Curve registration produces more accurate results in time-continuous analysis (e.g. PCA) of biomechanical signals, which have a sensitivity towards time-varying events. Signals in a dataset typically exhibit variation in amplitude and phase. When physical time may not impact or be relevant to real-life systems, the curves can be aligned on a system time rather than a clock time to correct phase variation. This is achieved by registering the curves to a specific landmark. In biomechanics and gait analysis, curves are registered by certain events - such as the maximum or minimum of a signal - to see a better representation of amplitude variation.

See the supporting literature.

Curves are registered by applying a time warping function, h(t), on the original curve, x(t), where x*(t) is the registered curve.

     x*(t) = x[h(t)]

The time warping function is unique to each curve and transforms the physical (typically clock) time to the system time. This requires a landmark for the whole system to be registered, by taking the mean location of a landmark across all curves. The time warping function then adjusts each individual curve so that the curve specific landmark happens at the same time through linear interpolation. The time warping ensures that the following equation is always satisfied. h⁻¹(t) is the inverse wrapping function, required to compute the registered curve values. It is used to map the registered time back to the original function values via interpolation.

     h⁻¹ [h(t)] = t

Located in the Explore Page, Curve Registration enables the alignment of curves to a shared landmark or event, with results viewable as a group. Curves can be registered by maximums, minimums, local maximums, local minimums, and defined intermediate events.

To register a curve, navigate to the Explore Page, select a group and the desired workspaces, then select the Register button. This will open a dialog to configure the registration settings.

In this example, the KneeAngleX query is selected for registration. The curves are registered to a local minimum between 25 and 50, and a local maximum between 60 and 90. The difference between the original curves (left) and the registered curves (right) is shown below.

In this example, the AnkleAngleX query is selected for registration. The curves are registered to the event sequence LHS, RHS, LHS.

Note: Event sequences must be defined in the query builder and must contain at least three events.

The difference between the original curves (left) and the registered curves (right) is shown below.

Curve registration results can be exported as an image or as text file containing all data points. To export an image of the plot, right-click on it to open the context menu and select Export. A dialog will appear to specify the image format and dimensions.

To export the data, navigate to the Export Results tab on the tool bar to open the Export Results Dialog. Change the Export Type to Registered Curves and export the results. The available export options include registered traces, warping functions, landmark mean locations, and original landmarks for all traces.

[1] J. O. Ramsay, Xiaochun Li, Curve Registration, Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 60, Issue 2, July 1998, Pages 351–363, https://doi.org/10.1111/1467-9868.00129