Gridded Smoothing

Table > Gridded Smoothing removes noise from 3D data that lies on an X-Y grid, and produces a smooth surface you can view, export, or add to the notebook as new data.

Gridded data — a measurement at every combination of X and Y values, as from an instrument scan, a designed experiment, or a simulation — often carries noise that hides the shape of the surface. Gridded Smoothing replaces each Z value with a smoothed value that follows the trend of its neighbours along both axes. The smoothed surface and its first and second partial derivatives are continuous, so it is also a sound starting point for derivative and contour work.

Data requirements

The data should lie on an X-Y grid: every X value paired with every Y value. The spacing need not be uniform. If some grid nodes are missing, TableCurve fills them by Renka interpolation before smoothing. At least 5 grid lines are needed in each direction.

The dialog

• Algorithm. Whittaker (default) smooths the grid along each X line and each Y line and then draws the result as a cubic spline surface. P-Spline fits a penalized cubic B-spline in a single step.

• Lambda. The smoothing strength. 0 means no smoothing; larger values smooth more. Lambda is not scale-free: the right value depends on the grid size and the noise, so try a value and watch the surface and the statistics. The surface updates about one second after you stop typing.

• GCV and rGCV (Whittaker only) choose lambda for you. GCV (generalized cross-validation) picks the smoothing that best predicts each point from the others. rGCV (robust GCV) leans toward more smoothing, and is the better choice when the data has only light noise.

• Statistics. SSE (sum of squared differences between the data and the smoothed surface) and r². Heavier smoothing lowers r²; the aim is to remove noise, not structure.

• Add places the smoothed surface in the notebook as a new data node under the current one. Update replaces the result of the node the dialog was opened from. Word sends the graph and settings to Word.

• Right-click the graph for Find Optimum Visualization.

Tips

• Start with Whittaker and press GCV. If the surface still looks rough, press rGCV or raise lambda; if real ridges or peaks are being flattened, lower it.

• Compare the smoothed node with the original in the notebook to confirm that only noise was removed.

• For scattered (non-gridded) 3D data use Smooth Loess instead.