Apple Inc. v. Samsung Electronics Co. Ltd. et al

Filing 558

REPLY CLAIM CONSTRUCTION BRIEF to re #461 Claim Construction Statement Pursuant to Patent L.R. 4-5 by Apple Inc.. (Attachments: #1 Declaration, #2 Exhibit R, #3 Exhibit S, #4 Exhibit T, #5 Exhibit U, #6 Exhibit V)(Jacobs, Michael) (Filed on 12/29/2011) Modified text on 12/30/2011 (dhm, COURT STAFF).

EXHIBIT T

Page 1
BEFORE THE
UNITED STATES INTERNATIONAL TRADE COMMISSION
___________________________
In the Matter of:

)

Investigation No.

CERTAIN MOBILE DEVICES

)

337-TA-750

AND RELATED SOFTWARE

)

___________________________
Hearing Room A

United States
International Trade Commission
500 E Street, Southwest
Washington, D.C.

Friday, September 23, 2011

PREHEARING AND TUTORIAL

The parties met, pursuant to the notice of the
Judge, at 9:00 a.m.

BEFORE:

THE HONORABLE THEODORE R. ESSEX

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OPEN SESSION
MR. DAVIS: We're ready, Your Honor.
JUDGE ESSEX: You found him, did you?
MR. DAVIS: We did, indeed.
JUDGE ESSEX: If you would remain
standing for just a moment and raise your right
hand for me.
Whereupon-WAYNE C. WESTERMAN,
having been first duly sworn, was examined and
testified as follows:
JUDGE ESSEX: Please be seated.
DIRECT EXAMINATION
BY MR. DAVIS:
Q. Dr. Westerman, could you please state
your entire name?
A. Wayne Carl Westerman.
Q. And you have in front of you a witness
binder. Could you turn to the first exhibit?
It is marked as CX-208C. It is entitled the
witness statement of Wayne Westerman. Let me
know when you find that.
A. Yes.
Q. And if you can look through that. Is
that the witness statement that you submitted

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in connection with this investigation?
A. Yes.
Q. And if you could turn to page 10. Is
that your signature that appears there?
A. Yes.
Q. Okay. And does this witness statement
contain your answers to the questions that are
set forth therein?
A. Yes.
MR. DAVIS: Your Honor, we turn the
witness over for cross.
MR. NELSON: Thank you, Your Honor.
CROSS-EXAMINATION
BY MR. NELSON:
Q. I think I have some material to pass
out here. Good afternoon.
A. Good afternoon.
Q. I am Dave Nelson. I don't think we
have met before, but I am going to ask you some
questions, all right?
A. Okay.
Q. Good. Let's put JX-3 up here. Now,
JX-3, a patent entitled ellipse fitting for
multi-touch surfaces, 7,818,828. Do you see
that?

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A. Yes.
Q. You are a named inventor on this
patent, correct?
A. That's correct.
Q. And you have one other joint inventor
on that; is that right?
A. That's right.
Q. And what is that gentleman's name?
A. John G. Elias.

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Q. But the '828 patent, you agree that
primarily concerns mathematical fitting of
ellipses to pixel groups that are received from
a touch sensing device; is that a fair
characterization?
A. Yeah, that's a fair characterization
of the claims.
Q. Okay. Of the claims of the '828
patent?
A. Yeah.
Q. Okay. So let's talk a little bit
about this elliptical fitting. The primary
reason that you wanted to do this elliptical
fitting was so that you could distinguish one
hand part from another on a touch device; is
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that right?
A. I'd say that's the primary reason. It
is not the only reason.
Q. But that is the primary reason?
A. Yeah.
Q. So let's look at this dissertation.
Can we put up -- well, it is JX-291. You have
it in the book if you want to look at the
original. Sometimes that is easier than the
screen.
A. Okay.
Q. Let's put up RDX-18.002. I have some
excerpts from here.
So this excerpt that I have on
RDX-18-002 is from your dissertation at page
19. So here you say, "nevertheless,
distinguishing palm contacts from finger
contacts on a large MTS is imperative for the
motion recognition algorithms to ignore palm
motions and allow palms to rest on the
surface."
Do you see that?
A. Yes.
Q. So, first of all, MTS, is that
multi-touch surface?

