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<"Title",
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<F44><Ref, Page #, Tag = "63458"><F44@Lam>Real-time Single-workstation Obstacle Avoidance Using <SR>
Only Wide-field Flow Divergence <F42@Lam>



<"authors">

<Ref, Page #, Tag = "58945">Ted Camus
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. This research was conducted while the first author held a National Research Council Research Associateship at NIST. <SR>
Current address: Sensar, 121 Whittendale Drive, Moorestown, NJ 08057. email: tedcamus@sensar.com

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, David Coombs, Martin Herman
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 Current address: NIST, Information Access and User Interfaces Division, 100 Bureau Drive Stop 8940, Gaithersburg <SR>
MD  20899-8940

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, Tsai-Hong Hong 


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<Ref, Page #, Tag = "70929">tedcamus@sensar.com, {dcoombs,mherman,thong}@nist.gov 


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<Ref, Page #, Tag = "23550">National Institute of Standards and Technology 


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<Ref, Page #, Tag = "95534">Intelligent Systems Division 


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Building 220 (Metrology) Room B-124 


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100 Bureau Dr Stop 8230 


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<Ref, Page #, Tag = "78852">Gaithersburg MD  20899-8230 



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ABSTRACT <F3@Lam><F3@Lam>


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<F15>This paper describes a real-time robot vision system which uses only the divergence <SR>
<F14@Lam>of the optical flow field for both steering control and collision detection. The robot <SR>
<F14@Lam>has wandered about the lab at 20 cm/s for as long as 26 minutes without colli<F14@Lam>sion.The entire system is implemented on a single <SR>
ordinary UNIX workstation with<F14@Lam>out the benefit of real-time operating system support. Dense optical flow data are <SR>
<F14@Lam>calculated in real-time across the entire wide-angle image. The divergence of this <SR>
<F14@Lam>optical flow field is calculated everywhere and used to control steering and colli<F14@Lam>sion-avoidance behavior. Divergence alone has<SR>
 proven sufficient for steering past <SR>
<F14@Lam>objects and detecting imminent collision. The major contribution is the demonstra<F14@Lam>tion of a simple, robust minimal system that u<SR>
ses flow-derived measures to control <SR>
<F14@Lam>steering and speed to avoid collision in real time for extended periods. Such a sys<F14@Lam>tem can be embedded in a general, multi-leve<SR>
l perception/control system.<F3@Lam>


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<F13>1<TAB>Introduction <F3@Lam>


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<TAB><TAB>Mobile robots that drive at reasonable speeds (<F14@Lam>e.g.<F3@Lam>, 20 cm/s indoors) must robustly <SR>
sense and avoid obstacles in real time. Image motion provides powerful cues for understanding scene structure. Divergence of op<SR>
tical flow (the sum of optical flow derivatives <SR>
in two perpendicular directions) is theoretically unaffected by camera rotation, so it gives <SR>
a robust measure of scene structure for a moving observer. The robot system described <SR>
here uses flow divergence to steer around obstacles while it attempts to achieve a goal <SR>
(which for now is simply to drive straight ahead). When the obstacle cannot be avoided by <SR>
changes in steering alone, the divergence data warn the robot of the impending collision. <SR>
The robot stops, turns, and resumes wandering straight ahead in the new direction. These <SR>
integrated behaviors have driven the robot around the lab at 20 cm/s for as long as 26 minutes without collision. Because this <SR>
wandering behavior is already a real-time capability, <SR>
there is promise that future increases in computational power will fuel development of <SR>
both increasingly robust basic skills and additional behaviors for robots. 

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<TAB><TAB>The simplicity of the system improves robustness and makes the system easier to extend. The system uses only a single framegra<SR>
bber, a single processor, a single image <SR>
stream, and a single low-level percept for all control functions. Simple robust filters are <SR>
chosen in lieu of complex filters that require sensitive system modeling and synchronization. These filters are able to ignore <SR>
momentary noise and artifacts that result from system <SR>
module interactions, which enables modules to cooperate without delicate synchronization.

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<TAB><TAB>In addition, the obstacle avoidance system is extensible. Egocentric hazard maps are <SR>
derived from divergence data, goals, and steering history. A composite hazard map is used <SR>
to steer the vehicle. This design supports the use of multiple cues, which can be incorporated with additional hazard maps. Add<SR>
itional redundant or complementary sensing modes <SR>
can be exploited by the existing framework. 

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<TAB><TAB>Our approach achieves real-time intelligent behavior by using minimalist visually-derived representations. In such representat<SR>
ions, a minimal amount of information required <SR>
to achieve the given task is extracted from the imagery [2][4]. The representations contain <SR>
only task-relevant information (<F14@Lam>i.e.<F3@Lam>, relevant to obstacle avoidance), and the information <SR>
is only represented in 2-D image coordinates. The control algorithms directly use observable image information represented in t<SR>
he 2-D image sequence; a 3-D reconstruction is not <SR>
required [18][31]. Such an approach is particularly useful in closing control loops with vision at lower levels of a multi-leve<SR>
l control system. The limited body-centered data that <SR>
are used are mapped into the local visual space for steering and speed control policies. A <SR>
minimalist approach requires fewer calibrations, fewer scene hypotheses, and less computation. It is, therefore, simpler and fa<SR>
ster. 

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<F13>Figure 1 <Ref, Page #, Tag = "35934">  Obstacle Avoidance System Architecture <F3@Lam>



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3. Apply spatial and <SR>
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5. Decide desired di <SR>
rection; detect immi <SR>
nent collision

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2. Compute full <SR>
optical flow

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4. Derive hazard <SR>
maps from diver <SR>
gence, goal, history 

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1. Compute diver <SR>
gence everywhere

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<TAB> 

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<TAB><TAB>The obstacle avoidance system we describe in this paper is designed in accordance <SR>
with the Real-Time Control System (RCS) hierarchical architecture described in [1]. RCS <SR>
decomposes goals both spatially and temporally to meet system objectives. The system <SR>
monitors its environment with sensors and updates models of the states of the system itself <SR>
and the world. Figure 1 describes the functionality of the obstacle avoidance system in the <SR>
first three levels of the RCS hierarchy. 

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<TAB><TAB>The RCS architecture is composed of three parallel legs (sensory processing (SP), <SR>
world modeling (WM), and behavior generation (BG)) that interact to control complex <SR>
systems. The hierarchical levels run in parallel. The present system uses the three lowest <SR>
levels: elemental-move (e-move), primitive (prim) and servo. Generally, BG modules <SR>
control physical devices. WM modules supply information to both the BG hierarchy and <SR>
the SP hierarchy. WM modules maintain a database of system variables and filter and analyze data using support modules. SP modu<SR>
les monitor and analyze sensory information <SR>
from multiple sources in order to recognize objects, detect events and filter and integrate <SR>
information. The world model uses this information to maintain the system's best estimate <SR>
of the past and current states of the world and to predict future states of the world. 

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<F13>Figure 2 <Ref, Page #, Tag = "15970">  Robot and Its View <F3@Lam>



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>

<Row,"Row">

<Cell>

<"CellBody">

(a) Test mobile robot 
<Cell>

<"CellBody">

(b) Robot's view of the lab <SR>
through its 115-degree wide <SR>
angle lens 
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB> 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The testbed mobile robot is shown in Figure 2 (a).Video images are obtained from an <SR>
onboard uncalibrated camera with a 
<"body",
        Line Spacing =   1.750 lines>

<TAB> field of view. The camera is mounted on a pan <SR>
motor. The robot's view from this camera is shown in Figure 2 (b). Figure 1 sketches the <SR>
obstacle avoidance system consisting of seven processing modules. The SP modules compute flow and divergence everywhere in the <SR>
image. The WM modules apply spatial and <SR>
temporal median filters to reduce momentary fluctuations in the divergence field. The BG <SR>
modules use divergence to steer the robot around obstacles seen in the wide camera view <SR>
and provide the body and gaze controllers with desired driving, steering, and gaze velocities. Using active gaze control, the c<SR>
amera is rotationally stabilized to reduce the magnitude of the flows in the image stream. When the camera points too far away f<SR>
rom the heading, a saccade is made toward the heading. These saccades introduce momentary disturbances of the flow data, but the<SR>
 temporal median filter effectively eliminates disruptive <SR>
effects. When divergence data indicate imminent collision ahead because steering alone <SR>
cannot avoid an obstacle, the robot stops, turns away, and resumes wandering. 

<"section",
        Font =           F3@Lam,
        Line Spacing =   1.750 lines>

<F13>2<TAB>Full optical flow estimation <F3@Lam>


<"body",
        Bottom Margin =  0.000 inches,
        Line Spacing =   1.750 lines>

<TAB><TAB>Robust, real-time optical flow is now becoming a practical means of robotic perception <SR>
given new fast algorithms and increasingly faster hardware. Given that our entire system <SR>
(flow, divergence, and body control) is implemented on a single workstation without the <SR>
benefit of a real-time operating system, it is important to have sufficient processor idle <SR>
time available to buffer the overhead of the operating system. Otherwise, the image capture frame rate could vary from frame to<SR>
 frame. Camus [7][8] describes a robust, real-time <SR>
correlation-based optical flow algorithm which returns dense data even in areas of relatively low texture. This is the starting<SR>
 point of our implementation.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>In correlation-based flow such as in [5][17][21], the motion for the pixel at 
<"body",
        Line Spacing =   1.750 lines>

<TAB> in <SR>
one frame to a successive frame is defined to be the displacement of the patch 
<"body",
        Line Spacing =   1.750 lines>

<TAB> of 
<"body",
        Line Spacing =   1.750 lines>

<TAB> <SR>
pixels centered at 
<"body",
        Line Spacing =   1.750 lines>

<TAB>, out of 
<"body",
        Line Spacing =   1.750 lines>

<TAB> possible displacements (where 
<"body",
        Line Spacing =   1.750 lines>

<TAB> is <SR>
an arbitrary parameter dependent on the maximum expected motion in the image). We determine the correct motion of the patch of <SR>
pixels by simulating the motion of the patch for <SR>
each possible displacement of 
<"body",
        Line Spacing =   1.750 lines>

<TAB> and considering a match strength for each displacement. If 
<"body",
        Line Spacing =   1.750 lines>

<TAB> represents a matching function which returns a value proportional to the match <SR>
of two given features (such as the absolute difference between the two pixels' intensity <SR>
values, 
<"body",
        Line Spacing =   1.750 lines>

<TAB> and 
<"body",
        Line Spacing =   1.750 lines>

<TAB> respectively), then the match strength 
<"body",
        Line Spacing =   1.750 lines>

<TAB> for a point 
<"body",
        Line Spacing =   1.750 lines>

<TAB>and <SR>
displacement (u,w) is calculated by taking the sum of the match values between each pixel <SR>
in the displaced patch 
<"body",
        Line Spacing =   1.750 lines>

<TAB> in the first image and the corresponding pixel in the actual patch <SR>
in the second image: 

<"equation">

<TAB><F2@Lam><TAB>(1)<Ref, Page #, Tag = "14956">
<"equation">

<TAB>

<"body",
        Line Spacing =   1.750 lines>

<TAB><F3@Lam><TAB>The actual motion of the pixel is taken to be that of the particular displacement, out of <SR>

<"body",
        Line Spacing =   1.750 lines>

<TAB> possible displacements, with the maximum neighborhood match <SR>
strength (or equivalently, minimum patch difference); thus this is called a winner-take- <SR>
all" algorithm.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>This algorithm has many desirable properties. Due to the relatively large size of the <SR>
matching window, the algorithm generally does not suffer from the aperture problem except in extreme cases [5][8], and it tends<SR>
 to be very resistant to random noise. Because the <SR>
patch of a given pixel largely overlaps with that of an adjacent pixel, match strengths for <SR>
all displacements for adjacent pixels tend to be similar (except at motion boundaries). <SR>
Therefore the resultant optical flow field tends to be relatively smooth, without requiring <SR>
any additional smoothing steps. In gradient-based optical flow, on the other hand, noise <SR>
usually results in direct errors in the basic optical flow measurements due to the sensitivity <SR>
of numerical differentiation. Finally, because one optical flow vector is produced for each <SR>
pixel of input (except for a small 
<"body",
        Line Spacing =   1.750 lines>

<TAB>border where flow may not be calculated), <SR>
optical flow measurement density is 100 percent. 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 3 <Ref, Page #, Tag = "22409">  Time Delays and Distances <F3@Lam>



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<Cell>

<Row,"Row">

<Cell>

<"CellBody">

(a) As the maximum pixel shift increases <SR>
linearly, the search area increases quadratically.
<Cell>

<"CellBody">

(b) However, with a constant shift distance and variable discrete time delays, <SR>
search over time is linear. 
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB> 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>A significant limitation with the traditional correlation-based algorithm is that its time <SR>
complexity grows quadratically with the maximum possible displacement allowed for the <SR>
pixel [5][9] (Figure 3 (a)). Intuitively, as the speed of the object being tracked doubles, the <SR>
time taken to search for its motion quadruples, because the area over which we have to <SR>
search is equal to a circle centered at the pixel with a radius equal to the maximum speed <SR>
we wish to detect.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>However, note the simple relationship between velocity, distance and time:

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>
<"body",
        Line Spacing =   1.750 lines>

<TAB>. 

<"Body">

Normally, in order to search for variable velocities, we keep the inter-frame delay 
<"Body">

 constant and search over variable distances (pixel shifts): 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>
<"body",
        Line Spacing =   1.750 lines>

<TAB>.

