Re: spatial autocorelation methods
From: jim (_at_m.sjedging@mwt.net)
Date: 10/13/04
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Date: Wed, 13 Oct 2004 12:54:00 -0500
Ara.T.Howard@noaa.gov wrote:
>
> On Wed, 13 Oct 2004, jim wrote:
>
> > Your not being very clear in defining the problem.
>
> sorry - i'm discovering the language to describe it as i go. i'll elaborate
> as best i can. in essence we are comparing two data sets using one as the
> reference. the reference data set is of much finer resolution than the data
> set for the study. both data sets are byte images where the interpretation
> is that values above a certain value (say 11) are fires. they are not
> binary images.
>
> > I don't understand what the problem is with input data needing to be square.
> > It seems to me your data *is* rectangular and should be easily divisible
> > into squares.
>
> it seems that way, but it's not. the reason is that one of the data sets is
> of very coarse resolution and has been reprojected/regridded onto the finer
> resolution in order to do the comparison. further, the grid averaging uses
> nearest neighbor and the sensor in question has massive pixel overlap all of
> which leads to an __original__ course pixel (on coarse grid) that might look
> like this
>
> -----
> | |
> | |___
> | |
> | ----
> | |
> ----
>
> then this coarse grid is reprojected/regridded onto the fine grid so that
> this shape ends up looking the same to the eye, but being comprised of, say,
> 10000 pixels or more. this set of pixels in the fine grid originating from
> one coarse pixel set (representaon of one pixel in the coarse grid) we are
> calling the pixel 'footprint'. the reprojecting/regridding to fine res.
> step is merely to make determining the footprint an O(1) operation - it
> could be calculated on the fly of course...
>
> the task then is to do an analysis of the coarse pixels using the reference
> data as 'truth'. so what is needed is to 'cut out' (mask) all the reference
> pixels from that footprint giving you a set of reference/fine pixels looking
> something like this
>
> -----
> |...|
> |.x.|___
> |.xx...|
> |..x----
> |x..|
> ----
>
> where '.' is < 11 (not fireness) and 'x' is > 11 (fireness).
>
> remember that the coarse pixel set at this point looks like
>
> -----
> |nnn|
> |nnn|___
> |nnnnnn|
> |nnn----
> |nnn|
> ----
>
> a 'set' of pixels with all the same value since the set is merely a result
> of reproj/regrid. this is of no matter - we consider this set as one sensor
> pixel and then are doing a one to many (data to reference footprint)
> comparison.
>
> the question is then: what set of factors in the reference (fine) data
> caused a detect in the test (coarse) data?
Ok. Let's see if I understand. You have an image sensor that
produces a
coarse image that is binary (I'm guessing it arrived as binary, but
maybe you converted it). You also have the good fortune to have a high
resolution image taken at the same time (hopefully exactly the same
time). Your task essentially is to find out how the low resolution image
came to be using the high resolution as reference. I will assume you are
fairly confident the high resolution image is pretty much free of noise
and registration of the 2 images is fairly accurate. I'm also assuming
both images are in a rectangular array in computer memory.
Your approach to this is to identify where groups of coarse
pixels
exist and compare them to the corresponding pixels in the fine image.
This really doesn't make sense to me. Think of it this way - aren't you
just as interested in why a pixel in the coarse image ended up as 0 as
you are in why another became a 1.
What you really would like to know is the "point spread
function" of
each pixel in the coarse image. That is for each coarse pixel what is
the contribution of each fine pixel in the surrounding neighborhood of
that pixel (only the light within a certain radius will contribute to
that pixel). This will probably be a more or less triangle shape
function where the fine pixel at the center of the corresponding coarse
pixel will have the greatest weight and the influence of the fine pixels
will decrease as you move farther from the center. This should be fairly
uniform throughout the image if noise doesn't play any significant role,
so you should really use all the pixels in both images.
The other problem is determining the threshold that is used to
make the
coarse image. That complicates things significantly. It would really be
a lot simpler if the coarse image was grayscale also. Once you throw
information away there really isn't any good way of figuring out how to
retrieve it. After you have figured out what gray value the coarse
pixels should be (correlation will tell how well you did at that),
arriving at the threshold level used should be pretty trivial.
-jim
>
> obviously we are looking at things like:
>
> - how many total fine fire pixels where there
> - what is there total brightness
> - etc.
>
> we also want some measure of clusteredness and here the problem starts:
>
> all the code and translations of moran's index i've found work on a
> rectangular image region and i've got something like this
>
> -----
> |...|
> |.x.|___
> |.xx...|
> |..x----
> |x..|
> ----
>
> i can clip it out and then stuff it into a minimum bounding box so that it's
> something like
>
> ----------
> |----- |
> ||...| |
> ||.x.|___|
> ||.xx...||
> ||..x----|
> ||x..| |
> |---- |
> ---------
>
> but then what to fill the missing values with. all the code i've read just
> isn't prepared to deal with the situation and the uses the fact that the
> data is rectangular when computing mean, weights, etc. bascially i need to
> create my own method where the input data is flat, but the weight function
> is aware of scanline adjacency (2dness).
>
> my original post was asking if this has been done somewhere.
>
> > Also, what do you mean by cluster and clusteredness?
>
> we don't know. we are searching for a some measure that will give an
> idicator. i'm open to suggestion on the meaning of this.
>
> my post is growing too long and so i'll stop here. hopefully i've clarified
> rather than confused. again, sorry i'm not able to describe the problem
> better - this problem is outside my normal domain.
>
> kind regards.
>
> -a
> --
> ===============================================================================
> | EMAIL :: Ara [dot] T [dot] Howard [at] noaa [dot] gov
> | PHONE :: 303.497.6469
> | When you do something, you should burn yourself completely, like a good
> | bonfire, leaving no trace of yourself. --Shunryu Suzuki
> ===============================================================================
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