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A. Yes.
Q. And so is that, that idea expressing
this concept that we just talked about, the
idea of being able to distinguish one hand part
from another?
A. That's one example, yes.
Q. Okay. And, similarly, down here at
the bottom, I have this sentence highlighted,
"identifying the thumb and maintaining a
consistent order for other finger contacts also
aids extraction of hand motion parameters."
Is that, again, that idea of being
able to recognize one -A. That's one example.
Q. We have to get a little rhythm here.
So I know that sometimes it doesn't seem like I
am done with -- or it seems like I am done, but
it takes me a little while sometimes. I
apologize. So let me start that over.
So this last sentence here identifying
thumb and finger contacts, that's, again, this
notion of being able to distinguish one hand
part from another, correct?
A. That's another example, yes.
Q. And if we look at page 84 now, it is

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on the next slide, RDX-18.3, here it says,
"while the user will not vary contact shape or
orientation intentionally, such parameters will
assist finger and hand identification in
chapter 4."
Do you see that?
A. Yes.
Q. Now, if you look -- and why don't we
put up the JX-291 at page 84 here.
So page 84 of your JX-291, this is
your dissertation, correct?
A. Yes.
Q. And this is in the ellipse fitting
section. So that sentence that I just pulled
out, if I look at it again, we can highlight it
here, Ryan. That's fine.
"While the user typically will not
vary contact shape or orientation
intentionally, such parameters will assist
finger and hand identification in chapter 4."
So are the parameters that you are referring to
there the parameters that are generated from
the ellipse fitting procedure?
A. Yes, contact shape and orientation
generally, yes.

Q. So that, again, that's consistent with
this idea that you talked about that you wanted
to be able to precisely fit ellipses to the
pixel group so you could identify one finger
from another, right?
A. Right, but elsewhere, I do -somewhere in the patent and the dissertation, I
do, you know, mention the possibility of
actually controlling something with the
rotation of your thumb or the orientation of
your thumb.
Q. Right. And that would be another
thing that you might want to do, recognize
exactly how the thumb is oriented and fitting
this ellipse precisely to that thumb touch
would help you do that, right? We've got to
get your audible answer.
A. Yes.
Q. Okay. Thank you.
So let me go to RDX-4 now. So this is
from your dissertation now into chapter 4 that
we just saw referred to on the previous page
that we looked at, page 84. This is now at
page 116 of your dissertation.
Here you say, "if the MTS" -- again,
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the multi-touch surface -- "was only to be used
for typing, trying to identify each surface
contact might not be worthwhile because key
taps should be distinguished by their spatial
location, not which finger strikes the key."
Do you see that?
A. Yes.
Q. So there, the idea, what you are
saying at least in the dissertation is if all
you are trying to do is detect key taps, then
you don't necessarily need to be able to
distinguish one finger from another, correct?
A. Yeah. I think you should keep in mind
I am talking specifically there about fingers,
and I don't think I would have said the same
thing about palms because if a palm tapped a
key, you would want to ignore it, right? But
maybe it doesn't matter whether it is the index
finger or the middle finger for typing.
Q. Right. You don't need to know which
specific one, just generate the key taps.
Now, with the palm, there are ways you
can detect the palm without knowing it as the
palm, correct? Meaning it is a fairly large
contact area, right?

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A. Well, that's another big topic of the
dissertation. I wouldn't simply -- want to
oversimplify that, yeah, there is a lot of -generally, for detecting palms, you need -- you
often need multiple clues at once, but that's
one of them, is the large size, yes.
Q. Okay. So then here, the next
sentence, you say, "but recognition of the
rich, bimanual chordic manipulations
demonstrated in chapter 5, demands reliable
clustering of surface contacts with their
originating hand as well as reliable finger
ordering and thumb identification within each
hand."
Do you see that?
A. Yes.
Q. So the idea was that you wanted to be
able to precisely detect which finger was
touching the screen, multiple fingers touching
the screen, the orientation of those fingers so
that you could implement these bimanual chordic
manipulations, right?
A. Yes, that was an important objective,
but I believe all along at the same time I was
-- another, as I say, another big part of doing

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a good multi-touch system is ignoring things
such as palms.
And so it is not just identifying the
fingers. It is identifying palms and other
instances where you want to -- fingers are
applied and situations where you want to ignore
contacts and reject them also.
Q. Sorry. I didn't mean to talk over
you. Are you done?
A. Um-hum.
Q. So then what you are saying is what
you wanted to be able to do was precisely
identify fingers, hand parts, some of which you
want to know their orientation and which finger
it is, others you want to ignore, correct?
A. Um-hum, yes.
Q. Okay. And the way that you are able
to distinguish these hand parts from one
another -- let me start over.
In order to be able to do that, what
you did was invented a very precise way to do
the measurements of touch data and help the
multi-touch system tell you useful things about
those touches, right?
A. Yeah, it is a combination -- I did

