(c) Warping functions

50 100 150 200 250 300 350 400 450 500 Time, h

(d) Deformation functions

Figure 6.38. Curve registration results on pH profiles.

and temporal occurrences of landmarks. The average profile obtained after alignment by curve registration resembles reference curves structurally in both landmark locations and amplitudes of the local peaks and valleys (solid curve). Aligned pH curves are presented in Figure 6.38(b) along with corresponding mean landmark locations (vertical dotted lines). Each curve is aligned with respect to its particular landmarks allowing for comparison of similar events in the statistical analysis, hence leading to the development of more consistent MSPM frameworks. Figures 6.38(c) and 6.38(d) show warping and resulting deformation functions used during alignment of variable profiles in each batch. Deformation functions are obtained from the difference between warped and actual times, and represent a measure of time distortion required for nonlinear feature matching. The rest of the

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