<"Body">

However, we can easily see from Figure 3 (b) that doing so results in an algorithm that is <SR>
quadratic in the range of velocities present. Alternatively, we can keep the shift distance <SR>

<"Body">

 constant and search over variable time delays:

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>
<"body",
        Line Spacing =   1.750 lines>

<TAB>. 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 4 <Ref, Page #, Tag = "36175">  Space-time correlation search of Camus' real-time optical flow algorithm <F3@Lam>



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(a) The search area for <SR>
the example pixel (1,1) in <SR>
this example is shown in <SR>
the current frame (Image <SR>
t). This search begins <SR>
from a previous frame (2 <SR>
such previous frames are <SR>
shown). 
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<"Body",
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(b) The correlation match <SR>
is the sum-of-absolute <SR>
differences between the <SR>
corresponding pixels' <SR>
intensity values in a patch <SR>
centered at the given <SR>
pixel (a patch size of 7x7 <SR>
is used in all examples; <SR>
these patches are not <SR>
shown for clarity). 
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<"Body",
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(c) Optical flow is calculated to be the best- <SR>
matching pixel shift <SR>
divided by the corresponding frame delay. 
<End Table>

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<TAB><F3@Lam> 

<"body",
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<TAB><TAB>In this case, we generally prefer to keep 
<"body",
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<TAB> as small as possible (for example a single <SR>
pixel) in order to avoid the quadratic increase in search area. (Note, however, there is nothing preventing an algorithm based <SR>
on both variable 
<"body",
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<TAB> and 
<"body",
        Line Spacing =   1.750 lines>

<TAB>.) This temporal matching <SR>
concept is depicted in Figure 4. This time-space trade-off reduces a quadratic search in <SR>
space into a linear one in time (at a cost of measurement precision), resulting in a very fast <SR>
algorithm: optical flow can be computed on 32x64 images, quantizing flow speeds into 5 <SR>
bins, at 35 frames per second on an 80 MHz Themis HyperSPARC
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<Ref, Auto #,Tag = "EiXYY2e4vr">.
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<TAB><TAB><F7@Lam>. Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the expe<SR>
rimental procedure. Such identification does not imply recommendation or endorsement by NIST, nor does it imply that the materia<SR>
ls or <SR>
equipment identified are necessarily best for the purpose.

<End Text>)
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<F7> 10 computer. Although this algorithm is not as accurate as many other optical flow algorithms, it is generally superior in term<SR>
s of computational efficiency [23]. 

<"body",
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<TAB><F3@Lam><TAB>In our implementation, an original image of 256x512 pixels, captured with a 
<"body",
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<TAB> <SR>
field-of-view camera, is subsampled to 32x64 pixels using a simple block-subsampling algorithm which averages an <F14@Lam>N<F3@Lam>x<F14@Lam>N <F3@Lam>block of p<SR>
ixels. This simple subsampling is very fast and <SR>
effective for this correlation-based algorithm (although perhaps not for other flow algorithms [8]). In this case, blocks of 8x<SR>
8 pixels would be averaged into a single value. In <SR>
practice, this requires more image bandwidth than is available using the framegrabber's <SR>
VME bus connection to the Themis HyperSPARC 10 board's main memory. Therefore, <SR>
the images are first subsampled by a factor of 2 on each side (yielding 1/4 the image data) <SR>
using the framegrabber's own image scaling function. (This is the only function performed <SR>
on the framegrabber other than capturing the images and transferring them to the host's <SR>
memory.) Because the framegrabber's method of subsampling is not as effective as the <SR>
one we use in software, the final subsampling by a factor of 4 on a side is performed on <SR>
the host workstation itself.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The above algorithm returns <F14@Lam><F14@Lam>quantized<F3@Lam> optical flow values. Although this is adequate <SR>
for various robotic vision tasks [6][14][15][25], it is not sufficient for our application, because the calculation of divergen<SR>
ce requires the ability to measure spatial derivatives of <SR>
the optical flow. Because quantized optical flow is basically a step function, these derivatives do not exist. Consistent with <SR>
theory, it was found that the divergence of the optical <SR>
flow field could not be estimated successfully using only the quantized algorithm.<F38@Lam> <F3@Lam>Attempting to interpolate the optical flow f<SR>
ield itself is not appropriate in this case because <SR>
the quantizations are relatively coarse and the flow field is already dense. Smoothing the <SR>
optical flow field would require extremely large masks and would, therefore, likely cover <SR>
multiple objects simultaneously. This would be especially problematic in our case where <SR>
a wide-angle lens is used and individual objects occupy only a small fraction of the visual <SR>
field. Calculating a least-squares best fit to the correlation surface as in [3] was ruled out <SR>
due to real-time performance requirements (see efficiency experiments in [22][24]). In order to satisfy our real-time requireme<SR>
nts, a fast approximation method was used to derive <SR>
continuously-valued flow fields.

<"FigureTableTitle",
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<F13>Figure 5 <Ref, Page #, Tag = "40725">  Image flow interpolation <F3@Lam>



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0)
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>

<Row,"Row">

<Cell>

<"CellBody">

(a) Parabolic and roof methods
<Cell>

<"CellBody">

(b) Angular estimation of flow vector
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB>

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>To avoid a computationally expensive search for the true flow, the 2-dimensional interpolation is decomposed into two 1-dimens<SR>
ional interpolations; the first estimates the <SR>
magnitude of a flow vector and the second estimates its precise angle. (The initial flow is <SR>
returned as X and Y components. This is then converted to polar coordinates.) Both the <SR>
directional component (consisting of one of eight possible directions or no motion) as well <SR>
as the magnitude component (consisting of the time delay in frames) are quantized. The <SR>
first one-dimensional interpolation is along the magnitude component of the flow. The <SR>
correlation match values for the best motion of a given pixel along with the match values <SR>
for the virtual" flow vectors of adjacent" magnitudes in the same direction (i.e., of plus <SR>
and minus one time delay in frames) are used. For example, in Figure 4 (c) assume that the <SR>
shift of (0, 1) pixels with a delay of 2 frames (equivalently a motion of (0, 1/2) pixels per <SR>
frame) has the best correlation match of any pixel shift. The correlation match values used <SR>
for interpolation in this example are those that correspond to the pixel shifts of (0, 1) over <SR>
3 frames and (0, 1) over 1 frame, or virtual" motions of (0, 1/3) and (0, 1/1) pixels per <SR>
frame respectively. (If the peak correlation match magnitude is 1 pixel per frame, interpolation cannot be performed.) Roof int<SR>
erpolation is used to find the total time delay corresponding to the minimum correlation match value as shown in Figure 5 (a). T<SR>
wo lines are <SR>
formed connecting the best correlation match strength and the match strengths corresponding to those two time delays which imme<SR>
diately bracket the former time delay. The negative value of the steeper of the two slopes is then substituted for the more grad<SR>
ual of the <SR>
two. The abscissa of the intersection point of these two lines is taken as the new interpolated magnitude component of the flow<SR>
.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The second interpolation is along the angular component of the flow (Figure 5 (b)). <SR>
The first step is to calculate the match values for virtual" flow vectors of neighboring vector directions but with the same m<SR>
agnitude as just calculated for that pixel. (Because we <SR>
only calculate the correlation match values for eight directions of motion, this means that <SR>
the motion vector with the best correlation match has two neighboring directions at 
<"body",
        Line Spacing =   1.750 lines>

<TAB> <SR>
on either side.) This interpolation is not trivial because the magnitude of the motion along <SR>
the diagonals is the 
<"body",
        Line Spacing =   1.750 lines>

<TAB> times that of motion along the north, south, east and west directions for a given velocity (time delay). In order to perform t<SR>
he second 1-dimensional interpolation, it is necessary to estimate the correlation match values of the neighboring directions at<SR>
 the <F14@Lam><F14@Lam>same<F3@Lam> magnitude as the best matching flow vector. Although the roof interpolation was slightly more accurate than parabolic <SR>
interpolation for finding a real-valued <SR>
magnitude for a given optical flow vector, it was found to have the disadvantage of not <SR>
returning as accurate a correlation match value estimate. A more accurate correlation <SR>
match value estimate was instead found by calculating the coefficients of an interpolating <SR>
parabola and taking the correlation match value at the same magnitude as found during the <SR>
roof interpolation stage (Figure 5 (a)). The following formulas for the parabola coefficients can be derived given a parabola 
<"body",
        Line Spacing =   1.750 lines>

<TAB>:

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>
<"body",
        Line Spacing =   1.750 lines>

<TAB>, 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>
<"body",
        Line Spacing =   1.750 lines>

<TAB>, 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>
<"body",
        Line Spacing =   1.750 lines>

<TAB>, 

<"body",
        Line Spacing =   1.750 lines>

<TAB>where 
<"body",
        Line Spacing =   1.750 lines>

<TAB>, 
<"body",
        Line Spacing =   1.750 lines>

<TAB> and 
<"body",
        Line Spacing =   1.750 lines>

<TAB> are the points used to fit the parabola.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB><F3@Lam>These formulas are used to estimate the correlation match strengths for neighboring <SR>
<F3@Lam>virtual" flow vectors that correspond to the same magnitude as that of the best matching <SR>
<F3@Lam>flow vector; these three parabolic interpolations are shown in <F3@Lam>Figure 5<F3@Lam> (b). A final para<F3@Lam>bolic interpolation is then calculated<SR>
 using these three estimated correlation match <SR>
<F3@Lam>strengths, and is also shown in <F3@Lam>Figure 5<F3@Lam> (b). 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 6 <Ref, Page #, Tag = "41046">  Quantized and interpolated optical flow results <F3@Lam>