measurements of the shape and orientation of
individual touches and then another part of the
dissertation is the overall arrangement of the
touches relative to one another. That is sort
of the inter-touch geometry is also -- also
provides important clues.
Q. And at least part of that precise way
to do this detection was this ellipse fitting
procedure that we looked at in section 3,
starts at around page 84 of your dissertation,
correct?
A. Yes.
Q. Okay. And now in order for this
ellipse fitting procedure to be useful and
detect these various things, these precise
touches and what part it is and what the
orientation of the finger was, it needed to be
precise, correct?
A. Yes.
Q. And if we look back at the
dissertation at page 84, this would be JX-291,
and let's just put it up there, no, page 84,
you had it right. Okay, good.
So on page 84 here in the
dissertation, this is the precise ellipse
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fitting procedure that you described, correct?
A. I believe it continues on to the next
page.
Q. Okay. It continues on to the next
page.
A. To the end of that section, including
the paragraph after equation 320.
Q. Yeah, okay. So we will talk about
that in a minute. Let me go back up to the
beginning of this.
So you say at the very end of that
first paragraph in this ellipse fitting
section, "the ellipse fitting procedure
requires a unitary transformation of the group
covariance matrix Gcov of second moments Gxx,
Gxy, and Gyy, correct?
A. That's what I say, yes.
Q. So that's the precise ellipse fitting
procedure that you were describing, correct?
A. Well, that's just the first step.
Unitary transformation means a rotation of the
coordinate system of the matrix.
Q. Then the rest of the steps are found
from 3.12 down to 3.18?
A. Yeah, once you find the Eigenvalues

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and Eigenvectors covariance matrix, which are
part of doing a unitary transformation off of
that -- the axis where the data is spread out
the most, it would be like the long axis for
thumb, the long axis, you rotate your
coordinate system to there, and that procedure
leads to Eigenvalues and Eigenvectors.
Equations 316 through 318, I show how to get
major radius, minor radius and orientation from
those Eigenvalues.
Q. And those equations then will give you
the parameters of the ellipse that you are
trying to fit to the touch data, correct?
A. Yes, in this case.
Q. Now, let's go to JX-3. Column 26,
Ryan, of JX-3. And let's pull that out a
little bit. Yeah, start with the since -about line 18, 17. Can you get the last three
equations in there?
So then here in column 26 of the
patent, this is from the application that you
drafted, correct?
A. Yes.
Q. And the portion that's here, is that
part of the application that you drafted?

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A. Yes.
Q. So again, it says, the ellipse fitting
procedure requires a unitary transformation of
the group covariance matrix G -- where it says
sub eov. Should that be sub cov?
A. It should.
Q. Of second moments Qxx, Qxy, Gyy?
A. That should be Gxx, Gxy, Gyy.
Q. So that shouldn't be a Q, that should
be a G, and that should be a G (indicating)?
A. Yes, apparently there was clerical
error during one of the many, I guess,
retypings of later versions of the patent.
Q. But then the equations that are shown
here in order to generate the ellipse
parameters, those are the same equations that
we just looked at from your dissertation,
correct?
A. Yes.
Q. So let's step back through an example.
Now we need to go up to the top of column 26.
You can blow up all of 26 down to the arc
tangent equation we were just looking at.
Now let's take an example where you
have the pixel group that you want to fit an

ellipse to. So you have that data. We have
the equations up here, Gz and there is a
summation of all Ez's, do you see that?
A. Yes.
Q. I think in the patent it refers to
this Gz as the group proximity value; is that
right?
A. Yes.
Q. And essentially that's just an
addition of all the points and the value of how
close the touch object is to the touch sensor,
correct?
A. Yeah, it is a sum of the sensor
readings at each pixel in that group of pixels.
Q. Right. So you just add them all up?
A. Yeah.
Q. Basically is what you are doing. Now,
this next one, we have Gx. And we have another
summation of Ez times Ex divided by that group
proximity value, correct?
A. Right.
Q. So basically -- and let me see if I
get this right -- what you are doing is you are
going through in the X direction, meaning let's
just say X is horizontal and Y is vertical.
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And I take my sense data and I sum up a row of
that X data and I multiply the X, that
coordinate value, that X value by the proximity
value for that pixel and I get a product,
correct?
A. Right.
Q. It gives me a number?
A. Yeah.
Q. And then I divide that by the total
group proximity, right?
A. Yes.
Q. So essentially what is going on here
is that at least for Gx, I am finding a
weighted average of the proximity of that touch
data, correct?
A. Right.
Q. So it kind of tells me in the X
direction, where is the center of that
pressure, essentially?
A. Right.
Q. That's a fair characterization?
A. Yeah. For -- it is sort of analogous
to center of -- well, what lay people would
hear of as center of mass, what is the center
of mass of something. It is not mass, of

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course, it is the touch proximity.
Q. Right. Basically how close the object
is and that kind of equates to a pressure,
right, is the idea? Is that fair?
A. I don't know if it -- it equates -- it
is being the center of something, not whether
it is the pressure, but it is the average
center, center averaged over the object.
Q. The center of the average of how close
the touch object is to the sensor in the X
direction, correct?
A. Okay.
Q. Okay. And so then we have got the
next equation here, 14, we have got Gy, and
then I have a similar equation here, but this
sums the product of Ez times Ey instead of Ex
and then divides it by that group proximity
value, right?
A. Yes.
Q. So that's doing exactly the same thing
but now in the Y direction, in the vertical
direction, correct?
A. Yes.
Q. So then basically what you get from
this, I think you described, is the center of

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mass or the center of proximity, let's say, you
get a center of proximity for your touch data,
correct?
A. Yes.
Q. In an X/Y coordinate system, correct?
A. Yes.
Q. All right. So then I take that
information, that information being those X/Y
coordinates that I just generated, and now I
need to generate these second moments, correct?
A. Yeah. The centroid is sometimes
called the first moment. So next we do the
second moments.
Q. Okay. And with those second moments,
can you tell us in some lay terms essentially
what those second moments are?
A. Second moments are -- in statistics,
they are kind of like -- they end up being sort
of the spread, like if you have a statistical
distribution like a bell curve, and your
centroid is the center of the peak in the bell
curve, and the second moment is going to tell
you about how wide it is, the spread of it, and
they also could -- you might know them as
standard deviation or variants.

