ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision‘, Graz, 2002
2. STUDY AREA AND DATA
2.1 LIDAR data
LIDAR data were acquired with a Saab TopEye system over a 5
km” area within Capitol State Forest, WA in the spring of 1999.
The sensor settings and flight parameters are shown in Table 1.
Data were provided in the form of an ASCII text file, with GPS
time, aircraft position, and coordinate position for the first laser
reflection included.
Flying height 200 m
Flying speed 25 m/s
Swath width 70m
Forward tilt 8 degrees
Laser pulse density 3.5 pulses/m?
Laser pulse rate 7000 pulses/sec
Table 1. Flight parameters and LIDAR system settings.
The LIDAR vendor also provided a LIDAR-derived digital
terrain model (DTM) for the study area with a 4.57-meter (15-
ft) resolution.
2.2 Aerial photography
Large-scale (1:7000) normal-color aerial photography was
acquired over the study area in 1999. This photography was
oriented in an analytical stereoplotter.
3. METHODS
3.1 Bayesian image analysis
In general, Bayesian image analysis provides a means to
incorporate prior knowledge or beliefs into the analysis of
remotely sensed data (Besag, 1993). These a priori beliefs are
represented in the form of a prior distribution, or prior model,
that is placed over the image and is updated upon observation of
the data. Formally, if this prior description of the image is
denoted as p(x), then the conditional spatial distribution of this
description, given the observed image y, is given by:
p(x| y) e I(y | x) p(x) (1)
In Bayesian parlance, this conditional distribution p(x|y) is
referred to as the posterior distribution, on which all inferences
are based. In Bayesian inference this posterior distribution is
always represented as the product of the /ikelihood K(y|x) and the
prior p(x) Typically, the goal in Bayesian inference is to
calculate expectations or credible intervals (explicit probability
statements made regarding the range of a parameter given the
observed data).
Bayesian image analysis has traditionally been carried out using
digital images consisting of a discrete grid of picture elements
(or pixels). Often the objective is to reconstruct an "underlying"
image that has been distorted through a noise process.
3.2 Bayesian object recognition
More recently, the methods of Bayesian image analysis have
been applied to the problem of object recognition (Baddeley
and van Lieshout, 1993; van Lieshout, 1995; Rue and
Syversveen, 1998; Rue and Hurn, 1999). The objective of this
type of analysis is typically to locate and characterize various
objects of interest in space, incorporating prior knowledge of
the spatial distribution of these objects. Therefore, prior models
based upon discrete grid-based neighborhood structures tend to
be less appropriate. The description of Bayesian object
recognition presented here generally follows van Lieshout
(1995).
In Bayesian object recognition, the observed data consist of an
image, y=(y,;teT)» where T (the image space) is an arbitrary
finite set. The class of possible objects U, is an arbitrary set,
termed object space. Objects can be seen as points in U, and
each determine a subset R(u)c T of image space that is
occupied by the object. Any particular configuration is a finite
set of distinct objects x =] ad xd The objective in
object recognition is to estimate the (unobserved) true
underlying pattern x given the observed image y.
This true configuration x is related to the observed image y
through the likelihood function /(y[x). As van Lieshout (1995)
describes, the likelihood /(y|x) represents both the deterministic
influence of the true configuration x, and the stochastic effects
within the remote sensing process that produces the image, y.
In a Bayesian analysis, the prior models will represent our prior
beliefs regarding the spatial distribution of objects, and can be
formulated to assign low probability to configurations that we
do not expect to occur frequently, such as a large number of
overlapping objects. The maximum a posteriori (MAP)
estimator of x is the configuration X that maximizes the function
((y\<)p(x), and the prior essentially is a penalty assigned to this
maximization. Therefore MAP estimation is also called
penalized maximum likelihood estimation.
3.3 Bayesian object recognition for the analysis of three-
dimensional LIDAR data in forested areas
While Bayesian object recognition has previously been applied
to the analysis of two-dimensional images, this approach can
also be applied to analyze structure within three-dimensional
LIDAR data. In this case, the observed data, y,, are not defined
in terms of a raster image space, 7. Instead, the scan space
becomes a collection of vectors, 7, determined by the LIDAR
scanning process. Therefore, an individual pulse vector, f,
represents the three-dimensional direction of each LIDAR
pulse, from the aircraft to the terrain surface. The observed data,
ys then represent range measurements along these vectors at
which point the returning signal intensity exceeded a
predetermined threshold (see Figure 1).
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