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 CECCCFD1CFD4D4D3D3D2D2D6D4D4D4D3D4D7D6D8D5D3D5D6D3D3D2D2D2D2D3D5D3D6D7D3
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 BBC1BFBFC0BFBDBDBEC0BBBBBDC2BFBEBDBFBFBDBDBEB9BABBBBBDBEBCBFC0C1C0BDBDBF
 BBBBBABAB9B9B5B5B4B3B4B4B1B2B0B0B0B1B0AFACABA9A9A7A6A3A19F9D9999BDBDBFC0
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 CFCED1D0CDD1CFD1D1D1D3D4D1D3D3D4D5D6D1D4D5D5D5D6D3D4D2D4D3D2D3D5D1D6D4D2
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 BBBDBFBDBCBCB9BAB7B7B4B3B3B4B2B3B3B2B2B2B1B4B3B2AFADABABA7A8A6A39F9F9B9B
 BCBCBCBFBCBCBFC5C3C2C4C6C3C5C3C5C7C8C5C6C6C4C5C6C5C7C6C9C9C6C9CCC8CBCACB
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 CDC8C5C8C4C7C7C5C3C5C3C3C3C7C4C0C1C2BDC1C0BFBDC1BEC1BFBEC0C3C1C1BDC1BFC0
 C1C1BCBEBFC0C2C2BEC0BDBDBFC0BEC0BCBABBBDBFBFBBBBBBB9B9C1BFBBB9BABDBDB9BB
 B9BABCBBBBBCB9BCBCBDBFC0BDC1C0C1C3C2BFC1C0C1C1BFBEC0BFC2C1BFBEBDBDBDBBBC
 BBBBBABDBABBBCBCBABAB9BBB7B7B6B3B3B5B1B1B1B2B2B1AEB1B0B2AFACA7A7A5A5A3A3
 A0A19B9CB9BAB9BBBABBBDC1BEBFC1C2C4C5C1C5C6C5C3C3C5C6C0C7C9C4C5CAC6C8C9C9
 C9CAC9CFCDCFCFCBCCD0CDCDCECFD0D3D0D1D1D1D1D3D3D5D4D6D3CFD5D9D2D3D5D3D0D5
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 BFC3BFC1C1C0BDBFC0C1BEC1C1BCBBBFBEC0BDBDBEC1BDBDBEBDBABABBBDBABEBEBCBBBD
 BCC0BFBDBCBDBCBDBABABCBCBCC1BFBFC1BFBFC3C0C3C3C1C0C1BEC1BFBEC1C2C1C2BDBD
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 BFC2BFBDBEBFBEBEBBBFBFBDBBBAB9BCB9BBB9B8B7B8B4B3B3B3B1B0ABADADAEADAEAEB1
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 BDC1BDC1C5C2C1C3C1C2C5C9C5BFC1C7C3C3C8C9C2C3C2C3C4C5C6C6C4C7C7CACAC9CCCF
 CCCFCFCFCFCFCBCFCFD1D0CFCFD2CED1D4D4D4D9D6D5D5D5D5D7D4D6D8D6D5D6D5D7D5D5
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 CBCACBD1CCCDD1D2D0D1CECFCFD1D2D1D0D2D1D2D4D1D2D7D5D7D8D6D4D6D4D6D7D3D2D4
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 CECFD2CFCACBC9CDCDC8C7CDCBC7C7C7C8C8C4C5C5C6C6C3C1C7C4C3C2C1C2C5C4C7C5C3
 C2C3C4C9C9C4C1C4C6C8C3C3C4C1BDC3C2C2BFBFC0BEBBBEBDBFBEBDBFC2BDBCBCBDBBBD
 BABCBCBBBABBB7BABDC2C1BEBBC1C0C0C1C2C2C3C2C3C2C5C6C3C1C5C2C2C4C3C2C5C3C6
 C5C3C3C3BEC1BFBFC2C1BCBCB6B3B4B4B3B3B1B1AEADACACACADABAEADACAAADA9A7A9AB
 ADAFADAEABACACABBFBFBEBFBDC1C0C2C5C5C6CCC6C3C4C5C4C7C7C8C4C3C7C7C7CDCBC8
 C9CFCFCFCCCFD1D1D0D3D0D1CFCFD0D0CFD2CFCFD1D3D1D4D3D3D3D2D4D8D7D9D5D4D5D5
 D3D6D3D3D7DBD6D5D5D4D3D5D6D7D5D6D4D3D4D3D3D5D3D5D6D3D2D6D5D7D5D4D4D6D5D7
 D3D1D2D1CDCECED1D0CCCCCDC9C8C5CAD0CCC7CBCBCECCCACACBC8CAC7C4C4C4BFC1C2C3
 BFBFC0C1BDC0C4CBCCC3BFC5C6C7C9C8C4C3C1C3C5C3C0C2BFBFBFBFBEC3BFC0BFBFBEBE
 BABFBEBCBDBFBBBFBDBCBCBDBFC3C1C0BDC1C4C3BFC2C1C2C2C2C3C7C4C7C6C5C4C5C1C5
 C3C5C7C5C4C8C5C2BFBEBEBFBEBFBCB9B8B6B3B4B3B5B6B5B1B1ADADADAAA9ACABADABAC
 AAA8A9ABA9ACAFAFADAEA9A9C1C0BDC0C0C3C3C5C6C2C3C8C3C3C4C3C3C5C3C5C3C5C6C7
 C7CAC9CACBCDCDCFCACDCFD1D2D4D0D1CFD1D1D1CFD2CFD1D4D5D3D6D3D4D4D3D6D8D5D7
 D5D4D4D7D4D6D3D6DCDDD7D6D5D8D5D6D7D8D6D8D4D3D3D3D3D4D1D3D4D3D4D7D3D3D4D3
 D4D5D3D5D4D7D4D0CED2CFD0CFCCC9CBC7CAC8C8CBCCC7CBCACDCFCCCACDC9CACBC9C7C8
 C4C4C5C5C3C5C5C6BFC3C7C7C8C7C3C5C8C9C9CBC5C3C3C2C1C2C1C3C0C2C6C3C2C2BDBD
 BDBCBDBFBEBFBCBBBDBDBCBFBBBFC0BDBEC1C0C2C3C4C5C1BFC3C1C3C3C3C5C7C4C5C5C6
 C5C5C3C4C2C8C9C6C5C9C5C3BEBCBDC1BDBDBCBBBAB7B2B5B3B5B5B6B5B3A8A8AAABAAAD
 ABAEACACABAAA7A7A6AAACACACAFAAABBDC0BCBFC3C3BFC3C3C3C3C2C2C5C3C5C2C5C7C5
 C5C9C5C7C7C7C7CAC9CCCACECDCECED3D2D3D1D1D1D3D0D3D2D1D1D3D5D9D4D4D3D2D1D5
 D3D5D6D4D4DAD7D9D8D9D7D5D5DAD5D4D6D6D4D7D5D7DAD8D5D9D6D9D8D2D3D8D5D7D5D5
 D7D6D6DAD6D6D8D7DAE1D7D5D3D2D3D1CCCDC8CACBC7C6CAC7C8C9C7C7CCCAC8C6C7C6C7
 C7CBC6C9CBC8C9CCC8CACAC7C4C6C8CBC6C5C6C7C7C9C9CBC9C5C5C2BDC3C4C3C3C3C3C3
 BFBFBFBFBBBDBCBDBEBCBBBFBDBFBEBBBBBDBEBFB9BBC1C0BEC7C8C6C3C2C3C6C2C3C5C5
 C4C3C2C7C3C5C5C3C3C8C6C5C5C6C5C5C1C3C2C3C2BEBCBEB9B8B7B3B2B6B4B5B4B3AFAD
 AAABAAADADACADAFACADACA8A7A9AAADACADACAABCBEBFC3C8C1BDC2C1C3C4C4C4C5C7CA
 C7C8C8C8CACDC9C9C7C7C8CCCBCCCDD0D0D0CFD1CFD0CFD1D2D4D1D3D3D2D3D5D5D8D4D3
 D3D3D2D5D3D6D6D5D9DCD7D8D7DBD9D4D3D7D5D7D6D6D6D9D6D7DAD8D7DAD7DCDCD7D6DA
 D8D7D3D7D9D9D9DDDADAD9D8DBDFD7D8D5D3D2D1CDCFCBCACAC9C8CBCACCCAC7C9CFC9C5
 C6C7C6C7C7C8C5CBCAC9C8C9C6CCCBC6C6C9C6CAC9C8C9CBCACCCAC9C9CACAC7C0C5C7C6
 C1C1C1C1BFC2C3C1BFC1BFC2C2BEBEC0BDC0BEBBBAC0C1BFBABEC1BFC1C7C7C8C5C3C5C7
 C2C4C4C4C3C3C4C7C5C7C6C3C4C6C3C6C6C4C4C5C3C7C5C4C4C0BCBFBABBB7AFB1B6B3B7
 B6B3AFB1B0B0AFAFAFAFADAFACADACA9A6A9AAACACAFADAEBEBEBEC2C5C3BEC3C4C3C5C7
 C6C8C6C5C6C8C5C8CCCBC8C7C5C6C7CECDCACDD1CBCECFCFCFD3D1D3D1D0D0D1CFD2D1D4
 D6D5D7DAD4D6D4D3D6D7D1D3D3DAD9D5D3D9D6D5D6D5D4D9D7DADAD7D5D8D6D9D8D8D9DA
 D8D7D4D9D9D5D5DBD7DADAD7D7DBD8D7D6D7D7D6D3D5CFD2D3CFCDCECACCCAC9CCCDC8CA
 CACDCAC6C5C5C2C6C7C3C4C9C4C5C5C3C4C5C4C6C1C3C5C5C5C7C4C8C9CACAC9C5CAC9C5
 C5C8C9CAC3C5C4BFC1C6C2C3C1C0C1C3BEBEBDBFBFBDBBBEBBBEC1BDBBBFBCBEBFC3C6C3
 C1C5C6C7C6C6C5C6C3C4C5C5C5C7C5C5C3C3C4C5C4C5C3C7C7C8C7C5C0C0BFBDBCBCB9B8
 B5B5B6B7B7B9B1B1B2B3B1B1AEAFAEAEACAEABABA9ABADACAAAFABAABEBDBFC2C0C2C1C3
 C3C3C2C3C3C6C6C6C7C7C5C8CBCBC8CAC9C9C8CECFCCCFD1CDCFCECFCED2D1D1D0D2D1D0
 CFD3D1D5D5D4DADCD5D7D5D4D5D4D1D5D4D9D8D7D6D7D3D8D9D7D9DBD8DADDDBD7D9D7D9
 D7D9DAD9D8D9D6D8D7D5D7D8D6DADAD7D7DAD7D8D6D7D7D6D3D3CFD0D4D3CFD0CCCFCDCC
 CCCCC9CAC7C9C7C6C6C4C1C6C7C5C4C6C5C6C3C4C6C5C3C7C3C6C8C6C6C8C6C8CACACAC7
 C7C9C9C7C8CACBC9C3C5C6C5C4C7C4C3C1C0C3C7C0BFBEBFBEBEBFC1BCBDC1C1BEC0C2C3
 C1C5C7C5C2C3C3C6C7C6C4C8C6C6C7C7C7C6C3C5C3C5C7C8C6C8C5CACBCBC8C6C3C3C1BF
 BEBFBCBDB8B7B7B8B9BAB4B4B4B5B5B5B0B2AFB2B2B2B0B1ACAFB1AFACAFABAABEC0BEC1
 C0C0C0BFBDC2C1C0C2C5C3C7C7C6C6C6C5CCC6C9CAC7C9CDCACCCDD1D5D3CDD1CFD1D3D0
 CFCECFD2D0D1CFD2D3D7D9D8D7D6D1D4D3D6D5D3D5DAD7D7D5D6D5D7D6D8D7D8D9D7D8DE
 D9D8D7D7D5D9D1DAD9D6D8D9D6D8D4D7DDD3D7D8D5D7D7D7D6D7D3D3D2D0D0CFCCCFCDCD
 CDCCCACDC9C9C9C9C7C8C4C9CBC6C2C5C7C9C3C9CBC9C6C7C3C6C6C3C4C5C3C6C5C6C8C8
 C8CAC6C8CAC9C9CAC6C9C9C7C7C6C3C6C3C2C5C4C1C4C4C7C1BCBDC1BDC0C1C1C0BFBFC3
 BFC3C5C3C1C7C3C3C2C4C6C8C5C8C6C6C9CCC9CAC6C5C3C2C3C6C3C4C4C4C3C7C8CAC7C7
 C6C3BEBFBCBEBFBCB9B8B4BEC3C0BAB9B8B8B7B8B7B6B3B7B6B5B5B4B2B3B3B3AFAEAEAD
 BFC1C0C1C0C2C1BFBDC2C1C3C2C3C5CAC7C9C7C6C7C9C7CDC9C5C9CDCCCEC9D1D9D2CDD2
 D0D4D1CDCFD2D0D3D1D1D0D2D3D7D6D7D7D5D5D7D6D8D7D5D7DBD5D7D7D5D2D8D9D6D3D5
 D7D8D8DDD9D6D7D6D6DAD9DBD9D7D6D7D7DAD7DAD9D8D8D9D6D8D8D7D6D8D5D5D4D2CFCD
 CDCFCECFCECCCDCDCACECFCFCECCC5CCD1CFC9C9CACDC7C9CACAC9CAC7CACAC7C6C7C6C8
 C7C7C9C8C6CDCACACCC9C7C8C7C9C9CAC9C7C6C8C5C4C4C3C3C6C5C6C3C1C0C1BEC2C3C2
 C1C1BFC3C1C3C5C2BFC5C5C5C5C7C9CAC6C7C6C9CCCFCDCFCBC9C6C4C3C7C6C7C6C7C6C6