Q. So then essentially what you are
getting here is a spread in the X direction off
the center, a spread in the Y direction off the
center, and then this, I think you said it
would be Gxy, would be kind of a spread along
the diagonal off the center, correct?
A. Something like that, yes.
Q. Okay. And that's going to give me the
second moments that I am going to use in my
covariance matrix, correct?
A. Yes.
Q. But so far the only thing I have found
-- from going through the equations, the only
thing I found in terms of anything I am going
to use for ellipse parameters is that center,
correct?
A. Well, the center, and I would also say
where we started equation 12, the total signal
that's also a very important parameter to
characterize the touch.
Q. It tells you how close the touch is?
A. How strong it is. It also tells you
-- it is a mix of how close it is and how big
it is, how much area it has. It is really kind
of both.
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Q. Is what you are saying is you sum it
up over all the pixels, so if I have a wide
touch that might not be so close, I will
generate a value, but if I have a more narrow
touch, so to speak, or smaller more pointed
touch, that's very close, that will generate
another value, correct?
A. Yeah.
Q. But in that example, those two values
could be pretty similar, couldn't they?
A. They could, but oftentimes in practice
you find that the large object -- I mean,
theoretically they could be, but in practice
you could often neglect that, you know, for
palms or something that are really large.
I mean, they are just -- even if they
are not real close, they are still going to
have a huge signal compared to a finger, or
tend to.
Q. Okay. So then after I have generated
the second moments, what I end up doing is
finding the first and second Eigenvalues of
that covariance values, correct?
A. Yes.
Q. We're going to spare everybody. We're

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not going to go ahead and explain what those
Eigenvalues are, okay?
A. Okay.
Q. Fair?
A. Yes.
Q. Let's just assume that they are
generated now, first one, second one, and those
are going to give me essentially the square of
the major and minor axes of the ellipse,
correct?
A. Yes.
Q. And then finally, this last one is
orientation, correct? I am figuring out the
orientation G sub theta; is that right?
A. Yes.
Q. Theta, that's this little Greek letter
here?
A. Right.
Q. Some engineers, mathematicians like to
use that to denote angles, correct?
A. Yeah.
Q. Okay. Now what I am doing is I am
taking the arc tangent of the first Eigenvalue
less the spread in the X direction divided by
the diagonal spread, correct?

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A. Yes.
Q. And that will give me an angle that
tells me how that ellipse that I am trying to
fit is oriented, correct?
A. Yes.
Q. And when I say oriented, I am talking
about with respect to my X/Y axis that we
started with, correct?
A. Yes.
Q. So then from that process, I have now
generated the X position of the center,
correct?
A. Yes.
Q. That's here in 13. I have generated
the Y position of the center, correct?
A. Yes.
Q. I have generated the major axis of my
ellipse, correct, in equation 19?
A. Yes.
Q. I have generated a minor axis in
equation 20, correct?
A. Yes.
Q. And I have generated the orientation
in equation 21, correct?
A. Yes.

Q. So those that I just went through,
those would be the five degrees of freedom, so
to speak, of an ellipse, right?
A. Yes.
Q. Basically, the five parameters that
you need to specify to specify an ellipse,
correct?
A. Yes, for an arbitrary ellipse, yes.
Q. By arbitrary, you could always have
special cases where you already know
information beforehand, but assuming I don't
know information beforehand, I don't know where
the touch is going to be, then I need those
five parameters, correct?
A. Yes.
Q. Now, you agree to mathematically fit
an ellipse, you need to calculate the
parameters that describe the ellipse, correct?
A. Yes. You need -- you need to
calculate parameters for an ellipse.
Q. And you also agree that fitting an
ellipse to a pixel group would not include
obtaining, simply obtaining measured data from
an object that is in general ellipse-like,
correct?
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A. Well, I would say it wouldn't include
just, you know, copying measure -- I think the
confusion and the words can come there is are
you talking about measuring kind of in the Z
axis in the pixel strength, if you are just
copying a group of pixels that happen to have
an ellipse shape and you aren't measuring the
spread, the spatial extent of them, then you
aren't fitting an ellipse. You are just making
a copy of an image of pixels, right?
Is that clear?
Q. Yeah, yeah, no, I understand what you
are saying. So, I mean, essentially what you
are saying is you can't simply copy the data,
you have to figure out these statistical
spreads that we talked about so that you can
actually fit an ellipse to that data as well?
A. Well, you have got to -- you have got
to figure out the spread somehow. You have to
make some sort of spatial measurement on it.
Q. And we talked a little bit before
about, just a minute ago, about these five
parameters to specify an ellipse, right?
A. Yeah.
Q. An arbitrary ellipse, I think you

