Re: How are feature vectors created from simple measurements?

On 20 Feb, 21:36, "ImageAnalyst" <imageanal...@xxxxxxxxxxxxxx> wrote:
You make a bunch of measurements on your image. Each measurement
represents a "feature" (for example the brightness of the image, or
the blob count, or whatever). Each measurement goes into a linear
vector that is called the "feature vector." When you say about the
books "none of these actually tell you *how* to derive features" --
well, you're supposed to know (perhaps by looking in the books) how to
derive a feature (such as mean intensity), and not only that but
you're supposed to know WHAT features you want to put into your
feature vector. Generally YOU select the measurements that you think
best describe what you're trying to characterize about your image.
So you feature vector might be
(mean gray value, eccentricity, size, perimeter length)
and you'll have one vector for each image.
Now, you can do a 2D scatterplot of two of those dimensions against
each other, just ignoring all the other dimensions. For example,
scatter mean gray value vs. size. Just plot that for each image
regardless of what the values of eccentricity and perimeter length
are. Similarly you can scatter whatever measurement you want against
any other measurement. As you say, you may discover some interesting
patterns in the scatterplot that will help you interpret your data.
As Bala also says, you can use PCA to get new measurements that are
more representative of your images. For example, perhaps 0.5*(mean
gray value) + 8.4*eccentricity is highly correlated to drug dosage (or
temperature or whatever is causing your images to look different),
more so than just mean gray value or eccentricity alone would be. You
can even plot 3D scatterplots (e.g. in MATLAB) to better visualize
more dimensions.

In your other message, you say "Anyhow, do you believe PCA can help me
derive a representative value from a set of measurements so that I can
later use to discover patterns?" Well I'm wouldn't exactly word it
like that. What you might say is that "PCA can identify models that
I can use to give a better figure of merit for my images than just a
set of separate measurements would." For example, the model I
mentioned above might pop out of PCA and you would have had no clue
about that if you were just looking at a bunch of separate
measurements of mean gray value, eccentricity, etc.
Regards,
ImageAnalyst

On Feb 20, 12:08 pm, eleutheroskaiwra...@xxxxxxxxxxxxxx wrote:

This question is related to digital image processing. Assume there are
a number of measurements taken from an image such as mean gray value,
eccentricity, size, perimeter length and more, how can these numbers
altogether be represented by an (x, y) location in a 2D plot? I have
seen that feature vectors are used for this, how are these created
from a series of such measurements?

My main concern is to have a collection of images of the same subject,
find one or two representative values for each, plot them in 2D and
see what sort of patterns (if any) come out of it. I have Gonzalez and
Woods book on Digital Image Processing along with various other books,
but none of these actually tell you *how* to derive features, they
mostly tell you how to manipulate them with statistical classifiers,
they tell you how to deal with these representative values that I am
struggling to compute.

I am really desperate here for something that makes sense, a weblink
that shows you some methodology, a PDF, an e-book whatever!

Any help deeply appreciated :(

vector that is called the "feature vector." When you say about the
books "none of these actually tell you *how* to derive features" --
well, you're supposed to know (perhaps by looking in the books) how to
derive a feature (such as mean intensity), and not only that but

Now that I am look at this with with a fresh pair of eyes I could have
conveyed the wrong message there. Specifically in Gonzalez+Woods book
(section 9 on pattern recognition) the method I see there has various
measurements that the book calls features all in a 1D matrix (the
vector) and then just like that it talks about using statistical
classifiers on values extracted from these matrices. I feel there is a
missing link there :( which made me believe that the various numbers
in those matrices are narrowed down to one measurement. This is of
course may have to do with my knowledge on linear algebra, I could
simply be looking at the wrong direction because I hooked on the
jargon too tightly.

I have digested that a feature can be anything that is measurable.

Now I also see that doing a 2D or 3D plot can only happen against 2 or
3 values respectively. I tried myself to plot various features against
other features and saw that certain measurements exhibit some nice
grouping when put together which I thought could be my handle to start
looking for more dense groupings. Now I see that I may have mixed what
I read and saw in the pictures in the book regarding these plots, I
thought that certain features could be put altogether in a vector and
somehow narrowed down to one number to be plotted against another
number...

OK... I think I am dragging this thread now.. I'll start looking into
linear algebra for a bit, then PCA to see if there is something of use
in there .. I just hope I won't lose my direction again :(

My main goal is to gather measurements (I have these) and look only at
those that can be used to create nice dense groupings when plotted
against each other so that I can do some pattern recognition with
them.

Cheers.

.

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