Package 'MBA'

Canopy LIDAR data

Description

This is a small portion of Light Detection and Ranging (LIDAR) data taken over a forested landscape in Wisconsin, USA.

Usage

data(LIDAR)

Format

A data frame containing 10123 rows and 3 columns corresponding to longitude, latitude, and elevation.

Source

Data provided by: Dr. Paul V. Bolstad, Department of Forest Resources, University of Minnesota, [email protected]

---

Point approximation from bivariate scattered data using multilevel B-splines

Description

The function mba.points returns points on a surface approximated from a bivariate scatter of points using multilevel B-splines.

Usage

mba.points(xyz, xy.est, n = 1, m = 1, h = 8, extend = TRUE,
           verbose = TRUE, ...)

Arguments

xyz	a $n \times 3$ matrix or data frame, where $n$ is the number of observed points. The three columns correspond to point x, y, and z coordinates. The z value is the response at the given x, y coordinates.
xy.est	a $p \times 2$ matrix or data frame, where $p$ is the number of points for which to estimate a z. The two columns correspond to x, y point coordinates where a z estimate is required.
n	initial size of the spline space in the hierarchical construction along the x axis. If the rectangular domain is a square, n = m = 1 is recommended. If the x axis is k times the length of the y axis, n = 1, m = k is recommended. The default is n = 1.
m	initial size of the spline space in the hierarchical construction along the y axis. If the y axis is k times the length of the x axis, m = 1, n = k is recommended. The default is m = 1.
h	Number of levels in the hierarchical construction. If, e.g., n = m = 1 and h = 8, the resulting spline surface has a coefficient grid of size $2^h$ + 3 = 259 in each direction of the spline surface. See references for additional information.
extend	if FALSE, points in xy.est that fall outside of the domain defined by xyz are set to NA with a warning; otherwise, the domain is extended to accommodate points in xy.est with a warning.
verbose	if TRUE, warning messages are printed to the screen.
...	currently no additional arguments.

Value

List with 1 component:

xyz.est

a $p \times 3$ matrix. The first two columns are xy.est and the third column is the corresponding z estimates.

Note

The function mba.points relies on the Multilevel B-spline Approximation (MBA) algorithm. The underlying code was developed at SINTEF Applied Mathematics by Dr. Øyvind Hjelle. Dr. Øyvind Hjelle based the algorithm on the paper by the originators of Multilevel B-splines:

S. Lee, G. Wolberg, and S. Y. Shin. (1997) Scattered data interpolation with multilevel B-splines. IEEE Transactions on Visualization and Computer Graphics, 3(3):229–244.

For additional documentation and references see:

https://www.sintef.no/upload/IKT/9011/geometri/MBA/mba_doc/index.html.

See Also

mba.surf

Examples

data(LIDAR)

## Split the LIDAR dataset into training and validation sets.
tr <- sample(1:nrow(LIDAR), trunc(0.5*nrow(LIDAR)))

## Look at how smoothing changes z-approximation,
## careful the number of B-spline surface coefficients
## increases at ~2^h in each direction.
for(i in 1:10){
  mba.pts <- mba.points(LIDAR[tr,], LIDAR[-tr,c("x","y")], h=i)$xyz.est
  print(sum(abs(LIDAR[-tr,"z"]-mba.pts[,"z"]))/nrow(mba.pts))
}

## Not run: 
## rgl or scatterplot3d libraries can be fun.
library(rgl)

# Exaggerate z a bit for effect and take a smaller subset of LIDAR.
LIDAR[,"z"] <- 10*LIDAR[,"z"]
tr <- sample(1:nrow(LIDAR), trunc(0.99*nrow(LIDAR)))

# Get the "true" surface.
mba.int <- mba.surf(LIDAR[tr,], 100, 100, extend=TRUE)$xyz.est

# Make nice colors for the rgl surface.
zlim <- range(mba.int$z)
zlen <- zlim[2] - zlim[1] + 1

colorlut <- terrain.colors(zlen) # Height color lookup table.

col <- colorlut[mba.int$z - zlim[1] + 1 ] # Assign colors to heights for each point.

open3d()
surface3d(mba.int$x, mba.int$y, mba.int$z, color = col)

# Now add the point estimates.
mba.pts <- mba.points(LIDAR[tr,], LIDAR[-tr,c("x","y")])$xyz.est
spheres3d(mba.pts[,"x"], mba.pts[,"y"], mba.pts[,"z"],
          radius=5, color="red")

## End(Not run)

---

Surface approximation from bivariate scattered data using multilevel B-splines

Description

The function mba.surf returns a surface approximated from a bivariate scatter of data points using multilevel B-splines.