 C4C6C6C6C4C4C2C3C0C1BFBEBBBAB8C6CCC8C0BDBCBFBBB9B9B8B6B9B7B8B7B1AFB6B7B6
 B0AFAFADBFC1C1C2C2C7C1BFC3C2C0C5C2C3C7C7C7CAC7C9C9C9CACBC7CBC8C9CDCDC9CF
 D2D2D1D0D5D7CECFCFD1D5D4CED4D5D1D2D6D6D7D4D3D2D3D5D6D3D5D6D5D4D2D4D6D1D7
 DAD6D4D6D5D7D7D7D8D9D7DAD8D5D8D7D5D7D4D6D8D7D7D9D7D9D8D7D8D8D6DAD7D4D8D6
 D1D5D0CFCFD0CECDCCCDCBCDCECCCED7D0CDCECFD3D6CCC9CAC8C9C9C7CBC6C7CCCAC9CD
 C4C5C8C8C6C9C9CAC9CACBCBC7CBC8C8C9CAC8CDCAC7C7C7C4C6C3C4C5C6C6C5C0C4C2C2
 C3C3C2C3BFBFC1C2C2C5C4C6C1C1C6C7C4CAC9C7C3C1C3C9C8CDCECFCFC6C1C4C2C3C7C6
 C2CACBC2C0C5C5C8C5C5C2C1C1C1BDBFBCB6B9BFC1C4C0BEBBBABABBB4B5B6B6B7B7B3B2
 AFB1B3B2AFAEADAFBEBFBFC1C3CAC4C2C4C4C5C7C5C8C7C6C8CBC7C9C8C9C9CAC7C8C7CB
 CCC9CBD0CDD0D0D1D5D5CED1D1D5D8D7D4DADAD6D5D5D5D7D2D5D4D3D7D8D4D6D3D3D5D5
 D3D5D3D7D9D7D7D7D4D8D8D8D8D8D6D9D8D8D7D7D6D7D4D7D9D7D7D9D6D9D8D7D7D8D8D8
 D3D3D7D5D4D5D1D3D3D0CFD1CFCFCECFD0D1D1D3CDCDCECDD0D3CDCCCDCAC7C9C9CBC6C9
 CFCCCACDC8C8C9C9C9CCC9C9CBCACBCBC9CDC9C9C9CACBCDC9CBCAC8C5C7C4C3C3C3C3C6
 C7C8C3C4C5C4C4C5C1C2C2BFBFC6C5C6C6C7C4C5C7CBC8C8C6C1C2C8C7CCCECECDCCC4C5
 C4C6C9CACCD1D1C8C1C6C7C7C4C5C2C1C1C2BEBFBCBCBCB8B6BBB9BBBCBBBABBB6B7B6B8
 B7B3B1B3AEB3B4B1AFB2AEADBFBEBDC2C8CBC7C4C3C7C4C4C7C9C4C8C9C7C9C9C7C8C7C8
 C7C8CBCBCACFCFCDCCCCCDD1D1D2D3D2D1D7D9D8D5D7D9D7D2D7D5D3D6D5D2D6D7DADAD5
 D4D6D5D5D5D5D5D7D6DBD9D8D9D8D5D7D5D9D9D9D9D9D7D9D8D6D7D9D5D7D6D5D6D7D9DD
 D9DADAD7D7D7D5D8D6D2D3D3CED2D0CDCDCDCCCFCCD1D2CDCBCBC9CDCDCFD1CDC7CBC7C7
 C9C9C6CAC9C9C9CAC9CBC8CBC9C9CACAC7CCCBCBCED1CECBC7CCCDCCC9CACACFC8C7C7C4
 C2C7C4C6C8C8C6C7C3C5C6C3C3C5C1C4C3C5C7C6C5C8C6C8C7C7C8C9C5C7C8C8CCCFCCCF
 CCCAC9C6C4C9C8CCCAC9CECDC5C5C6C5C6C5C1C2C0C0C1BFBDBFBDBEBCBABABCB9BCBBBB
 BAB9B6B9B7B4B4B3AEB2B1B2AFADAEAFC8C8C7CBCBCBCBCAC5C9C9C8C9CCC9CACBCCCBCA
 C8CBC9CCC9C9CBCEC9CDCFCDCACCCBD0D0D2D3D3D1D5D7D8D6D7D7D7D6D9D6D7D7D7D5D8
 D8DBD9D6D6DAD5D3D4D7D6DADBDDDADBDAD9DADCD9DBDAD9D8DBD9DAD8D7DBDDDCDDDADB
 DBD9DBE3DDDBDAD9D7D9D7D9D7D6D7D7D4D3D1D1CDCDCFD1CED2D2CFCDCFCDCFCECECECC
 CCCCC8CCCCCACBCCC8CCCAC9CACCC9CBCED0CCCBCDD1CDCDD0D3D1CDC9CDCDCCCCCECED0
 CACACAC8C8C9C6C6C8C8C7C7C4C7C5C5C7C7C6C8C5C8CAC7C7C9C8C8C9C9C8CAC8CAC7C8
 CDCFCDCFCAC8C9C5C3C9C9CAC8C7C6C7C4C5C3C6C4C2C1C3BFC2C3C1BFC2BDBEBCBCBCBC
 BABFBDBFBCB9B8BDBABAB8B5B4B5B3B2B0B0B0B2CACACBCDCCCFCDCDCFCDCCCFCDCDCDCC
 CBCECCCDCCCDD1D1CCCECCCDCECECED1CFD1D0CED1D3D1D5D4D5D7D6D3D7D5D6D9D9D6D8
 D6D4D5D7D6D7D9DAD6D7D9D7D6DBD7D7D9D9D9DBD7D5D8D9D9DAD9DCD7D6D8D7D6DAD8D8
 DADDDBDBD7D7DBDBD8D7D6DCD8D7DBDAD7D9D6D9D5CFD3D4CBCFD1D0D1D1D0D4D0CDCFCE
 CCCFCACBCBCACACECBCECCCBCCCCC9CBC9CAC9C9D1DBD0C9CBCFCFCFCFD2CCC9C9CBCACF
 CCCDCCCACACECBCBCBC9C8C8C6CBC8C6C6C5C5C9C5C7C7C7C4C9CACBC6C7CACBC9CCC9C8
 C8C8C7CCC8CACBCCC9C8C6C6C2C4C7C6C5CBC7C3C6C3C0C5C4C2C1C0BFBFBEC0BEBCBCBC
 BABDBABBBDBBBBBFBBB8B8BCBFBEB8B7B4B3B2B3B1B1B1B2C9CACACBC9CBCACDCFCDCFD3
 CDCCCFD1D0D3D1D2CFD1D4DAD4D2D0D3D5D3D4D8D3D4D4D3D2D4D4D7D4D3D3D4D4D5D2D7
 D9D7D6D7D4D7D6D6DADFDCD9D7DADAD9D8DBD9DBD9D8D9DBD7DADADADCDBD8DDD9DADBD7
 D7D8D5DADCDBD9DAD7DADBD9D9DAD9DBD8D9DCD9D8DCD5D5D7D5D4D6CFD3D5D2D1D1D1D5
 D1D1D1CFCFD1CDCDCDCCCCCFCFD1CFCDCBCDCECEC9CBCFCED3DAD0CCCED2D2D3D3D1CBCC
 CCCDCCCFCCCCCBCACBCECBCBCACDCAC7C7CCCBCBC9C8C9CAC7C7C5C6C5CACCCAC3C5CACD
 CACCC9CBC9C6C7CCCACBCBCBCACCC9CAC9C9CAC9C7CBC9C8C8C9C8C8C4C4C1C1C1C1BFC3
 BDBBBEBBB7BDBDBCBABDC1C1BCBDB9BCC0BDB8B6B3B3B5B5B2B2B1B3C4C7C5C7C7C4C5C7
 C7CBCBCAC9CBCBCFCDD0D1D0CED1D3D5D2D0CFD1D2D7D5D4D6D6D4D8D5D5D6D5D3D6D5D6
 D5D6D6D6D4D8D7D6D7D8D7D7DBE6E2DADADBD9DAD8D9DFDAD3D8D7D7D9D9D7DCDBDDDBDA
 DADAD7D9D8D7D9DCDEE0D7D7DBDBD9DEDBDCDBD9D9DAD6DBD9D7D5D3D1D7D4D3D4D5D1D2
 D0D2D3D4D3D2CCD0CDCCCDCECACFCDCCD0D2CFCEC8CFD3CFC9CCCCCFCFD2D0CDCBD0CFD1
 D2CFCDCECBCDCCCDCDCCCACDCACBCBC9C8CFCDCAC5C7CDCBC5C9CBCAC9C7C4C8C5C4C8C9
 C7C5C6CBCACACCCECACDCCCBCCCCCACECDCDCDCBC8C9C7CACACACACBC8CDCBC6C3C3C3C3
 C0C1C1C3C1BFBBBDB9B7BDC0BBBFC0C0BDBCB6B4B6BAB6B5B3B3B2B7B4B2B1B2C4C9C5C6
 C5C3C3C7C7C8C8CACAC9C9CDCACECFCDC9CDCDCFCECDCDD1D3D6D4D3D4D5D4D7D3D5D7D5
 D4D9D7D6D9DDDDD8D7DBD8D5D7D7D6DADEE4E0DCDDDFDBDBDADFE3DCD6DBD9D7D9D7D8DF
 DDDDDCD9DADDDBDCD9D8DADDE4E0D2D7DDDADBDFDADDDDDADBDCD7D7D8D8D4D2D1D6D2D3
 D4D2D1D4D2D5D5D5D3D0CDD2D0D0D0CDCBCFCDCFCFD0D0D1CDD3D4CECBD2D3D1CFD5D7D3
 CED2D1D3D2D0CFD2D1D2CFD1D1D1CFD0CBCDCECDCBCFCDCDCBCCCDCECACBC9CBCAC9C7CB
 C9CAC9C8C7C9CACECFD1D0CFCACFD1D0CECCC9CFCFCFCFCCCACBC9CACACBCAC9C9CDC9C9
 C7C5C5C6C3C3C3C3C1C1BFC1BDBCBFBFBCBEBDBFBFBDBAB7B7B9B9B7B3B4B2B6B3B1B1B2
 C8C7C9C9C4C7C4C4C7C7C6C9C7C8C8CAC9CBC9CBCAC9C9CBCACECDCFD1D3D2D3D0D3D3D5
 D4D3D3D7D7D6D6D6D4DDDBD6D7D8D7D7D4D7D7D8D9DCD9DDDFE1DCD7DCE8E8E0DBDDDCDC
 D6DADADADBDBD9DFDCDCDCDCDBDAD7DDDFDCD8DAD7DADDDCDCDDDBDFDEDBD9DAD9DCD7D3
 D3D2D1D6D6D6D3D2D3D1CED3D3D3D1D1D0D3D1D1D1CFD1D1CDD1D1CFD2D6D3D3D3D8D9D2
 D1D7D6D7D3D0D3D9D5D2D0D2D3D3D1D5D3D3D1D0D0D1CECECECECFD0CCCDCDCECFCCCBCE
 CCCCC9C9CED2CBCBCBCCCDD2CFCFCFCFCCCDCBCECCCDCDCCCCCEC8C9C9C7C6CACACBC6C6
 C8C7C6CAC7C7C7C5C4C5C1C1C0C0C0BFBCBCBABBBABCBCBDBABDBCBBBABAB8B9B6B4B4B5
 B5B6B3B3C9CACAC9C6C7C4C5C7C6C5C9C6C6C9C7C7CBC9C9C8C9C9CACCCFCCCFD3D3D0D3
 D2D3D3D2D3D6D5D5D3D6D7D5D5D9D7D7D8D8D6D7D5D7DBDBDBDBD9DCDCE2DDD4D9E5E5E2
 E0E0DEDCDADDDCD7D8DBDADCD9DADCDAD9DCDADDDDDDDBDCDADCDFE2E2E0DCE0DEDCDCDA
 D9DFDAD6D6D6D4D9E0DDD6D6D6D5D3D3D1D3D4D3D1D4D2D4D4D4D4D2D1D5D2D2D4D5D4D4
 D2D3D5D3D1D5D2D4D3D2D5D8D6D7D3D3D4D4D3D6D2D3D3D3CFD1D0D3D0D2D3D1CFD1CDCD
 D0CFCDCFCBCCCCCDD1D7CEC9C8CCD0D1CFD0CCCBCCCBC9CDC9CCCDCDCDCBC6C9C9C9CACC
 C8CAC7C7C7C4C5CAC9CAC7C7C6C5C2C3C1C2C4C3BFC1BEBDBDBEBDBFBDBDBBBDBEBBB7BB
 BCBAB7B5B3B5B4B3CCC9C6C7C4C6CACBC2C5C9C7C7CCCBCCC8C9C9CBCCCDC9CDCDCACCD1
 CED1D1D2D0D1CFD3D2D3D5D5D3D7D4D5D5D5D6D8D7DCD8D6D4DBE2E0DAD9D9DADFE2D9D7
 D9D9DCDBD7DFE3DDDBDBD7D9D8D8D9DADADAD8DCDCDBDEDFD9DCDDDEDCDBDDE1E0DFDCDF
 E1DDD7DBDCDBD9D6D3D6D4D8DDD7D4DAD7D9D8D3D4D6D2D3D3D2D3D6D4D3CFCFD1D6D5D0
 CDD2D5D3D2D5D0D1D1D1D1D5D2D2D1D4D5D1CFD2D6DBD4D2D3D4D1D1CFCFCECFD1D4CFCF
 CDCDCCCFCDD2CFCBCCCFCED1CFD1CECACBCDC9CECDCBCACBC8C9C9C7C9CDCACCCBCBC9C8
 CACDC6C6C9C7C3C7C3C4C5C8CDCCC5C5C3C5C4C1C1C5C3C4C4C2BEBDBDBDBCBDBDBDBCC0
 BDBCBCB9B8BBB5B3B4B2B0B3C7C9C5C7C7C7C7C8C6CAC7C7C8CBC9CECDCDCCCCCBCFCDCE
 CCCCCFD2D1D2D1D3D3D2D0D3D0D4D5D2D2D7D4D4D5D7D4D3DCE3D9D6D7DFE4DFD7DADBD7
 DCE1D9D8D8D8D9D9D9DFE1DBD9D9D8DAD6D8DCDBD9DBDBDCDBDDDEDDDCDDDCDFDCD8DADF
 DEE0DFDEDDDCD7D9DADBD9D6D5D9D6D6D9D6D6E0DDDAD9D5D4D5D3D4D3D2D1D4D7D7CFCF
 D3D7D5D3D0D3D4D2D1D3D0D3D0D1D4D6D6D8D4D3D3D1D1D3D8DDD5D1D1CFCFD2CFCECCCC
 D1D8CECACED0CCCFCDD1CFCCCDCFCED1CFCDCBCBCACFCCCACDCFCCCBCACDCBCBCBCBCCCF
 CCCCCBC9C9CCCACAC8C7C6C5C4C5C4CACECAC3C2C0C3C4C2C1C6C4C2C1C3C1BFBFC2BDBC