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called it. So the X position to Y position,
the length of the major axis, the length of the
minor axis, and the orientation, right?
A. Yeah.
Q. But in addition to that, even if I
know all five of those things, I have to know
that I am also fitting an ellipse to those five
things, correct?
A. Well, hold on. What is -- I have to
know it for what? What was the question?
Q. Because I could take those five
parameters I just described and I could draw a
rectangle, too, right?
A. Yeah, I mean, you can always take -circumscribe a circle or a rectangle with an
ellipse, and -- and I think the measurements
you may do might really be the same in both
cases, depending on what your source data looks
like, you would do the same thing, and I think
the result would seem to be kind of equivalent.
To me, regardless of the objective, if it was
the same process, I don't know.
Q. Okay. I am just trying to -- I mean,
the idea is even if I have all those five
things, in order to fit an ellipse, as opposed
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to one of these other things, I need to know
that I am fitting an ellipse, correct?
A. No, I am not sure I agree with that
exactly.

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REDIRECT EXAMINATION
BY MR. DAVIS:
Q. Dr. Westerman, could I ask you to turn
in your notebook to your thesis, JX-91.
A. Yes.
Q. Do you recall being asked questions
about this at the beginning of your
examination?
A. Yes, I do.
Q. Does your thesis describe fitting an
ellipse to a pixel group?
A. Yes, I believe so.

Q. Can we -- and, indeed, counsel
directed your attention to the section entitled
3.2.8.2, ellipse fitting, correct?
A. Yes.
Q. And that was page 84 of your thesis -A. And 85.
Q. And 85. Starting at page 84, going on
to 85 with JX-291.114 to 115. So how many ways
of fitting an ellipse are described in that
section?
A. Well, there is two ways. There is the
more involved statistical approach that we
stepped through on page 84. And then on page
85, it talks about situations where -basically where the pixel group isn't big
enough for those approaches to work as well,
and that might be when you have a very small
finger touch or a low resolution electrode
array.
Q. Could you identify where in this
section of ellipse fitting in section 3.2.8.2
that that second approach is described?
A. It is after equation 320, the
paragraph there, yes.
Q. Could you describe how this method
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works?
A. Well, it talks about what to do when
basically the finger gets too small or the
pixels too weak compared to the resolution of
your image. And at this point, we don't want
things to just kind of -- well, we find it
advantageous to set some limits or defaults for
the ellipse parameters, so that we can report
consistent parameters always to other parts of
the system.
So, for example, if the contact is
very small, we can assume it is circular and
set the eccentricity to one and implicitly
since major radius and minor -- the ratio of
major to minor radius is eccentricity, then you
would set the major and minor radius equal to
like a lower limit default value or it is
suggested here you could also set them
proportional to your total group proximity Gz.
Q. Okay. And what kind of shape do you
get when you do that?
A. You would get a circle.
Q. Okay. And is a circle a form of
ellipse?
A. Yes.

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Q. And why set a default value? Why not
just not use any value for those particular
parameters?
A. Well, you have to remember we're
building, you know, a multi-layered system.
And other parts of the system, maybe they are
trying to identify the fingers or whatever. We
always kind of want to report good values or
within ranges that make sense, and sometimes
when you just take the textbook equations, and
your data is insufficient, those equations
produce values that don't make as much sense.
And so as a good engineer, you look -you alter your method to take that into account
and try to produce values for the parameters
that make sense all the time, 100 percent of
the time. And then that makes it easier to
engineer the rest of the system.
Q. If you performed the second method
described in your thesis rather than the first
method, do you still get a circle or other form
of ellipse that is indicative of where the
touch event occurred?
A. Yes, yes, you do. You are still
getting contact size, you get a circle

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representative of like the smallest finger that
you are expecting from the system and you get a
fixed orientation. Really for circles,
orientations don't matter but for other parts
of the system it is better to have that
orientation fixed vertical than to have it just
spinning around randomly.
Q. Okay. Could you -- I want to talk now
about your patent, the '828 that's at issue
here, which is JX-3. Could you turn to figure
18?
A. Figure 18?
Q. Figure 18 of the patent, JX-3. Let me
know when you have got it open.
A. Okay.
Q. Generally speaking, what does figure
18 show?
A. Figure 18 shows the segmentation of
the whole proximity image into groups of
pixels. And then in step 272, it shows fitting
ellipses to the pixel groups and the output of
a set of parameters for each pixel group.
Q. Okay. Let's turn now to the part of
the specification that talks about step 272,
which is fit ellipsis to combined groups.

