Fig. 3.

Fitting criteria, registration procedure and automatic picking. (A) Left panel: The squared difference (SD) fitting criterion can lead to the warped curve (x*; brown line) being distorted when the to-be-warped (x; black dashed line) and target (Tgt; black solid line) curves differ in amplitude. Middle panel: The maximum correlation (MC) criterion avoids distortion in x* (grey line) when the amplitude difference is constant over time. Right panel: The warping roughness penalty controls the relative curvature of the warping function, h(t), illustrated here as h(t)−t. Curvature tends to be greater for distorting (brown) than non-distorting (grey) warping functions. (B) Ramsay and Li [18] proposed to register the curve derivatives, x′(t) (red/blue line; right ordinate), rather than the original curves, x(t) (black line; left ordinate). The derivative indicates where a curve rises (red) and falls (blue). (C) Left panel: In the average-target (at) registration procedure, the average of the first-warped responses (W1; grey solid line) differed substantially from the average of the original responses (“Avg”; black solid line), but little from the average of the second-warped responses (W2; green dashed line). Here, this is illustrated using the broadband chirp-evoked ABRs shown in Fig. 1A. Right panel: Illustration of the pairwise (pw) registration procedure [58], which warps each individual response (current example: S23; grey and red lines) to every other individual response (current example: S2; black line). (D) Individual wave-I and -V latencies and amplitudes were extracted by finding the latencies of the waves’ peaks and troughs (short vertical red and green lines) in the structural grand-average response (average aligned response across subjects and high-pass-masking conditions) for each stimulus condition (click/chirp; bold black lines). The thin grey lines show the corresponding individual responses.