So here's an example of 18 different moves,
and it's showing you some of the motion history, motion energy images of it.
So we now have this problem of how do we recognize motion energy,
motion history images.
Well, these are kind of gray-scale blobby-like images.
And the good news is even in 1999, there have been about 150 years, or maybe
20 years, pick your favorite number, of computer vision describing gray blobs.
And trying to say,
okay, I recognize this gray blob as being different than that gray blob.
And that's basically all we had to do.
So, basically, 1999, we did some sort of,
what I think of as old style computer vision we're going to compute some,
summarization statistic of that blob.
We're going to compute some features of that blob that have something to do with
the distribution of the, where the pixels are and
their intensities in the MHI, and we're going to build the generative model.
Okay. There are a couple reasons we were doing
generative models.
One is that discriminative models hadn't become as popular as they had been and
so Jim Davis' advisor was not smart enough to tell him to
go make sure you're using the discriminative model.
I will tell you that people have subsequently used it, and of course,
it makes your recognition better.
Generative models also have the nice properties as we mentioned before,
that when I come in, if I come up with a new, aerobics move, right, so
I want to add one, I just have to build a model of that category.
I don't have to, to retrain my entire system.
Okay, whether you use generative or discriminative,
the idea is that we're going to compute these statistics and
then do the recognition.
So, how are we going to describe this sentence?
And this allows me to spend a little bit of time telling you about some very old
computer vision work that becomes, that's still important, and fundamental.
And that's the notion of the moments of a shape.
So, so some of you from physics, you know about second order moments, right?
Axis of inertia.
The moment is the distribution of matter about a point or an axis or
something like that.
So in computer vision, the moments are defined in a very simple way, right?
So the I J moment, okay, is just the sum over
the X Y of the whole image of X raised to the I power, Y raised to the I power.
But you're only counting points where the image is non-zero.
Okay?
So, if I is a binary image, then this is a one or zero, so
you're only counting it at points that are turned on.
If it's a grayscale image, then you're weighting the point by essentially how
heavy it is, which is a little bit like when you do moments of inertia.
If you've got little points that are heavier than others,
they add more to the inertia without the axis.
So these are the moments, and so you can talk about the second order moments,
or the first order moments, or even the zeroth order moments, right?
What would this be for the zeroth order moment?
Well, if I is zero and J is zero then these are one,
this would just be counting up the number of non-zero pixels.
Which means that M zero zero is the area.
[NOISE] Right?
because the area of the picture that's non-zero, that's just the sums,
the counting of the non-zero pixels.
All right?
The problem with regular moments, of course,
is that they're sensitive to what the X and Y position actually is.
Right? So,
you kind of want the moments of a shape to be independent of where the shape is.
So there's something called the central moments that just take X, but
they subtract off the mean of X, and Y, and subtract off the mean of Y.
And it is, otherwise just the same.
So, that's this Mu P Q, and it's X minus X bar to the P, Y minus Y bar to the Q.
All right?
And, you know, what is X bar?
Well, one way of thinking, it's the average X, so the average X
would just be the sum of all the Xs divided by however many Xs there are.
Well, that's what this is, right?
X bar is M one zero, the first moment in X divided by the overall area,
remember the M zero zero, same thing in Y.
So that's regular moments, but the problem with moments,
of course, is that they're very sensitive to a variety of changes,
so if I scale the image up, right, obviously, the moment's going to change,
the area will get bigger, the distances get, get larger.
If I rotate it things might change.
All sorts of problems.