Could you turn to column 25 of the
patent. Do you see starting around like 54
where it states, "the last step, 272, of the
segmentation process is to extract shape, size,
and position parameters from each of the
electrode -- from each electrode group." Do
you see that?
A. Yes, I see that.
Q. For how long in the patent does the
description of step 272 go on for?
A. It goes on through column 26 and the
first paragraph of column 27.
Q. And let's talk about that top
paragraph of column 27, since the question
stopped with regard to the embodiments shown in
column 26.
Does -- what is the method that is
described here at the top of column 7?
A. Well, there is, in the first sentence,
it is talking about, again, using the total
proximity as an alternate indicator of contact
size rather than the fitted ellipse parameters,
which I'm kind of implicitly referring to the
minor radius and major radius, which are other
direct measures of the size.
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And then I talk about, again, for your
smaller contacts and in the situation where the
size of your pixel group to the size of the
finger is low, then we can set default values
for some of the ellipse parameters.
Q. Okay. And what kind of shape do you
get when you practice the methods shown at the
top of column 27?
A. You would get a circle.
Q. I'm sorry, go ahead.
A. Assuming you -- I mean, in practice,
what we -- we would set eccentricity to, say,
one or a small value and then a major/minor
radius have to be set to be equal again.
Q. Okay. And does the method described
at the top of column 27 that we're looking at
now, does that require that a unitary
transformation of the covariance matrix be used
to set all the ellipse parameters?
A. No, in this case, you are kind of
bypassing or overriding all of that and you
would most likely make this sort of alternate
determination based on the thresholding, the Gz
or maybe counting the number of pixels or
something in your contact, you would decide

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whether to use this alternate method.
Q. Okay. I want to turn now to the
language that you were directed to on column
26, lines 18 or so where it says -- do you see
where it says the ellipse fitting procedure
requires a unitary transformation of the group
covariance matrix and it goes on? Do you see
that sentence?
A. Right.
Q. All right. If all you do is obtain a
unitary transformation of the group covariance
matrix, Geov of second moments Gxx, Gxy and
Gyy, do you -- would that by itself provide you
any parameters for an ellipse?
A. No, not -- I mean, not by itself.
That just means rotating the coordinate space
of that matrix.
Q. And can you turn to claim 3 of the
'828 patent, which should be column 60.
A. Okay.
Q. Do you see where it states, "the
method of claim 2 wherein the one or more
ellipse parameters is selected from the group
consisting of position, shape, size,
orientation, eccentricity, major radius, minor

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radius, and any combination thereof"?
A. Yes.
Q. All right. So according to the
specification, are the parameters, shape and
size always computed from the covariance matrix
transformation procedure that's described in
column 26?
A. No, no, they are not. An example
would be in figure 25 for contact size so here
we're trying to create what we call this thumb
size factor, and it is -- it is like a special
detector for something that's sized more like a
thumb than either a finger or a palm.
And here you will see we're using on
the X axis the contact size, but in this case
we're using the normalized total proximity,
which is Gz or equation 12 that we talked about
earlier as that indicator contact size.
And that was, you know, again, it is
just an alternate way of doing things, because
the prototypes at the time, the Gz was more
reliable than the major and minor radius
measurements explicitly output from the
Eigenvalues.
Q. Okay. And speaking of the

Eigenvalues, are there any claims of the patent
that specifically claim competing Eigenvalues
or Eigenvectors to fit an ellipse?
A. Yes, I believe there are. That would
be dependent claim number 5, dependent claim
number 9, and then there is also dependent
claim number 20.
Q. Okay. And let's go back to column 27
and the method that's described there. Is that
an example of mathematically fitting an
ellipse?
MR. NELSON: I am going to object as
leading, Your Honor.
JUDGE ESSEX: I'm sorry, what is the
nature of the objection?
MR. NELSON: I'm sorry. I don't have
my mic on. I am going to object as leading,
Your Honor.
JUDGE ESSEX: Let's rephrase it. What
does this depict?
MR. DAVIS: It is a yes-or-no
question.
JUDGE ESSEX: Give me the question
again.
MR. DAVIS: The question I had asked
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was, does that disclose mathematically fitting
an ellipse? Or does that disclose some other
way of fitting an ellipse?
JUDGE ESSEX: Why don't you tell me
what that discloses, Doctor?
THE WITNESS: Yes, I believe it is an
alternate way of fitting the ellipse
parameters.
JUDGE ESSEX: What parameters?
THE WITNESS: Eccentricity,
orientation, setting it to a default, and there
is another example where we use, in figure 25,
where we use the ratio of eccentricity to
proximity as a stand-in for the width of the
contact, which is like an alternate way of -and another -- well, that's an alternate way of
-- sorry. My words are backwards.
So the minor radius is sort of the
first way of measuring the width, but if you
divide -- if you interpret the total proximity
as an area that's roughly the minor radius
times the major radius, and you divide that by
eccentricity, which is the major radius divided
by the minor radius, then that value in, I
think it is figure 25C, is basically equivalent