 BFBFBDBFBBBABCBBB7B5B4B7B4B3B3B1C7C8C9C8C3CACAC9C8CAC9CBC9CAC8CACDCFCCCD
 CDCDD2D3CBCED1D2D0D1D3D4CDD1D1D2D3D5D1D4D4D4D3D5D3D5D3D5D8DAD7D5D4DCDCD6
 D6D9D7DBDCDDD9DAD8DBD7D8D9DBDDDAD7DBD8D7DADBD8DBDAD8D8D8D9DBD9DADAD9DCDF
 D8D8DBDEDFDBD9DDDCDBDAD7D7DBD9D8D8D7D7D9D6D7DADDDBD7D4D8D6D4D4D3D1CDCCD6
 DBD5D1D2CDD4D6D3D5D5D1D4D4D3D3D2D3D3D2D7D7D1D0D3D1D3D3D3D5D4CDD1D0D1D0D1
 D6D6CECACCD2CDCFCFD2CECACACFCDCDCDCFCDC9C9CCC9CCCCCDCDD0CFD1D0D0CECECCCC
 CACDCDCCCDCEC8CBCBC9C9C9C7C9C6C6C4C3C4C9C9CAC7C5C3C5C1C3C3C3C3C5C2C2C1C2
 C1BFBCC0BEBEBCBCBBBFBBBAB8B7B6B7B6B5B2B3C7CACDCBC7C9C9CBCDCDC9CDCCCFD0D1
 D1D1CDCFCCCBD5D8CBCBCED1D3D3D3D6D2D3D5D6D7D7D5D7D4D6D9D7D5D7D5D7D8D7D6D7
 D7DAD9D8D9D9D9DBD8D8DBDBD9DBD8D8D9DAD9DBD9D9DADCDDDDD9DCD9D9DAD9D9DBDADC
 DBDDDFDFD9D9DCE2E1DCDADEDAD9DAD7D6DBD7D6D9DAD6D7D7DAD9DAD9D9D7D8D5D6D6D3
 D2D4D2D7D8D7D6D4D2D7D6D7D7D4D3D5D1D2D3D3D2D4D3D7D7D6D6D5D1D6D3D2D3D3D1D3
 D0D2D3D6D6D7D3D5D1D3D8D7D0D1D0CFCFCECCD1CFCDCCCCCCCDCBCECDCCD0D2D1D3CFCF
 CFCFCDCFCDCECDCFCFCDC9CDCBCACBCAC8CBC7C6C8C6C6CAC8C7C6C7C8C5C3C7C3C0C3C7
 C4C4C1C5C4C1BDC2C0C0BFBFBFBDB9BCB9B8B9BAB6B6B3B3C6C8C8C9C9C9C9CBC7C9C9CA
 CCCFCDD0CECCCDCFCACBD1D6CFCBCDCFCFD4D5D4D3D5D3D7D7D6D5D6D3D7D7D8D6D7D7D7
 D3D7D7D6D7D9D8DBD8D7D9D9D5D7D7DBDAD9D9D9D6D9DADBDCDDDCE1DEDDDCDEDDDAD7DB
 D9DADBDCD9DCDBDCDBDBDCE1DEDCDDDDDCDCD8DAD9D7D8DAD5D5D7D9D9D9D8DDDAD7D7D7
 D7D8D2D4D5D3D3D4D2D6D6D5D5D5D4D6D4D5D4D4D6D7D4D6D3D2D3D2CFD5D5D4D4D1D0D4
 D3D3D3D3D3D3D0D3D5D4D3D5D1D2D1D5D3CDCFD2CED0CECFD0D1CCD0CFCCCCCECDD1CFD3
 D3D1D1D2CED1D0CFCFCFCFD2CFCFCDCDCBCECACCCBC9C8CAC9CBC8C7C9C9C6C9C6C7C8C8
 C5C4C0C3C3C2BFC1C0C2BFBDBBBDBDBDBABCB8B7BCBDB7B6B5B7B6B5C1C4C5C6C7C5C4C6
 C6CAC8C6C9CDCED1CDCECFCCC9CFD0D2CECCCDCFD0D5D5D4D5D2CFD3D3D3D3D3D2D5D5D5
 D4D5D7D6D2D6D4D4D7D8D9DAD3D7DFDAD2D4D5D7D7D6D7D8D7D9D9DADCDDDCE1E1E2DCDF
 E2DCD7DCD9DADADBDCDFDAD9DBDBD9DEDBDDDDDDDADBDBDED9D8D9DAD6D8D7D7D7D7D7DC
 D9D9D7D6D4D6D3D4D3D3D4D3D1D7D5D4D5D6D5D6D3D7D5D8DCDCD4D5D3D5D6D3CFD5D4D1
 CFD0D1D3D0D3D1D3D3D3D0D3D2D3D4D3CFD0CFD2D2D0D0D2CFCFCFD0D1CFCCD1D0D0CFCE
 CDD1D1D3D3D3D4D3D0D2D0D1D1D0CECFCECFCECCCDCCCBCECBC9CBCCC9CCCAC8C7C7C7C7
 C4C7C7C7C4C2BDC3C1BFBFC1BCC0BEBDBDBEBDBEBCBDBABBBBBAB9BDB9B5B4B5C6C5C5CA
 C7C6C1C3C4C5C9CCC7C7C9C9C9CAC8CBCCCCCDCFCDCFCDCECDCED1D3D0D3D1CFD1D0CED3
 D3D3D5D4D1D6D4D4D4D3D4D7D4D7D9D5D2D6D9DCD9D7DADBD9DBD9D7D6D6D9DCD8DBDCDA
 DEE3DBE0E3E1DDDAD9DBD8D9DDDDDBDCD7DADAD9DBDBD9DDDBDADCDAD8D9D8D9D7D3D4D9
 D4D5D6D7D9D9D5D7D6D7D6D3D3D5D1D1D0D1D4D6D3D6D7D4D1D4D3D6D8DDD4CDD3D8D2D2
 D3D2D1D2CFD2D3D3D1D3D1D3D1D3D1D1D1D6D0D1D1D0D1D3D0D1CED0D1D0CECFCBCECECD
 CFD2CFD0D1D1D2D3D3D6D6D7D3D1CFD1CED1D1CFCED1CDCDCCCBCBCCC9C8C3C5C8C9C9C9
 C5C8C9C6C3C4C3C5C3C1C1C2C2C3BEBDC0C1C1C1BCBEBFBFBEBDBDBCB8BABDBFBFBAB4B5
 C8C7CCCCC8C8C6C7C9CBC9C9C7CBC9C7C6C9C9CAC9C9CCCDCACDCCCCCDCFCFD1D0D2CFD1
 D2D2D2D6D5D5D5D7D5D6D5D7D7D6D4D7D7D8D8D9D5D5D7DDDADCE0DFD9DEDCD9D8D9DBDB
 D9DDD9D8DCDFDCE0DEDEDDDCD9DAD8DCDFDFDADAD9DDDADADBDBDADDD9D8D9D9D7D8D7D8
 D5D6D8D7D5DAD7D8D8D8D7DBD9D7D6D6D7DAD3D0CED2D5D6D2D7D6D3D3D3D3D8D6D9D7D4
 DADCD3D5D5D2D1D1D0D5D5D6D5D4D3D3D1D6D3D0D2D3D0D3D1D1D3D3D0D2D0CDCED0D0D2
 CFD2CCC8CFD4D0D2D1CFCFD2D3D5D4D6D3D2D0D1D0D2D1CFCFD0CCCFCCCBCCCDCAC9C7C7
 C5C7C7CAC7C9C8C7C7C7C4C8C8C7C5C6C5C4C0C2C2C5C8C5BFC2C0BFBEBFBCBDBBBCBCC2
 C4C1BABAC7CCC9C9C9C9C9CCCED2CAC7C9CBCACBCACDCECBCBCECCCCCECDCBCCCBCDCCCF
 CECDCED2CFD1D2D3D5D7D3D3D7D6D4D5D4D6D3D4D9D8DBE1D5D3D8D9D8DADADBDADADBDA
 D6D9D9DADFE2D9D9D7D8D9D9D9DBD9DCDDDBDADEDFDFD9DADDDCDBDFDADBDAD9D9DDD9DA
 D9D9D7D7D3D6D6D8DDDDD9DAD6D9D7D7D8D9D5D5D9DFD5CBCCD5D5D5D5D5D5D8D3D4D5D4
 D2D9D9D7D9D8D4D3D1D4D1D3D3D4D2D5D2D2D3D3D1D4D5D5D1D3D4D2D1D3D1D2D3D1D1D4
 D1D1D3D5D3D2CFCECDCFD1D0D0D2CFCFCED0D0D4D4D4D1D2D2D2D0D1CDCFD0CFCBCECDCF
 CCCCCCCDCBCBCACACBCBC9CBC9C8C6C5C9CBC6C5C6C8C5C3C0C6C6C5C1C0BFC0BCBCBCBC
 BBBCBBBDBEBEBEBCC6CACBCBCACBCAC9CCD3CDC9CBCCCACDCACBCDCDCCCDCBCFD0D0CFCF
 CDD2D1D0D0D1CED0CED2D4D3D4D6D2D4D5D4D3D2CFD5D3D1D5D8D9DDD4D5D7D7D7D6D3D8
 D8D7D7D6D6DAD9DAE4E8D7D5D6D9DADAD8DADCE0DCDADBDCDBDFDCDBDCDDDCE0DEE0DFE0
 DFDFDBDCD9D8D8D6D3D6D6D9DCE1DBD6D5D8D8D8D7D7D2D5D7D8D4D2D3D8D7D8D4D3D6D7
 D5D7D5D3D2D6D5D5D3D3D2D2CFD1D1D3D1D2D3D3D0D3D2D1D1D2D1D5D1CFD1D0CFD2D1D3
 D0D0D0D2CFD1D4D5D1CFCDCECDCECFCFCFD2D0D1CFD0D3D5D3D6D3D3D4D3D1D4D1D1D0CD
 CACDCDD0CDCBCCCDC9CAC9CCCDCBC8C9C6C8C7C4C6C8C4C6C4C3C4C3BDC4C3C1BFBFBDBD
 BCBEB8B9B9B9B9BCBAB8B9BACACACACCCBCCCBCBCBCAC9CDC9C8CCCBCBCDCACCCDCDCED0
 D1D4CFD0D2D1D1D3D1D3D3D1D0D3D1D3D4D5D8DAD9DBD6D1D1D3D2D2CFD2D4D3D2D6D3D7
 DADAD7D4D3D7D5D3D3D3D4DADDDED5D5D6D8D5D9DADCDEDFD9D8D4D7D8D8D9DBD8DEDED9
 D9DCDADFDDDAD9DAD7D8D5D5D4D2D1D5D6DAD9D4D3D4D3D5D4D7D7D3D3D8D3D1D3D5D7DC
 D6D3D3D5D5D3D1D3D0D3D5D3CED1D0D2D1D0CFCFCFD2CFD1D3D2CFD2D0D2D5D5CFD0CFD0
 D0CFCED0CECFD0D3CFC9D1D8D0CFD0CFCED0CECECFD2D1CFCFD2D1D3D4D3D1D4D2D3D3D4
 D3D2CFCFCDCDCECDCBCDC9C9CBCAC9D1CCC6C7C8C7C5C4C5C3C5C7C5C1C5C3C2BFC1C1C3
 BDBEBDBCBCBDBBBEBCBBB9B7B7BCB9B3C9CBCDCECDCCCACACACBCACBCACBCBCCCDCFCDCF
 CED1D2D1D3D6D0CFD0D1D2D3D3D4D2D2D3D5D3D7D7D7D8D9D9DDD9D6D5D8D5D5D4D8D7D4
 D5D7D7DADBDDDFDCD6D6D5D5D3D5D8DAD9DCD9D7D8D9D8DCD9D9DDDDD7D8D7D8D7DBDBD8
 D7E1DDDCDCDCDCDFDAD6D8D9D6D7D5D6D3D3D4D6D7D8D3D3D2D3D3D7D3D4D5D3D1D2D0D4
 D3D7DBD9D3D3D3D6D4D3D4D6D1D1D3D5D2D3D0D2D0D1D1D1CFD3D2D2D3D2D1D5D3D3D8DD
 D5D0D1D5D2D0D3D3CFCFD1D3D1D0D2D6D1D0D0D0D1D1CFD1D0D2D4D5D3D6D4D3D3D3D1D4
 D2D3D2D2D4D6D0D2CFCDCDCFCDCDCACCCDCBCACFD1CEC7C6C7C5C3C5C2C4C8C7C3C3C1C2
 C1C2C1C1BDBFBFBEBDBEBBBDBBB8B7B9B8B9B9B9C7C8C7CACBC9C9CBC9CACACACACAC9CC
 CBCCCDCECFD1D0D1D1D2D2D3CDCFCFD0D4D5D1D5D3D3D1D4D7D9D4D5D8DAD8D7D5D7D7D7
 D8D9D6D8D5D7D8D7D9DDDBDFDDD7D7DCD9D9DDE1DFDCDBDEDBDBDBDBDBDCD8DBDAD9D9DA
 D8D9D6D8D9DADBDED9DBDDDDDBDBD7D9D8D8D9DAD8DAD8DFE1D6D8DFD6D5D7DBD9D7D5D7
 D4D3D4D6D2D4D4D7D7D7D7D7D3D5D7D5D6D7D4D5D1D3D3D1D3D3CFD1D1D1D2D7D4D4D3D3
 D6DBDBDFD7D4D5D3CFD1D0D2D3D2CFD2D1D1D0D0D1D4D2D4D2D2D3D3D3D4D3D7D7D4D3D3
 D2D5D5D3D2D5D3D4D3D6D4D0CECFCECFCECFCCCCCACBC8CBCDCECBCCC8C5C6C7C5C6C4C4
 C3C2C2C3C2C2BEBFBFC1BFC0BCBBBDBAB6B9B8BAB8B8B9B8C9CBCACAC9C9CACAC8CBCAC8
 CBCBC9CDCBCDCDCFCDCFD1D2CFCFD0D0CDD2CDCFDAD9D2D5D3D3D3D5D7D8D3D6D5D7D6D5
 D5D9D6D7D6D7D6D8D5D7D8D7DADCD8DFDCD7D9DBDAE1E1E0E1E1DEDFDDDFDDDBDADCD9DB
 DBDADBDAD8DBD9D9DADCDCDFDCDBDAD9D9DBD9DCDADADCDAD9DEDDE3DED7DDE0D9DADADE
 DCD4D4DBD9D7D7D6D3D7D8D9DADFDDD7D5D8D9D9D8D7D4D7D4D5D6D6D4D1CDD1D3D5D3D2
 D1D5D3D1D5D8D7D9D5D4D4D3D0D3D1D1D0D1D1D2D1D3D0D1D3D3D1D3D2D1D1D4D4D4D2D6
 D4D3D2CFCFD4D4D5D5D4D3D4D3D5D2D0CFD1CED2D3CFCDCEC9CCCACACACDCACCC8C6C4C6