Usage

mba.surf(xyz, no.X, no.Y, n = 1, m = 1, h = 8, extend=FALSE,
         sp=FALSE, ...)

Arguments

xyz	a $n \times 3$ matrix or data frame, where $n$ is the number of observed points. The three columns correspond to point x, y, and z coordinates. The z value is the response at the given x, y coordinates.
no.X	resolution of the approximated surface along the x axis.
no.Y	resolution of the approximated surface along the y axis.
n	initial size of the spline space in the hierarchical construction along the x axis. If the rectangular domain is a square, n = m = 1 is recommended. If the x axis is k times the length of the y axis, n = 1, m = k is recommended. The default is n = 1.
m	initial size of the spline space in the hierarchical construction along the y axis. If the y axis is k times the length of the x axis, m = 1, n = k is recommended. The default is m = 1.
h	Number of levels in the hierarchical construction. If, e.g., n = m = 1 and h = 8, the resulting spline surface has a coefficient grid of size $2^h$ + 3 = 259 in each direction of the spline surface. See references for additional information.
extend	if FALSE, a convex hull is computed for the input points and all matrix elements in z that have centers outside of this polygon are set to NA; otherwise, all elements in z are given an estimated z value.
sp	if TRUE, the resulting surface is returned as a SpatialPixelsDataFrame object; otherwise, the surface is in image format.
...	b.box is an optional vector to sets the bounding box. The vector's elements are minimum x, maximum x, minimum y, and maximum y, respectively.

Value

List with 8 component:

xyz.est	a list that contains vectors x, y and the $no.X \times no.Y$ matrix z of estimated z-values.
no.X	no.X from arguments.
no.Y	no.Y from arguments.
n	n from arguments.
m	m from arguments.
h	h from arguments.
extend	extend from arguments.
sp	sp from arguments.
b.box	b.box defines the bounding box over which z is estimated.

Note

If no.X != no.Y then use sp=TRUE for compatibility with the image function.

The function mba.surf relies on the Multilevel B-spline Approximation (MBA) algorithm. The underlying code was developed at SINTEF Applied Mathematics by Dr. Øyvind Hjelle. Dr. Øyvind Hjelle based the algorithm on the paper by the originators of Multilevel B-splines:

S. Lee, G. Wolberg, and S. Y. Shin. (1997) Scattered data interpolation with multilevel B-splines. IEEE Transactions on Visualization and Computer Graphics, 3(3):229–244.

For additional documentation and references see:

https://www.sintef.no/upload/IKT/9011/geometri/MBA/mba_doc/index.html.

See Also

mba.points

Examples

## Not run: 
data(LIDAR)

mba.int <- mba.surf(LIDAR, 300, 300, extend=TRUE)$xyz.est

# Image plot of the surface.
image(mba.int, xaxs = "r", yaxs = "r")

# Perspective plot of the surface.
persp(mba.int, theta = 135, phi = 30, col = "green3", scale = FALSE,
      ltheta = -120, shade = 0.75, expand = 10, border = NA, box = FALSE)

# For a good time, I recommend using rgl.
library(rgl)

# Exaggerate z a bit for effect.
mba.int$z <- 10*mba.int$z

# Make nice colors for the rgl surface.
zlim <- range(mba.int$z)
zlen <- zlim[2] - zlim[1] + 1

colorlut <- terrain.colors(zlen) # Height color lookup table.

col <- colorlut[mba.int$z - zlim[1] + 1 ] # Assign colors to heights for each point.

open3d()
surface3d(mba.int$x, mba.int$y, mba.int$z, color = col)


## End(Not run)

---