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Mapping without the sun
Zhang, Jixian

P. Caccetta
* CSIRO Mathematical and Information Sciences, Private Bag 5, Wembley, Perth, Western Australia 6913,
classification, hidden Markov model, segmentation.
Here we consider a hidden Markov model for jointly estimating class label images and region boundary positions using information from
imaging sensors and region boundary starting estimates. The required final class label images and updated region boundaries are treated
as latent variables, induced from a corresponding set of observational variables. This model is motivated by the desire to incorporate
information captured and represented by boundary information from processes independent of a given classification task, and the wish to
use the information both to improve classification accuracies and to update the boundary positions based on image observations. We use
the incorporation of (possibly) incomplete forest boundary inventory data with landsat satellite observations as an example of model
Classification and/or segmentation approaches are typically
employed for estimating land use and cover type change
information from digital imaging satellite and airborne sensors.
The method used for performing the classification is generally
called the classifier, while the recorded measurements are referred
to as data. The state of the process recognised by the classifier is
labelled as belonging to a particular class. After this stage, the
labelled data are called the classification and the data are said to
have been classified. Typically results will be prepared as maps or
images of class labels.
The process of classification requires that a) the number of
possible classes are defined; and a choice of model is made for b)
assessing the information in the available data; and c) deciding the
class label after having assessed the information in the data. The
accuracy of the resulting information is a key consideration in
determining the suitability of an approach for a particular
To improve classification accuracies, there has been a long
tradition of augmenting a source of remotely sensed data with
other data, as well as many alternate methods for analysis and
classification proposed. For instance, a popular classifier is the
maximum likelihood classifier (mlc) (Rao, 1966). Early examples
of incorporating ancillary data (by using the data to specify class
prior probabilities) into this classifier was provided by Strahler,
1980. More generally, modem methods for combining multiple
sources of data, possibly for the task of classification, are
commonly referred to as data fusion methods.
Here we concentrate on the problem of combining ancillary data,
which exist as a set of closed boundaries, with mlc with the view
to improving classification accuracies. Acknowledging that the
ancillary data may be incomplete or incorrect, we wish to update
the boundary positions to better reflect the class label positions
observed from remotely sensed data while at the same time using
the boundary information to influence the class labelling. We use
as our motivation the desire to incorporate forest inventory
boundary information with the classification of time series
remotely sensed landsat TM data. In section 2.2 we specify a time
series model that is compatible with that used for current
Australian national mapping of forest presence/absence (Caccetta
et al 2003, 2007), with some extra terms to incorporate the option
for boundary updating. In section 3 we use a simple (contrived)
example of classifying a single date of imagery for forest
presence/absence while updating a boundary known to be wrong.
We note that in its single date formulation, the model has
conceptual similarities with that proposed by Wu and Albert,
2007. In section 4 we experiment with the more difficult problem
of using real inventory boundaries for improving a multi-class
forest classification problem characterised by poor class spectral
2.1 Model
Given a set Y = {Y b Y 2 , ... Y n } of n images representing n time
steps , B = {B!,B 2 ,...,B n } boundary images each composed of Bj
= {bi,b 2 ,...,b q } q region boundaries starting position (that is, each
boundary image may be composed of multiple region
boundaries), and training data sufficient to define L =
{Li,L2,...,Ln} class label images, we wish to estimate the 'true’
class label images L’ = {L’ 1 ,L’ 2 ,...,L , n } and boundary positions
B’ = {B’ 1 ,B’ 2 ,...,B’ n }. The boundary images are 2 class class-
label images having labels “inside” and “outside” (the boundary).
The model to be described is applied iteratively, successively
updating the estimates for L’ and B’, and we will use the
superscript ’ to identify those terms where information derived
from the previous iteration is used.