 C6C5C1C3C3BFBFC4C3C2BFC1BFBFBEBFBBBCBAB9BABAB7BBBDBBB8B9C9C8C7C6C7CBC9CB
 CAC7C8CDCBCCCDCBCBCECDD0CFCECFD1CFD2D1D2D2D1CDD5D9D7D3D2D3D3D0D5D7D7D7D5
 D5D9D5D5D8D8D7DCD6D3D6D5D4D8D5D7D8D9D9D9D9DCD8DADBDBDCDFE1E6E3DFDCDDD8D9
 DADCDAD9DCE0DCDBD8D8DADDD8D9DEE2DEDAD7DBD8DADBD9D9DCD9DBDFDFD9DCD8D7D9D9
 D6D7D5D9D5D1D5D7D6D8D6D5D5D6D7D9DBDFD8D7D6D6D8DCD8D8D8D7D5D8D5D7D4D3D3D3
 D3D4D0D2D2D1D2D5D3D4D7D7D3D5D3D3D2D3D2D2D0D1D1D2D2D1CDD1D0D0D1D1D0D2D2D5
 D4D3D3D2D1D5D2CFD2D3D4D7D3D5D3D3D3D3D1D2D2D3D0CFD3D5CFCFD0CFCCCDCBCCC9CA
 C9C4C1C6C5C3C2C2BFBDB9BFC3C2BFC1BABCBEBEBCBCB9BEBCBBB8B7B7BAB7B7C9CCCDCC
 CACECBCCCBCBCCCDCBCFCDCDCED0CED2D1D2D1D2D2D5D2D5D5D2D1D4D1D6D6D4D4D6D3D7
 D6D6D6D5D6D9D5D6D7D9D9DBD6D9D7D6D6DAD9DCDAD9D9D9D8DAD8DADBDBDDDFDEE4E1DD
 DDDDDBDDDAD9D9DBDADDDBDDDCDADCDEDADCE1E5E1DDDADEDBDBD9D8D8D8D5D6D9DDD9D7
 D5D8D7D4D5D7D5D8D6D5D4D6D3D3D3D6D4D3D6D8D7DBD7D5D7D8D9DDDAD9D8D7D7D8D7D7
 D4D3D4D5D3D5D4D5D3D2D2D7D7D6D5D6D5D5D0D4D4D2D4D6D3D5D6D7D3D3D1D3D1D3D2D2
 D1D4D1D3D5D5D0D3D4D5D3D5D4D3D5D6D3D6D3D3D4D6D2D4D6D7D4D3D2D3CFD1D1D2CFCD
 CDD1CBCAC9C6C3C7C4C3C2C1BFBDB6BCC1C2C0BFBDBFBEBDBBBDBCBCBBBCBBB8B8BAB5B5
 CCD0CACBCCCCCBCFCCCBC9CCCDCECCD0CED0D1D1D1D4D0D0D2D3D1D5D4D3D0D1D3D4D3D6
 D4D3D4D5D4D7D5D6D6D6D5D5D1D4D5D5D8D6D3D8D7D7DADBD9DAD6D8D7D8D9DBD9DBD9DA
 DDDFDBDEDADBDCDCDAD9D6DBDADADCDCDADBD9DBDDDDDEE7E3E1DFDCDDDED9DAD9D7D8D8
 D7DBD7D6D8D8D5D8D6D8D8D6D7D9D8DBD6D2D5D6D5D8D6D6D8DBD9D8D7D7D6D8D5D4D6D8
 D7D7D8D7D3D5D3D3D3D5D4D5D3D3D3D6DDDED4D5D5D3D4D6D4D5D2D3D3D3D4D6D3D4D2D0
 D1D3D1D4D1D1D1D2D1D4D0D2D3D6D5D5D3D5D3D3D3D5D5D7D2D5D4D3D4D6D2D1CCCBCED1
 CCCFCDCACACDCACBC9C7C5C5C4C6C3C3C1C1BFC1C0C2C0BFBFC0BEBFBABCBDBEBCBBB9BB
 B8B8B9B9CBCBC9CBCACBCFD1CACBCCCCCDCFCCCFCECFD0D0D0D2CED1D1D1D1D2CFD0D1D1
 D1D3D3D7D5D4D7D8D7D7D4D6D5D2D3D5D3D5D6D7D7D6D4D8D6D6DADCD9D7D5D9D7D7D9DC
 DBDDDDDCDADDDDDDDCDDDDDEDDDDD8DBDCDADCDDDBDCDCDDDDDBD9DCDDDEDCDDDDDBD9DB
 DBDBDCDBD9D9D9DBDBD9D9DBD8D8D6D7D7D6D5D9D5D3D6DAD9D8D7D9D7D9DBD9D6D7D6D5
 D5D5D3D7D6D6D4D4D3D2D1D5D3D2D3D5D2D4D5D8DCDDD7D6D5D6D5D6D4D6D3D6D5D3D3D3
 D1D5D3D2D2D3D1D2D1D3D3D3D3D4D0D3D5D5D6D7D3D6D4D5D5D7D8DAD7D9D4D2D4D4CDCF
 CFCDCBCAC8CCCBCBCACBC9C8C5C8C9C6C7C9C4C4C4C3C1C2C1C2C0C3C5C2BFC0BCBFC0BD
 BCBEBBBAB8B9B8B8C9CAC9C8C7CDCECDCCCBCACECDCFCCCFD0D2CFD1D0CFD1D2CFD2D1D1
 D0CFCDD1D2D4D4D5D7D6D3D6D4D3D3D3D2D6D4D5D8D6D3D6D6D6D4D7D9D7D9E1DBD8DBDC
 D9DCD9D6D9DCDBDCDADDDBDBDBDBD9DDDDDCDBDBDBDEDCDBDADADADBDADCDAD9DADCDEE1
 DBD9DCDBD7DAD9DAD9D9D8DBDADAD9D9D9D6D3D6D6D6D6D6D6D8D6D9DBD8D6D7D6D9D9D8
 D9D7D3D5D3D3D3D4D4D5D4D6D3D1D1D2CDD4D5D3D4D5D4D9D7DADBD5D1D4D3D6D5D3D3D4
 D1D3D3D5D3D5D3D4D1D3D6D7D5D6D4D5D3D2D2D2CED1D4D5D4D4D2D3D3D6D6D6D7D7D3D3
 D2D2D3D2CECFCED0CDCDCDCEC9C9C9C8C6C6C3C6C7C5C5C5C2C3C2C4C3C1C1C5C7C6BFBF
 C0C1BFC1C0BFBDBDB9B9B7B9CAC7C7CBCACFCCC8C9CDCDCFCDCFCFD1D1D3D2D3CDCBD1D3
 D0D3D1D3D2D3D2D4D2D6D6D4D5D9D6D8D5D2D1D5D3D6D4D5D6D8D8D8D7D9D8D7DBDCDDE5
 E0DBDADCDADCDADBD9DADDDDD9DCD9DADAD9D7DDDBDBDBDCDDDFD9DADAD9DBDFDCDDDCDD
 DDDDE1E3DEDCD9D8D6D8D9DAD8D9DADBD7D9D8D8D8D6D6D7D6D7D5D5D8D8D4D7D7D5D7DD
 D9D7D8D8D8D8D6D6D4D6D4D4D1CECCD3D5D3D4D5D3D7D6D3D5D5D5DAD9DCDBD4D0D3D1D4
 D3D4D3D3D3D4D3D5D3D2D3D7D4D7D8DADBDAD5D6D3D2D3D6D2D3D3D5D4D4D5D7D6D8D7D4
 D2D4D2D4D1D1D1D3D0D1D0D3CFCDCDCECACAC7C5C6C6C2C4C3C2C1C5C6C4C1C4C4C2C2C6
 C9C8BFBCBDBFBEC3C3C4BFBDBEBDB7BACACCCAD1D3D0CDCCCACDCCCCCDCDCDD2D1D1D2D1
 CFD3D3D5D5D5D5D6D4D6D3D4D5D6D3D5D4D7D9D7D4D2CFD6D6D5D5D7D7DAD8D5D7D7D6DC
 DCDADDE1E0E3DFDBDADADBDCDADCDBD9DBDCDBDDDAD8D9DAD8DBDBDDDDDCDBDBD8DBD9DA
 DCDAD9DEDBDCDCDDDAD7D5DADBDBDBDAD7DFDDD7D7D7D6DAD7D7D7D7D7DAD5D7D7D8D9D6
 D4D8D6DFE0D5D2D7D6D8D7D5D4D8D6D6D4D5D7D6D3D7D5D1D0D6D6D4D2D2D3D6D7DDE1DD
 D3D1D2D5D4D5D1D2D3D3D4D4D2D5D4D5D4D4D5DCDAD8D8D8D3D5D6D7D5D6D7D8D5D6D5D6
 D6D7D7DBD6D5D3D4D3D3D1D2CFD1D1D0CDCFCFCDCBCBC6C7C8C6C2C3C6C5C2C4C3C0BFC1
 BFC1BFBFBFC1BFBFBABBBCBEC1C4C0BFBCB9B9B9CBCAC9D5D5CECBCDCBCECDCFCFD1CFD2
 D1D3D4D5D2D5D5D6D3D5D4D3D5D7D1D3D5D7D4D3D1D5D6D8D6D3D3D7D6D5D6D7D7DADAD7
 D6D7D6DBDBDCDFDFDFE5E0DBD8D8D9DAD9DDDDDDDFDFDDE0DDDBDADCDBDDDADDDBDCDBDD
 DDDDDDDFDCD9DADCDBDCDDDDDAD9D7DCDCDCDCDBD9E6E7D9D6D9D9DAD9DAD8D7D8DAD7D9
 DADBD9D5D3D5D7E1E0D8D9DAD7D9D8D9D9D7D6D7D5D5D4D5D3D6D4D5D3D1D3D5D3D4D3D3
 D4D9DCD8D1D3D2D4D6D5D1D6D6D6D6D7D3D6D5D5D5D5D6D8D6D8D8D7D5D6D5D9D9D5D5D8
 D6D8D7D6D6D6D9DCD6D5D3D2D2D3D1D3CFCFCFD2D0D1CFD0CFCDC9CAC8C8C7C7C6C1BBC3
 C6C5C2C1BFBFBCBBBDBFBFBFB9BBBAB9BDC1BDBFBCBAB7B8CBC8CBD2CFCFCED1D1CFCCCD
 CDD1D2D2D3D4D3D5D6D8DCD8D2D8D6D3D5D5CFD1D3D8D5D3D5D8D5D8D7D8D9D8D6D9D6D5
 DADBD9D8D7D9D7D6D9DBDADBDBE1DFD9D7DAD9D8DADCD9DADCDED9DCDFDCD9DDDBDDDFDD
 DADCDADEDEDEDEDDDBDFDDDBDCDCDADDD9DADCDBD9DCDAD9DAE1E2DAD5DBD9DAD9D9D8D9
 D8D9D7D8E0E1D6D3D7D5D4D8D7D7D7D6D4D5D5D8D6D7D6D5D4D5D5D8D6D5D5D5D1D5D4D3
 D4D5D2D4D2D4D6D5D3D4D3D6D3D5D6D4D3D7D6D5D8D7D2D4D3D5D9D8D5D8D5D7D5D4D4D7
 D6D5D3D3D5D7D5D7D4D1D3DAD9D7D3D5D4D3D3D3D1D2D1CFCDD0CFCFCDCECBC9C9CAC7C9
 C7C6C5C3C3C6C4C2C0C1BFBCBABFBFBEBDBEBCBDBEBFBEBEBDBDB9B9C6C7CDD0CFCFCECF
 CDCDCFD1CFD4D3D1D2D4D4D8D8D8D9DAD9DBD8D7D4D3D5D5D1D6D8D8D9DBD9DADCDBD9DA
 DADBD9DADBDCDBDBD7D9D9D8D9DCDADCDCDDDDDCDAD9D9DCDDDDDCDCDADCDDDDDEDEDBDD
 DCDDDBD9DDDEDCDFDFDDDFE0DDDEDEDEDFDFDCDEDBDADADBDBD9D4D9DBDADDDFDADBDBD9
 D9D9D8DAD7D7D7DAE2E4D7D1D1D2D5D8D5D5D4D5D4D6D5D6D6D8D6D7D9DAD9DFD9D5D4D7
 D6D6D4D5D4D5D5D5D4D7D6D3D3D3D2D2CDD2D4D5D4D6D3D9DDDAD7D7D2D8E1DDD7DAD7D7
 D3D3D4D5D5D5D0D4D6D6D6D8D7D5D4D7D6D6D5D5D3D3D2D3D7D9D3D2D1CFCFCDCCD0CECC
 CBC9C7C9C7C5C5C5C5C8C6C6C3C1C0C0C1C4C3BFBABDC1BFBBBDBDBBB9BCB7B7C8CCCCCD
 CDCECFCFCCCFD0CFD3D5CFD2D3D3D3D6D9DEDCDAD9D9DADAD5D7D6D4D7D8D6DADADADAD9
 D9DEDDDCD9DBDADBD9DCDAD7D8DAD7DCDADADCDDDDE1DEDFDBDADBDCDBE0DCDBDCDDDCDD
 DDDFDBDADCE2DDDEDDDCDFE1DEE0DDDCDDDFDEDEDBDDDDDCDADCDADDDCD9D7D8DADDDBDA
 D9DAD9DCD8DAD6D6D6D5D4DADADAD6D3D1D5D5D7D5D6D7D6D7DFD9D2D5D9D6DBDAD6D9DE
 D7D5D4D4D4D5D4D5D2D5D5D4D5D7D6D9D7D5D3D3CFD2D3D3D3D6D6D9D9D9D5D3D5D6D9DE
 DAD9DADAD8D6D3D6D5D5D4D6D5D8D8D7D6D7D4D7D8D8D7D5D4D6D3D5D7D7D3D4D1D1D1D0
 CFCFCCCDCCCDC9C7C6C6C2C4C3C3C3C4C0C1BFBDBDC1C1C2BCBFC0BDBBBCB9BAB8B8B9BA
 CDCECACDCFCFD0D1CDD0D1D2D2D4D3D4D3D5D5D6D8DFE1E1DEDCDBDAD6D7D7D8D7D7D9D9
 D7D8D9DCDBDCD8DADCDEDADADADCDBDCDBDADADDD7D4D8DCDCDDDBDCDBDAD9D8D8DCDCDD
 DCDDDDDFDEE3E1DCE0E8E1DCDDDFE0E1DDDDDBDDDDDDDDDFDCDFDFDFDFDFDDDFDDDCD7D7
 DADFDADADCDCD7D9D6D9D8D6D6D4D4D7D8D8D7D6D4D8D7DBD9D5D8DADCE5D9CFD5DAD7D8
 D8DAD7D5D5D7D4D7D7D5D4D7D3D4D3D3D5D6D4D6D3D3D3D3D3D5D3D4D6D7D4D6D5D7D4D4
 D5D7D7DBD9DCDAD6D7DAD6D7D8D7D5D6D6D7D7D8D8D7D6D9D6D7D7D4D3D7D4D6D8D9D6D4
 D1D3D2D2D1D0D1D2CACACBC8C6C6C1C1C1C2C1C3C1C2BFC0BFBFC0BFB7BCC1BCB8BABABB
