MQSINT

Description

Generates a raster image by interpolating image values between specified pixel locations using a Radial Basis Interpolation Algorithm. This module implements the multi-quadric scheme.

Parameters

Name	Type	Length	Value range
Input: Input vector segment *	Vector port	1 - 1
Output: Output raster channel	Raster port	0 - 1
Field Name	String	0 - 1	Default: ATTRIBUTE
Pixel X Size	Float	0 - 2
Pixel Y Size	Float	0 - 2
Flatness	Float	0 - 1	0.0 - 1.0 Default: 0.5

* Required parameter

Parameter descriptions

Input: Input vector segment

Specifies the vector segment from which the attribute values or the z coordinate will be used as the basis for interpolation.

Output: Output raster channel

Specifies the image channel to receive the interpolated result. The output channel must be 32-bit real.

Field Name

Specifies the field name that contains the elevation values.

If this parameter is specified as ZCOORD, the actual z-coordinates of the vectors are used. Field names are not case-sensitive, and they do not need to be specified in complete form. If more than one match exists, the first name is used.

The Field Name (FLDNME) parameter is required only for vector layers that contain 3-D points or contours. For 3-D lines and 3-D polygons, the z-coordinates are automatically used. For 2-D layers, the elevation values are not specified.

The same name applies to all contour and 3-D point segments specified in the input vectors (DBVS) parameter. The segments that do not satisfy this requirement can be converted to the required format using ZVALTRNS.

If a field name other than ZCOORD is specified but is not found, this function attempts to use the z-coordinates of each vertex or point; this may, however, lead to unexpected results.

Pixel X Size

Specifies, in meters, the horizontal (X) pixel resolution for the output raster channel.

If this parameter is not specified, the projection information is taken from the georeferencing segment of the input file.

This parameter applies only when a new output file (FILO) is being created.

Pixel Y Size

Specifies, in meters, the vertical (Y) pixel resolution for the output raster channel.

If this parameter is not specified, the projection information is taken from the georeferencing segment of the input file.

This parameter applies only when a new output file (FILO) is being created.

Flatness

Specifies the model parameter. This parameter takes any real value between 0.0 and 1.0.

Details

MQSINT is used to read the gray-level values for an arbitrary number of pixel locations to generate a raster image based on the multi-quadric method of interpolation between the specified gray levels.

The gray-level values are read from a vector segment in the specified input file.

The multi-quadric method of interpolation is computationally expensive. The coefficients must be calculated by solving a system of equations. The number of equations is proportional to the size of the data set. After the coefficients are calculated, the interpolation is calculated. The complexity of this calculation is based on the number of data points related to each point to be interpolated. For example, for N data points on an MxM grid, approximately NxMxM calculations are required to calculate the interpolation.

Algorithm

MQSINT implements the Multi-Quadric radial basis function interpolation scheme. This interpolation scheme is defined by mathematical series (sum of terms).

(i) Interpolation Algorithm

                  N

      f(x, y) =  SUM  a sqrt[sqr(distance((x , y ), (x, y)) + sqr(r)]
                       j                    j   j
                j = 1

MQSINT determines the set of coefficients for the interpolator by solving a system of linear equations defined at a set of control points. The result is then substituted back into the interpolator and interpolation is computed at any point by summing the series. Further mathematical justifications on how these interpolators are derived and why they work can be found in papers cited in References.

References

R.L. Hardy, "Theory and applications of the multiquadric-biharmonic method" Computers Math. Appl. , Vol. 19, No 8/9 (1990), pp 163-208.

I Barrodale, D Skea, M Berkley, R Kuwahara, R. Poeckert, "Warping Digital Images Using Thin Plate Splines", Vol. 26, No. 2 (1993), pp. 375-376.