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We present a technique called corrected integral shape averaging (CISA) for quantifying shape and shape differences in a set of signals. CISA can be used to account for signal differences which are purely due to affine time warping (jitter and dilation/compression), and hence provide access to intrinsic shape fluctuations. CISA can also be used to define a distance between shapes which has useful mathematical properties; a mean shape signal for a set of signals can be defined, which minimizes the sum of squared shape distances of the set from the mean. The CISA procedure also allows joint estimation of the affine time parameters. Numerical simulations are presented to support the algorithm for obtaining the CISA mean and parameters. Since CISA provides a well-defined shape distance, it can be used in shape clustering applications based on distance measures such as k-means. We present an application in which CISA shape clustering is applied to P-waves extracted from the electrocardiogram of subjects suffering from sleep apnea. The resulting shape clustering distinguishes ECG segments recorded during apnea from those recorded during normal breathing with a sensitivity of 81&#x0025; and specificity of 84&#x0025;

Corrected Integral Shape Averaging Applied to Obstructive Sleep Apnea Detection from the Electrocardiogram