Integral shape averaging and structural average estimation: a comparative study

Classical signal averaging is an important operation in signal processing applications but is meaningless if shape or time variability is present among the signals being averaged. Structural Average Estimation (SAE) and Integral Shape Averaging (ISA) are recent methods that deal with these types of variability by providing a "structural average" for SAE and a "mean shape signal" for ISA that can act as a complement to the classical average in signal analysis. In this paper, these two techniques are regarded from the perspective of the time warping problem. We approach ISA using a new formalism that emphasizes the theoretical connections between the two techniques. A simulation study is then carried out to compare the two methods in three kinds of time fluctuation. Two SAE algorithms are employed, namely, Dynamic Time Warping (DTW) and Self-Modeling Registration (SMR). The discussion of the results obtained in this comparison offers specific guidelines for the application-dependent use of each approach.