 B9B7B7B9CFCDCECFCDD0CFCFCFD1CFD0D0D3D2D2D4D6D4D6D7DDE2E3DFDCD9D8D5D7D6D7
 D3D7D8D7D7DBD8D9D7D4D6DDDCDDDCDDDBDAD9DBDBDEDDDAD5D2D6DDDBDCDCDBD8DAD9DB
 D8DFE5DFD7DDDFDCDCE3E3DFDFE2DFDDDBDDD9DCDDDADADDD9DBDCDDDAD9D9DFDCDBDEDE
 DDE3DCDADCDDDCDCD9D9D9D8D7D9D5D7D6D8DBD8D6DAD5D3D6DCDCD9D3D5D8D8DADDD6D2
 D5DAD7D3D4D6D3D5D7D5D4D5D2D5D5D6D3D2D2D2CFD2D3D2D1D5D1D1D3D5D5D5D3D6D5D5
 D7D9D6D7D3D5D9D8D9DAD7D7D7D8D7D8D7DAD8D7D7D7D7D9D3D4D5D5D5D6D4D3D1D5D5D5
 D5D7D3D2D2D2D1D1CECECDCFCCCAC7C9C6C6C6C4C1C1BDC0C0BFBDC2BEBDBDBEBCBBBDBF
 BBB9BABAB9BBB5B5CDCCCCCFCCD0CFCFCED0D2D5D3D5D3D4D4D5D5D7D6D9DADDDDDCD9D7
 D3D6D8D8D6D8D7D7DADBDADCDAD9DADCDBDDDCDDD9D7DADDDADCDCDBD9D7DAE2DFDDDBD9
 DADDDCD9D9E9F1E0D5DFE3E2DDDDDEDFDFDFDAD8DCDDD7D9DBDBDBDDDFE0DCDCDCDBDADF
 DEDCDCDCE0E8DFDADADBDCDCD9D9D9D9D9D8D7DAD8DBDAD7D9D9D7D9D9DFE0D9D5D7D9DA
 D8D7D5D7D7D8D6D5D7D7D3D7D6D2D3D7D3D2D4D5D2D3D3D6D3D5D5D2D3D7D3D3D3D3D3D5
 D5D7D5D7DCE1D9D8D6D7D7D7D7D9D6D7D6D7D8DAD7DAD9D8D8D7D7DAD6D6D7D7D4D6D5D5
 D3D6D5D6D5D7D4D4D0CFCFCDCACDCCCCC9C8C7C7C5C5C3C5C5C3BCC0C2C2C3C4C1BEBABE
 BFBFBEBFBDBAB3B6BCBEB5B6CACCCBCECFCDCDD2CFCFD1D2D0D2D3D8D6D3D4D7D7D9D9DB
 DCDBDADBD9DAD9D8D6D7D8DAD9DADADCDADADBDCDADCDDDDDBDBDADDDBDBDCDEDBDDDFDD
 DADDDDDFDDDEDDD9DBEAEBDCDBDFE3EADFDCDDDCE1E4DBDFE5E1DBDEDEDFDDDDE2E1DADD
 DADCDFDDDCDBD9DCDDE1DFDDDDDDDCE1E1D9D7DAD6D8DBDAD9DDDBDDDCDAD9D9D9DEDAD5
 D7D8D9DAD4D7D7D5D6D7D3DADAD4D7D9D7D6D3D5D4D3D4D6D3D4D5D6D5D6D2D5D6D7D5D2
 D3D6D3D5D4D4D7DBDEE5E0DAD7D8D4D7D6D8D9D9D9DAD8D9D7D7D6D8D9DAD9DAD9D9D9DC
 DADBD9D6D6D8D3D3D4D4D1D3D2D2CDCDCDCFCCCDCBCBC8C9C9C9C5C7C6C5C3C3C4C7C2C1
 C2C1BDBFBFC1BEBCBBBDB8BBC2C2BDBBCCCECCD0D0D0D0D1CED0D1D1CFD1D0D4D4D5D4D3
 D3D6D4D8D9D8D9D8D7DADADAD8DBD9DCDADBDCDFDDDDDBDFDBDCE3E1D8DADCDDDCDDDCDD
 DBDDDCDDDDE0DEE0DFDDDDDCDADFDFDEDDE1E3E5E3DFDBDCE1E2DBDDE0DEDCDEDDE0DDDE
 DEDCDDDDDBDDDDDCDBDBD9DBDCDBDBDDDBDAD7E3E8DBD7D9D7DBDCDBDBDCDBDBD8D8D6D7
 D7DBD9DADADAD9DAD6D8D7D7D7D6D4DAD9D4D5D9D5D4D2D6D6D5D4D6D4D4D3D7DADAD6D6
 D5D9D9D6D1D2D2D6D3D3D4D8DAE1DDDAD7D7D7D8D6D9D9D9D9D9D8DBDAD8D9DBD9DAD7D7
 D7D8D8DBD6D6D6D4D3D3CFD2D3D4D3D5D3D4D3D3D1D0D0D1CCCECAC8C9C8C4C7C9C9C4C5
 C5C6C3C3C3C1BEC1BFC1BCBBBCBDB9BCC1C3BDBBCFCDCFD3D1D3D3D5D4D3D3D5D3D4D5D6
 D5D8D5D5D3D3D5D7D7D8D6D7D6D7D9DBD7D7DADBD9DDDBDFDFDCE0E7DCDAE3E4DDDDDBDC
 DADFE0DAD7DBD9DBDDDFE0E0DFDFDBDCDADADBDDDADCDEE1E1DDD7DCDBDADBDCDBDDD9DC
 DDE0DCDAD9DDDEDCDADDDBDBD9DBDDDBD9DDDADAD9D8D7DBDDDCD9D7D6D8D9DBD9D8D9DA
 D8D8D4D7D7D6D7D9D6D8D8DAD8D9D8D8D6D6D3D4D6D5D4D9D7D3D4D6D3D5D2D3D4D3D4D6
 D7D7D4D5D6DCDBDAD6D1D1D4D2D3D4D6D8D9DBDBD6D9DBDCDADCD9D6D7DCDADBD7D7D5D7
 D6D6D6D8D5D5D5DFDFD6D3D8D4D4D4D5D3D4D2D3D5D6D3D4D1D1CFCFCECFC9C9C9CAC4C5
 CCCDC4C3C6C6C3C5C1C1C0C2C3C2BDBFBCBCBBBAB9BEBABAD0CFCED1D2D3D3D5D4D4D6D9
 D5D5D7DADDDDDADDDBD9D7D9DBDBD9DAD9D7DADED9DAD9DADAD9D7DDE1DCDDE7DDD8DDDD
 DADADBDCDADFDFDCDBDDDBDEDEDFDDDDDCDEDBDBDADADADDDCDDDDDDDDDBD9DDDDDDDDDC
 DBDDDDDDDCDFDEDFDDDFDEDEDDDCDADEDDDFE0DED9DBDADCD9D8D8DBD9D9D9D9D6D9DBDE
 DBDAD9D8D8D8D5D7D5D6D6D9D8D9D9DBD9D9D9DAD6D9D8D5D3D6D7DBD7D6D5D6D6D7D5D6
 D5D7D4D7D7D9D5D5D7DEDDDBD7D7D2D6D8D6D5D8D5D7DDDED9DBDBDADADDD9D7D6DAD9DA
 DADBD7DBD9D8DBDEDCDDDDE2DFDBDCDDD6D6D6D6D6D8D5D4D5D4D3D6D5D5D1D1D0CFCBCB
 C8CAC9C9CFCFC7C3C4C5C4C4C1C2C1C2C1BFBDBFBCBAB9B9B9BCB8B8CACFCED0D0D1D1D4
 D3D5D4D3D3D5D5D9D9DADADCDCDDD7DADCDDDDDDD9DADBDBDAD9D9DCD9D9D7DBDEDEDCDC
 D7D7D9DBD6D9D9D9D9DCDCDDDADCDBD9D9DBD7DADCDBDADEDCDCDCDEDDDCDEE1DBDADCDC
 DEDEDADCDBDCDCDCDBDFDDDDDDDFDFE0DBDFDEDEDCDADDE7DDD4D8DBDBDBD7D7D8D8D9DB
 D6D8D9D9D9DAD8DBD8D7D6D6D6D9D8D7D8D9D8DBD8D9DADAD9D9D8DBD9DADFE2DAD6D4D8
 D6D4D4D7D4D5D5D3D3D5D3D5D8DDDBD7D8DBD3D3D4D5D6D8D5D8DAD9D4D7D8DAD9DDDCDA
 D8DCDBDCDDDDDCDDDBDBDBDFDFE0DDDFDDDDDFE1DBDAD6D5D5D5D4D5D3D5D3D3D3D3D1D3
 D0D0CECBC8C7C5C6C7C6C4C3C3C6C3C2C4C1BDC1BFC1BFBDBBBCB9B7B7B8B7B7CFD1CFD1
 D2D2D1D3D3D5D4D6D4D5D7D7D7D9D9DCDEDDD9DBDBDDDEDCD9DBDADEDEDCDCDFDCDCDBDA
 DCDEDADCDBDDDCDBD9DBDADDDEDEDCDCD9DDDFDCDBDDDADDDFDFDDDEDCDBDADFE0DDDCE0
 DDDDDDDFDFDFDDDDDBDCDCDDDBDDDCDFDDDCDCDFD9DADFE1DDDBDFE6DDD9DADDDBDCDADB
 DBDAD7DAD7D9D9DAD9DCDBDCDADCDAD9DADCD9D9DAD9D8DBD8DADADAD9D9D8D9D6D7DDE2
 DCD8D6D8D9D7D4D5D2D4D5D5D5D7D5D3D9E4DFD4D4DBD8D8D9D9D8D9D9DBDBDDDDDDDEDE
 DBDCDCDBDBDFDDDBDADFDEDCD9DAD9DBDCDEDFE1DDDFE1E3DDDDDBD8D6D9D8D5D3D5D1D0
 D1D3D3D4CFCFCDCBC9CAC7C7C5C8C6C4C1C6C3C3C4C3C0C4C3C3C0C0BDBFBBB9B5B8B9B9
 CDD1D3D3D1D4D2D3D4D3D3D3CFD1D5D5D5D7D7D8DADBD9DADADFDBDCDCDBDADDDCDBDBDD
 DDDEDADBDDDCDCDDDEE1DDDCDCDBDADDDCDDDCDCDCE1E0E1DDDADBE1DFDEDDDFDDDBD9DD
 DBDBDBDBDADBDCDCDADCDBDBDCDDDADCDCDBDBDDD8D9D9DBDAD9DDE2DCD7DCDFDEDDD9DC
 DDDDDBDCD9D9D8DADAD8D7DAD7D9D9DADBDDD8DBE1DDD6D9D6D7D5D5D4D8D8D8D6D6D5D5
 D4D6D6DAD9D8D7D6D5D9D4D3D5D5D3D7D5D7D7D8DBE1DCDBDBDCDAD9D6D8D7D8DBDCDBDB
 DADDDDDDDCDDDADCDBDBDDDEDBDCDBDCDCDAD6DBDCDBDADDDCDEDFDFDBDDDDD7D5DBD9D6
 D5D7D3D1D0D1CFD0D0D0CCCDCAC9C9C8C5C7C3C1C2C2C0C2C1C2BFBEBEBDBBBDBCBABBBA
 B5B5B5B8CDD1D2D2D2D3D2D5D2D0D2D3D0D3D4D5D6D7D6DBDDDDD9D8DADFDCDDDEDDDDDE
 DCDDDEDFDEE1DFDFDFDFDCDDDFE2DFE0DDDCDCDFDCDCDCDCDBE3E4E3DFDDDCDEDEDFDDE1
 DEDCDDE1DFDEDCDDDCDDDCDFDDDFDEDEDDDFDDDFDDDCDBDCDBDEDDDCDBDAE3EFDBD2DADF
 DCDCDBDFDFDFDDDDDCDDDBDDDBDAD9DBD9DCDBDADADDD7DAE1DBD6D9D9D8D6D9D9DBD9D9
 D9DDDCDBDADAD8D9D8D8D9D7D9DDD7D7D6D5D5D7D7D9D7D7D7DAD9DBD9D9D8D9DADAD9DD
 DCDADBDBDADFDDDBDBDBDADCDCDDDEE0DFDDDCE2E0DCDADDDDDDDCDDDCDBDDDEDBDEDCD7
 D7E0E0DBD8D5D3D4D2D2CFD1D1CDC9CECBC9C8C7C5C7C4C3C3C3C1C2BFC1C0C1BFBCBBBD
 B8B8B9B9B6B9B9BBCFD3D2D3D4D4D4D6D3D5D5D5D3D3D3D7D7D8DBDADCE1DBDADBDDDCDF
 DCDEDDDEDDDEDDE1DFDFE0E0DDDEDBDDDFE1DFDEDCDFDCDFDDDBD9DEDEE0E3E1DDDEDADC
 DDE0E1E0DCDFDEDFDDDDDCE0DDDEDFDFDEE0E0E2DEDFE1DFDCE3DFDCDDDDDCE1DDDCF0FD
 E2D1D7DFDEDCDCDDDCDFDFDFDADBE0E2DADCDCDBDCDDDADDDBDBDADCDADDDADAD9D9D6D9
 DBDCDADBDDDFDDDFDCDDDDDCD8DDDEDCDAD9D6D6D5D7D6D9DADAD7D7D6D7D8D9D6DADBDA
 DADADADBD9DADADBDDDCDADCDCDBDBDCDCE0DFE1DFDFDDDFDFE1DDDDDFDEDBDCDCDFDEDD
 DBDCDBDAD8DEDFDAD4D7D2CFD1D1CDCFCECFCCCCCBCBC7C8C6C5C4C3C1C2C2C1C0C1BEBF
 BCBDBEBEBDBCB9BCB6B5B6B4D2D6D3D4D2D2D5D5D3D5D5D7D4D4D5D6D5DADAD9DBDDD9DB
 DBDCDBDCDADCDCDCDCDCDEE1DDDCDDDEDCDCD9DDE1E1DFDCDADFE1E0DDDDDBDCDCDDDDDF
 DFDDDBDFDFDFDFDFDDE0DEDFDDDFE2E1DDE0DFE0E1E1DFE3E1DFE0E1DDE0DFDFDEDDDEDE
 D6DDF3FBE2D3D9DEDCDCDCDDDDDDDFE3D5D2E1E3D9DFDED9DADDDADDDADAD9D9D7DBD9DB
 DBDBDCDEDCDEDCDCDEDFDDDDDBDEDDDDDBDEDEE1E0D9D5D8D7DAD9DDE1E1DBDAD8D9D6D6
 D6DAD9DCD9DBDCDDDBDCDBE0E3E2DFDFDCDDDBDCDDDFDDDFDFE0DFDEDDDFDEDEDEDFDEDD
 DBDEDDDCDADAD7D7D7DADAD9D5D5D0D0D0CFCDD1D3CFCACCCCCCC8C8C8C9C6C3C3C3C1C2
 C1BFBEC0BCBCBDBBBABDBABAB9BBB9B5)
0)
)
>

