSIM, so local errors are averaged out.
  • SSIM is insensitive to modest amplitude scaling, which is useful when gain differs but can hide clinically relevant voltage changes (for example low-voltage ECGs).

Use it with ECGEN-Eval

ecgen-eval eval --real real.npy --synthetic synth.npy -m ssim --output report.html

from ecgen_eval import load_ecg_npy, AVAILABLE_METRICS

real = load_ecg_npy("real.npy", fs=500)
synth = load_ecg_npy("synth.npy", fs=500)

result = AVAILABLE_METRICS["ssim"](k1=0.01, k2=0.03).compute(real.data, synth.data, lead_names=real.lead_names)
print(result.score, result.per_lead_scores)

Parameters are in the Metric Reference.

Learn more

  • Wang et al., Image Quality Assessment: From Error Visibility to Structural Similarity, IEEE TIP 2004.
  • Shahriari et al., applied to ECG signal quality in IEEE TBME 2018.