# Metric Clustering and Smoothing Dialog

This dialog is used for both clustering and smoothing of metric data.

## Surface

Choose the surface that is used when clustering or smoothing metric
column.

## Metric Column

**Input** - This is the metric column that will be modified.
You may select "All Columns" for smoothing in which case all
columns will be
smoothed.

**Output** - The output of the process will be stored in this
column. This may be an existing column or a new column. If
a new column is selected, be sure to enter its name on the right side
of this line. This control is disabled when the input is "All
Columns" in which case the data is replaced.

## Clustering

### Cluster Minimum Size

**Any Size** - clusters of all sizes are retained.

**Minimum Number of Nodes** - only clusters with at least the
specified number of nodes are retained.

**Minimum Surface Area** - only clusters with a surface area greater
than or equal to the specified area are retained.

### Cluster Value Threshold

To be in a cluster, the node must have a value within the range of the
**Minimum** and the **Maximum**.

## Smoothing Algorithms

Average Neighbors - Smooths a metric by averaging the metric's
value with the metrics from all of its neighbors.

Full Width Half Maximum -
Smooths a metric to an estimated full width half maximum.

**Gaussian** - Smooths by applying a gaussian-like weighting to the
neighboring nodes. See the Gaussian Smoothing description below.
Note: Gaussian smoothing is MUCH SLOWER that the other smoothing
algorithms.

**Weighted Average Neighbors** - Smooths a metric by averaging the
metric's value with the metrics from all of its neighbors. The
distance
of the neighbors is taken into account so that neighbors close by have
greater influence than neighbors far away.

## Smoothing Parameters

**Iterations** - This is the number of iterations of smoothing.

**Strength** - Determines how the node and its neighbors are
combined when a smoothing a node. A value of 1.0 weights to only
the neighbors affecting the output. A value of 0.0 does not use
any neighboring values, and, results in no smoothing. Values
between 0.0 and 1.0 blend the
node's metric along with the metrics of the node's neighbors.

## Full Width Half Maximum Smoothing

Prior to each iteration of smoothing, the Full Width Half Maximum is
estimated using formula 2 on page 1094 from the article Smoothing and
cluster thresholding for cortical surface-based group analysis of fMRI
data by Donald J. Hagler Jr., Ayse Pinar Saygin, and Martin I. Sereno;
NeuroImage 33 (2006) 1093-1103. If the estimated FWHM exceeds the
desired FWHM entered by the user, smoothing ceases. If the
desired FWHM is not exceeded, another iteration of smoothing is
performed. The
Iterations parameter is the maximum number of iterations of smoothing
that will be performed even if the desired FWHM is not reached.
For each iteration of smoothing, the node's new value is the average of
the node's previous value and its neighbors' values.

## Gaussian Smoothing

Gaussian smoothing applies a gaussian-like weighting to the node's
neighbors. Two gaussian functions are used with the formula
e^{-(x*x/2.0sigma*sigma)}.
For the first gaussian, X is the
distance from the neighboring node to a plane tangent to the surface at
the node being smoothed and sigma is Sigma Normal.
If the node is above the plane and greater than Normal Above Cutoff
units from the plane, the neighboring node receives a weighting of
zero. If the node is below the plane and more than Normal Below Cutoff
units from the plane, the node receives a weighting of zero. For
the second gaussian, X is the
distance from the neighboring node to the normal vector and sigma is Sigma Tangent.
If the distance from the neighboring node to the normal vector is
greater than Tangent
Cutoff units, the node
receives a weighting of zero.

Full Width Half Maximum is approximately (2.3548 * Sigma), see
http://mathworld.wolfram.com/GaussianFunction.html.

**Sigma Normal** Standard deviation for gaussian along the
node's normal vector.

**Sigma Tangent** Standard deviation for gaussian along plane
tangent to the node.

**Normal Above Cutoff ** The cutoff distance in the direction
of the node's normal vector. ("Above" a plane tangent to the node).

**Normal Below Cutoff** The cutoff distance in direction
opposite of the node's normal vector. ("Under" a plane tangent to the
node).

**Tangent Cutoff ** Cutoff distance along a plane tangent to
the node.

**Gaussian Spherical Surface**

For gaussian smoothing, all nodes within a "neighbor depth" of 5
are used when determining the neighbors of a node. This of it as
your first, second,..., fifth cousins. Or, think of it as five
(six) degrees of separation from Kevin Bacon. If a fiducial
surface was used for determining the distance to a node's neighbors,
the Euclidean (straight line) distance may be very short across a
sulcus but the geodesic distance (distance traveled on the surface) may
be very long. Unfortunately, the geodesic distance calculation is
too slow. As an result, we have chosen to approximate the
geodesic distance by using the distance between two nodes on a
sphere. If the distance between a node and its neighbors on the
sphere is greater than the maximum of the three cutoff values (normal
above, normal below, tangent), the neighboring node is ignored during
gaussian smoothing.