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to a minor radius squared, but it is obtained
without directly using the minor radius.
Again, we did that because for those
prototypes and the noise characteristics of
them, that actually gave you a more stable
answer to kind of take this round-about method
than to use the minor radius directly.
BY MR. DAVIS:
Q. Do you assign numbers to the, to the
-- to each of the five parameters that you use
to define an ellipse?
A. Yes. In this paragraph we do this,
and we have basically always kind of had these
limits then and still do in the code, to do
this.
Q. And do you use the numbers to define
the ellipse?
A. Yes, they become the ellipse
parameters.
Q. And does it result in a circle or an
ellipse of a certain size once you plug in
those numbers?
A. Yeah, it -MR. NELSON: Your Honor, I am just
going to object. It is leading again. It is

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the same exact issue we had before.
JUDGE ESSEX: You are kind of leading
the witness. Can you rephrase and let him
answer?
BY MR. DAVIS:
Q. Sure. Well, what do you get from the
numbers that are assigned to the five
parameters?
A. Well, what you get is a circle. We
have limits like for the major/minor radius of
something like 5 or 6 millimeters, that those
values are not allowed to go -- regardless of
what the equations originally put out, we don't
let the numbers go below 5 or 6 millimeters in
that same function. We limit them, sort of cap
them at 5 or 6 millimeters and then those get
transmitted as like a 5 or 6 millimeter circle
throughout the system.
Q. Okay. When you were working on your
Ph.D., were you aware of others who attempted
to address the problems that you were
addressing in your thesis?
A. Well, obviously, I think I have
hundreds of references talking about earlier
work, but no one had attempted to, I guess,

develop a multi-touch surface so ambitiously
with identifying the fingers and trying to
merge typing and pointing and gestures and many
different modalities on the same surface.
Q. Did you -- did you refer to a Rubine
reference in your thesis?
A. Yes, I find a quote by Rubine, I
believe from his Master's or Ph.D. thesis in
'93 where he was working with a sensor frame,
which is another early -- it was a multi-touch
device. Would you like me to -Q. Could I ask you to turn to JX-291.150.
What is shown there?
A. So this is my discussion of Rubine and
his work with multi-path gestures on the sensor
frame. And I quote him in the lower paragraphs
there where he says that for the devices such
as data gloves, which are attached to the hand,
and you have actually got sensors, wires
running down to each finger, then those devices
know exactly which finger is which, which
finger is associated with different sensor
input.
And so, you know, he says they could
build one class for thumb paths and one for
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forefinger paths and you could easily assign a
different operation to each finger. Then he
says for the sensor frame and multi-finger
tablets, they cannot tell which of the fingers
is the thumb, this is the forefinger and so on.
Thus, there is no a priori solution to the path
sorting and he says the solution he adopted was
to just try to apply a consistent ordering
between the paths.
MR. DAVIS: Thank you, Your Honor. I
have no further questions at this time.
MR. NELSON: Just a couple.
RECROSS-EXAMINATION
BY MR. NELSON:
Q. All right. Let's put column 27 back
up there of JX-3, the '828 patent. In that
paragraph we were just talking about, let's
blow that up again.
The one right at the top there. There
you go. The first sentence you just looked at
with counsel, it says, "on low resolution
electrode arrays, the total group proximity Gz
is a more reliable indicator of contact size as
well as finger pressure than the fitted ellipse
parameters." Right?

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A. Yes.
Q. So I think you said that that's used
instead of the fitted ellipse parameters in
what's described here in this paragraph at
column 27, correct?
A. Well, what I said is -- I mean, in
practice, what it really means is it is used
instead of minor radius and major radius
individually. I mean, that's the intended
meaning.
Q. Right. And instead of the fitted
ellipse parameters, right?
A. That's what it says.
Q. Okay. And then if you go down below,
you talked about in this next sentence,
"therefore, if proximity images have low
resolution" -- first of all, what is low
resolution?
A. I don't define that. And that's why,
you know, in practice, we still use this, and
that's not to say that the resolution is low,
but in practice what this means is it is, when
the size of the fingertip contact gets so small
relative to the resolution you have, whatever
it is, that you only get a few pixels out, then

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you are probably in a situation where this
applies.
Q. So but here in column 27, you don't
tell people that are reading the patent when
something is low resolution or when something
is not low resolution, correct?
A. No, I don't.
Q. Okay. And then it goes on to say,
"the orientation and the eccentricity of small
contacts are set to default values rather than
their measured values and total group proximity
Gz is used as the primary measure of contact
size instead of major and minor axis lengths,"
do you see that?
A. Yes.
Q. And so let's focus on the orientation
and eccentricity. Set to default values, that
means they are not calculated, correct?
A. I don't agree with that, because to me
in the work that I do, we're always computing
these things. And, as I say, having to place
limits and sort of post-process. And to me
that's part of the process is to keep values
within a meaningful range. And that's what
this is talking about.

