# Qimera Apply Spline Filter Dialog

## How to Start

*Apply Spline*option from*Dynamic Surface*menu of Main Menu bar

## What it Does

This dialog allows you to change the parameters and options used by the spline algorithm.

## General Description

The underlying principle of this filter is that it attempts to fit a surface through noisy multibeam echosounder data and clip all footprints that lie too far from this surface.

the Spline Filter does more or less the same as a data processor would do manually: it attempts to determine what the bottom, or a feature on the bottom, is by fitting a surface spline through the noisy footprint data and filter out any footprints that lie far away from this surface. This is done in two passes:

- The first pass will filter large blunders to create a well-fitting surface spline.
- A second pass will filter noise.

The surface spline used in this algorithm is known in literature as a Thin Plate Spline see: (Bookstein, 1989). “The Tin Plate Spline is the two-dimensional analog of the cubic spline in one dimension.” (Belongie)

### The First Pass.

A surface spline will be deformed if large spikes are present. In other words, blunders (large spikes in the data) have an effect on the fitted surface. These spikes need to be removed to achieve a surface that fits ‘nicely’.

A surface spline is considered a nice fit, if the RMS of all differences between the surface and the actual points is smaller than the set threshold. This value will be called the deviation in this report and is expressed as Pα.

The threshold is the first filter parameter and is expressed as a percentage (default 0.5%) of the depth.

As the surface is calculated if the deviation is larger than the threshold, four points are removed from the spline dataset:

- the footprint with the maximum height,
- the footprint with the minimum height,
- the footprint with the largest positive difference with the surface and
- the footprint with the largest negative difference with the surface.

The surface is then recalculated and if the deviation is now below the threshold, the surface is determined to be a ‘nice’ fit. If the deviation is still above the threshold, four points are removed again, as described above and a surface is fitted again. This process iterates until either the deviation target is reached, or more than half of the initial points are discarded.

As soon as a surface, that fits nicely, is available, all points that have a larger difference than are filtered out. The parameter is the first-pass SD factor.

### The Second Pass

Once the largest errors are filtered all remaining points are used for new spline surface. This second pass (C2.Pα) is then used to filter out all the soundings with a Standard Deviation difference greater than C2.

Note that points that where filtered in the first pass can be unfiltered in this pass. This is needed since the surface that was determined in the first pass was calculated with a reduced dataset.

#### Filter parameters

To summarize, the Surface Spline filter has four relevant parameters.

- The number of points processed at once. If this number is reduced, the filter takes significantly less computation time, but accuracy is affected. Intuitively, one can understand that if not enough points are considered, a local cluster of blunders may be considered as a valid surface. The number of points should be set as high as possible, while a reasonable filter speed is maintained. A higher number of data points will allow the filter to more accurately follow the surveyed terrain.
- The first-pass SD factor. Recommended range: [1.0 … 4.0], where 1.0 is a strong filter action and 4.0 a weak one. It is important that this factor is set to such a value that large blunders are eliminated, so it should not be too high. Since the surface spline determined in the first pass is not as accurate as the spline of the second pass, this factor should also not be set too low, to prevent the accidental filtering of valid data points. A good starting point seems to be: 2.0.
- The second-pass SD factor. Recommended range: [1.0 … 4.0]. This is the most important parameter in my opinion. Once a surface with a certain difference to the original data points has been determined, this parameter determines if a point is filtered or not.
- Approximation factor, expressed in a percentage of the depth. This is similar to the IHO orders that specify a minimal vertical TPU to be achieved when surveying. One can say that the expected accuracy of the survey must be used as this parameter.

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