So, when we think about variables, data,
I think about them as states.
And in order to get to these variables,
we have to work out a measurement process.
This is fundamentally important.
Underneath that measurement process,
we’re probably thinking about processes.
And so,
this diagram is really fundamental
to everything that I am saying today.
The idea that reality is out there somewhere
and we obtain data on reality
through a sampling framework.
So data,
the things that we handle
and all of you are handling in your PCs
and in your work etc.,
they are a function of 2 things.
They are a function of reality,
what’s out there,
and the sampling framework.
If we change the sampling framework,
we change the data.
And we often forget that.
So that’s fundamentally what this is about.
We’re going to start by looking at the
measurement processes in detail
as part of the motivation.
Sampling processes and measurement data.
So sampling processes,
could be divided as, sort of, a number of parameters.
These are:
the Extent,
Scheme,
and the Support.
These concepts might not be so familiar.
In this particular example,
the extent is just a square space,
where we define the space of the sampling.
And within that, we do 2 things.
We have the geometry, and size, etc.,
or the Scheme—
the number of observations and their arrangement.
We also have a Support.
The support is the space on which
each individual observation is defined.
And for each observation,
we define a measurement error
that is added to each observation.
So data is now a function of a sampling framework
and some uncertainty that we have.
We’re going to focus in here, on one particular part,
which is the Support—
the space in which these observation is defined.
Now support is important in a variety of different fields.
And we think about handling the support in different ways.
For example, in regularization,
in geostatistics,
concepts in relation to variogram.
The Modifiable Areal Unit Problem
where I’m handling census data,
Stan Openshaw’s work and many others.
David Wong and many many others.
Fractals.
Data fusion,
the idea when we have different observations
on the same underlying scene,
we can fuse those observations in order to
get closer to the underlying scene.
And in remote sensing
which is the focus of today’s talk.
So in remote sensing, we have a trade-off
between resolution and frequency and coverage.
So for example Landsat Thematic Mapper
has a return period of 16 days
in a resolution of 30 meters
but MODIS has a daily return period
and a resolution of 250, 500,
or 1 km spatial resolution.
And so,
we have a sort of trade-off for resolution
for frequency of coverage and the extent.
So in a sense,
for remote sensing,
the support defines the sampling framework.
And so,
the support becomes the basis of choice.
What resolution do we need
in order to do a particular job.
So we often think about choosing the images
based on the resolution because the resolution
defines the sampling framework.
Also in remote sensing we have a thing called
“Complete Coverage”.
We often talk about
the benefit of remote sensing
as being an image providing
complete coverage.
But does it?
Does it really?
Does an image really provide a complete coverage?
Is there something missing?
And when we have a proliferation of
images in remote sensing,
it’s a massive field these days,
I mean in East Copernicus program
we have multiple different sensors
being launched providing images of different resolution,
different wavebands etc.
So fusion becomes an important issue,
how to put all these data together.