Q. Well, what this says is you set to
default value, correct?
A. You do, but it is based on -- you are
setting it to default value, but it is usually
-- you know, it is based on a decision, which
is, you know, all part of the calculation.
You are setting, you know, at the end
of the equations your default value, too, but
it is based on, you know, a set of decisions
and formulas and this would be as well.
Q. Well, here in column 27, you don't
tell anybody that's reading this patent, set it
to a default value that's dependent upon
something that you measure, do you?
A. I don't say it, but I say the
eccentricity of small contacts, I don't say it
is large, and so I think there is an implicit
decision in there that you are only going to do
this for the small ones, so implicitly you are
making a decision somehow, as I suggested
earlier, probably based on Gz, of what's small
and what is large and whether to do this.
Q. But you don't say any of that here in
the paragraph in 27, correct?
A. I don't give the details of that.
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Q. Okay. So then in the example that you
were talking about with counsel, I think you
said that what you do, what you did in practice
is you set the eccentricity value to 1,
correct?
A. Yep.
Q. Eccentricity value of 1 is a circle,
correct?
A. Yep.
Q. So that's a value, right? That's not
calculated, correct?
A. I mean, it is a value. To say it is
not calculated, as I say, to me, the
calculation is still -- the process you are
taking to get there is still a calculation.
Q. So what you are saying is you
calculated something to determine that I
shouldn't use any of those values, I should set
it to a default value?
A. Yes, I think so.
Q. But the determination of the default
value is not a calculation in and of itself,
correct?
A. Not -- not as explained here.
Q. Okay. Thank you very much for your

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time.
MR. NELSON: I don't have any further
questions at this time, Your Honor.
MS. KATTAN: No questions, Your Honor.
MR. DAVIS: Just a couple of
questions, Your Honor.
REDIRECT EXAMINATION
BY MR. DAVIS:
Q. Could we pull back up column 27, JX-3.
So in the example that's provided at the top of
column 27, do you use the numbers that are
assigned as default values to determine the
size or shape of the circle?
MR. NELSON: I am going to object as
leading, Your Honor. He can ask him what he
uses the values for, but he can't keep
suggesting the answers.
JUDGE ESSEX: Rephrase your question,
please.
BY MR. DAVIS:
Q. Sure. So what is used to determine
the size and shape of the circle?
A. That would be -- I mean, the default
values become like, you know, they would become
like the major radii and minor radii. And

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those would have been chosen, as I said,
probably like representative of the smallest
fingertip you would reasonably expect to see,
like, you know, a child's fingertip or
something.
Q. Is the default value a number value or
is it some other type of value?
A. It is a numeric measurement, like 5 or
6 millimeters.
Q. Okay. And are number values assigned
to each parameter or are there certain
parameters for which no number value is
assigned?
A. Well, typically when we engineer these
systems, in order to allow layering of them
and, you know, or in order to keep the layers
independent, you want your bottom layer, let's
call it the ellipse-fitting layer, to always
provide values for all parameters.
And you may have many different
alternate ways that you calculate those in
different conditions, but you always provide
them, so the next layer of the system doesn't
have to have any special knowledge about, oh,
is this value good now or is it only -- it

doesn't have to worry about whatever -- all
those different conditions. It can be
100 percent rock solid confident that values
for all parameters are always provided from
lower layers.
Q. Okay. And under the example that is
provided at the top of column 27, what are you
using the values to do?
A. Well, we can be using them -- sorry.
I am not sure what level.
I mean, in that layer, you know, they
are filling in the ellipse parameters. And
then in the higher layers, they could be using
them to decide if something is a finger or a
palm or a thumb like on the edge of a phone or
for debugging to display -- to display the
touches for purposes of just seeing what
touches are on the screen and how big they are.
Q. Okay. So is the example that's
provided at the top of column 27, is that an
example -- is that mathematically fitting an
ellipse or not mathematically fitting an
ellipse?
MR. NELSON: Objection, leading, Your
Honor. It is exactly the same question you
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have already sustained the objection to.
JUDGE ESSEX: Let me ask the question
here from my -- having listened to the three of
you go over this and that, is there a point
where the contact seems so slight to the system
that it fits a value and that value is always
the same? Is that what is going on here?
THE WITNESS: Well, it is for
particular parameters. It is not for all.
JUDGE ESSEX: I understand not for all
parameters, but for particular parameters, if
it is below a minimum, then it has a value that
will always be the same value?
THE WITNESS: Yes.
JUDGE ESSEX: Is that what is going
on?
THE WITNESS: Yes.
JUDGE ESSEX: Okay.
MR. DAVIS: Thank you.
JUDGE ESSEX: Are you happy with that?
MR. DAVIS: I am happy with that, Your
Honor.
JUDGE ESSEX: Are you happy with that?
MS. KATTAN: Yes, Your Honor.
JUDGE ESSEX: All right. Anything

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else?
MR. NELSON: Nothing from us, Your
Honor.
JUDGE ESSEX: All right, Doctor. I
think we're done with you. Thank you very
much.
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