<Cell>

<Frame,
       Placement = At Anchor,
       Width = 2.559 Inches,
       Height = 2.559 Inches,
       Size Contents to Width = Yes, 
       Size Contents to Height = Yes, 
       No Border = Yes,
       Diagram = 



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 C9CACCD0CECCCDD0D1D1CED2D1D2D3D1CFD4D1D2D4D6DDDAD0D4D5D4D4D5D1D4D2D4D6D6
 D4D7D4D5D4D5D6D7D4D6D5D5D7D8D4D8D7D9DAD8D8D9D4D7D8D6D5D8D6D9D6D2D3E0E5D7
 CDD2D7D4CFD2D1D1CFCBCBCDC9C8C6C7C7C5C3C5C0C2C5C5C4C5C2C6C6C6C7C9C6C6C2C2
 C2C0BFC2BFC0C2C3C2C2C0C3C2C0C2C4C2C3C0C0C2C0BEC0BDBEC1C3BFC2CDCFBDBABEBF
 BDBDBCBDBDBCB8BDB9B6B8BFC2C0BCC0BDBDBBBEBEC1BFC0C2C3C1C6C3C4C2C0C2C5C5C5
 C0BFC1C2C0C4C1C0BFC0C0C1BEC0BDBDBFBDBABDBBBAB8B5B4B3ADAFB0AEABAEABADACAB
 ACABA7ADACAAA9A7A6A9ACAEC1C5C0C2C2C2C2C2C1C6C4C3C3C2C2C7C4C3C5C9C7C7C5C8
 CAC9CACCCACCCACCCECFCDCFCECECECECED2CFCFD0D0D2D2CED5D7D6D6D4D2D5D2D3D3D2
 D2D3D1D5D4D1D3D5D2D6D4D5D6D6D5D8D6D6D5D5D6D7D5DAD8D5D8DAD6D7D6D6D7D5D4D6
 D2DDDED6D1D1CFD4D1CFD0D0CACBC9CCCCC9C8CCC8CAC7C2C0C4C3C8C8C5C7C9C4C7C6C5
 C4C4C2C3C1C4C3C2C4C2BDC1C1BFC1C5C2C5C4C4C4C4C2C6C3C5C0BCBABEC0C0BBC2CCC8
 BABCBCBFC0C0C0C6C1BEBBBABABABABCBCBEBDBCBABBBABDBEBFC0C2BFC1C2C2C2C2C0C2
 BEC0C2C1C0C4BFC0C0C0C2C2BDC0BFC1BFBFBEBFBBBDBEBAB8BCB6B5B4B2B2B2AEAFABAA
 AAAAAAADA8A9ABABABABA7A8A5A5A8AAC4C8C2C0C2C3C2C2C1C6C4C3C3C4C7C9C2C4C7C6
 C6CBC8C8C9CBCCCFCCCDCBCCCCCED0D3CDD0D0CECFD4D1D2D2D4D4D4D0D5D4D4D5D3D0D6
 D2D4D4D2D1D5D3D4D3D3D3D4D0D4D4D6D6D5D4D7D4D6D5D4D4D6D6D8D6D6D7D7D5D8D6D7
 D9D6D4D8D5D6D5D4D1CFCFD4CFCFD1CCC8CAC7CACAC8C8CCCCCAC6C4C2C3C4C8C3C4C9C6
 C0C5C4C4C5C4C2C6C4C1C0C0C0C2C1C4C3C5C6C4C4C8C6C8C7C4C2C6C8C6BEBEBEBDBDC0
 BCC0C7C4BDC0BEC1C1C1C1C4C2C1BCBEBFBBB9BEBBBCBDBDBCBEBDC2C2C3C2C2BEC4C5C5
 C4C4C2C6C4C1C3C6C5C5C2C4C5C4C2C3C0C1BEC0C1BFBCBFBEBEBCBCB9B9B6B6B6B6B4B2
 ADB0ADAEADADABAEAEADA9AAABABA8AAA8A9A8A9C2C2C2C2BEC4C2C0C2C3C0C4C3C5C6C5
 C3C2C2C8C8C6C9C9C7CACACACCCBCCCFCDD2D2D0D0D1CDCFD0D2D3D3CFD4D6D5D5D3D4D7
 D3D5D5D3D6D7D3D5D2D3D5D6D2D5D4D4D3D4D3D5D6D8D5D4D7D8D4D6D3D4D7D9D7D7D4D5
 D4D4D6D7D3D6D5D2D4D5D2D6D1D0D1D2D1D3CCCAC9C8C7C7C6CAC6C7C8C9C2C4C3C3C3C5
 C4C5C2C6C5C3C2C4C2C5C4C5C5C1BEC2C1C4C2C1C2C4C0C5C6C6C4C2C3C6C2C2C6C9C7C5
 BEBCBCBBBFC2BFC0BEBCBEBFBEC0BEBEC2C0BCBFBDBDBDBCBCBFBABCBDBABAC0C0C2C3C4
 C2C1C2C5C4C5C2C1C2C7C4C4C3C3C4C2C2C6C2C2C2BFBCBEBDBFBCBABABDB8B9B9B8B7B8
 B4B5B3B4B0AEAFB1AAABABADAAA7A8ACAAAAA9A9A9A8A4A9C0C0BFC0C0C3C0C2C4C4C4C6
 C4C7C6C4C5C8C5C5C6C8C9CAC9CBCACCCECFD0D2D1D4D4D1CFD1D0D1D0D6D9D4D1D6D5D8
 DADADCDED6D6D4D5D6D8D5D6D4D6D8D6D4D6D6D9D8D7D7D8D8DBD8D7D6D6D6DAD6D8DAD8
 D8DAD5D6D6D4D6DAD6D7D5D5D4D4D4D7D3D5D6D3D2D5CEC9C8CBCACAC8CAC8C8C7C4C1C4
 C3C6C6C5C6C6C2C4C6C7C6C6C5C6C5C6C7C4C3C6C4C5C6C4C2C6C4C5C4C5C5C5C4C6C2C2
 C8CCCAC7C0BEC0C0C1C3C2C3C1C0C0C0C0C2BEBFC1C0BEBEBCBDBFC2C1BFBCBFBCBCBEC0
 C0C4C3C6C3C0C2C6C4C5C4C6C5C4C3C6C1C2C4C6C5C6C3C2C2C2BFC1BFC0BBBCBCBAB6BB
 B9B9B8B4B2B5B0B0B0B1ADAFACABA9AAACAAA8ACAAAAACABAAABA7A6BFBCB3B8BFC4C2BF
 BCC4C4C4C8C9C6C7C7C9CACAC5C5C8CDCAC9CCD1D2D4D1CFD1D2D1D4D3D3D2D2D4D7D5D4
 D2D3D6D7D2DAE2DCD4D6D6D8D7D9D6D4D5D5D3D8D6D5D7D9D5D8D6D6DBDAD7D9D7DAD9D8
 D7D7D4D9D9D6DADFD7D7D6D6D8D8D7D9D5D7D8D5D5D5D1D2D2D0D1CFCACDCCCBCBCBCACA
 C6C8C5C2CBCEC2C7CCC7C4C7C7CCC9C4C5C6C6C8C3C4C5C2C2C4C0C1C2C4C5C6C6C6C4C4
 C5C6C7C6C0C5C8C5C2C1BEC2C1C0C0C1C0C3C0C0BFBEBFC0BDBDBDBDBCBFBEBEBBBEBEBD
 BCBFBDBFBEC0C3C6C2C1C2C4C2C5C3C5C2C2C4C4C2C4C2C4C3C2C3C4C0C3C2C2C0C1BFBE
 BBBBB8B8BABEBAB8B4B2B3B6B3B3B1B2AEABA8AAA9A9AAABA9AEADACA8A9A9A9BCC1C0C0
 C0BFC0C2BFC2C4C6C8C6C5C8C4C6C9C8C6CBC8CACBCAC8CED1D2CCCFD1CDCCD2CFD1D2CF
 D0D4D0D2D2D3D4D5D3D8DBDCD7D6D5D8D6D6D2D3D6D8D5D8D6D6D6D6D5D7D6D7D7D6D6D9
 D6D7D6D5D6D8D6D9D7D8DBDFDDD9D6D8D8D6D6DAD7D8DBD8D4D4D4D6D3D2D4D1CDCECCCF
 CFCAC7CAC7C7C4C5CFD2C8C8C7C6C4C5C4CAC8C8C6C4C3C5C4C5C4C2C3C3C1C6C5C4C4C5
 C3C7C5C8C8C8C5C3C2C8C1BDC0C0BCC2C1BFBFBEBABEBDC0C0C0C2C2BEC0BDBCBCBCBCBE
 BABAB8BABBBFBCBEC2C4C4C4C0C4C2C2C5C6C4C6C6C8C6C5C5C4C1C4C3C3C4C5C2C6C4C2
 C3C4C0C1C1C0BCBCBCBEBFBFB8B4B5B4AFB2B3B1B0ADAAADAAA9AAA8A8ACACABA8AAACA8
 BFC4CBCCC2C2C1C5C2C0C4CAC5C3C3C2C3C7C6C9C6C4C4C6C5C8C6CBCFCDCBCFCCD0D0CF
 D0D2CED2D2D1D0D0D0D4D1D4D5D6D7DAD6D7D5D5D5D7D3D6D6D7D5D6D7D8D4D7D8D9D8D9
 D5D8D7D6D6D6D4D6D6D5D4D5D4D5D4DADBD6D5D7D1D1D5D6D3D6D9D8D1D2D4D3D1D4D0CF
 CDCACACCCCCCC9CAC9C5C4CBCCC9BFBDC2C8BFBFC6C4C0C4C5C8C6C4C5C4C2C3C4CAC6C2
 C3C7C4C7C8C8C7C9C5C6C4C2C3C5C0C0BCBEBEBCBBBFBEBEBEBEBFBFBCC2C3C4C0BDBCBE
 BABEBFBCBBBDBABAB8BCBEC0C2C5C2C2C3C4C2C6C4C3C4C5C1C4C5C6C4C6C5C4C3C6C4C5
 C5C4C4C6C4C2C2C0BFC0BFC0BCBABDBEBAB8B5B5B3AFB0B3AFAFAEAEACAAAAAEABACAEAC
 ACADA9A7C2C7D2D0C3C4C3C4C4C2C6D0C7C0C0C4C6C8C7C9C5C5C8C9C4C8C8CACDCDCDD0
 CCD0D1CFCFCECCD0D0D0D1D0CED2D3D4D3D3D6D9D8D8D4D5D6D5D2D6D6D6D7D6D4D7D6D8
 D7D7D8D8D2D6D6D6D6D5D2D6D2D2D6D6D2D2D5D8D7D6D7D9D3D1D2D5D6D6D4D5D0CFCFD1
 D0D1CED0CCC8C9CCCBCDC8C6C9CCC8C9C6C7C7C8C4C4C5C9C7C6C6C5C4C9C6C2C4C6C2C5
 C6C8C4C2C6C8C4CDCFC7C3C6C6C9C4C2C4C4C0C2C2C4C2BFBFC0BDC0BFBEC0C2BDC0C2C2
 C0C0BEBEBCBEBDBCBEBEBABEBDBDC0C1C5C9C4C4C4C6C6C6C2C4C4C3C4C5C2C5C6C5C5C5
 C4C5C2C5C5C4C3C6C2C3C4C2C0C2BDBEBEBABABCBABCB7B2B2B0B2B3B0B3B2AFABADACAC
 ABACACACABACABAAC1C5C7C7C2BFC2C4C0C3C5C8C7C6C3C6C6CACDCBC6CAC9CCCCCACACF
 CED1D0CFD1D4D0D0CED0D1CFCFD1CCD0D3D2D2D3D2D3D2D4D6D8D6D6D2D3D6D5D5D6D3D4
 D6D8D7D6D4D6D4D4D4D6D4D7D4D6D7D5D3D6D3D5D6D9D8D5D3D6D6D8D8D5D6D9D6D6D6D2
 D2D4CFD1D0D1D2D0CCCECACACCCCCACBCBD2CCC4C7CDCBCFC9C7C9CAC8CCC6C4C6C6C4C5
 C1C3C4C4C2C4C1C2C0C2C5CBCDCBC6C8C9C8C7C8C5C6C4C5C6C7C5C6C2C2C4C2BFC1C3C3
 C0C1C2C4BFC1BEBDBDBDBBBEBCBDC0BFBDC2BFC1C5C5C5C5C3C8C6C4C5C3C2C5C3C4C5C8
 C6C8C6C6C4C0C2C6C4C5C4C5C6C5C3C8C3C1BDBABBBFBBBCBAB8B7B8B4B4B2B2B3B3B1B4
 B2ACA7A9A89D94A5ACACA6A8C1C3C4C6C0C0C2C2C1C4C4C5C6C5C3C7C8CBCCCBC9CCCCCE
 CECECECBCCD2D0D0D2D2CFD2D0CFD1D1D0D0D0D5D2D2D5D5D0D3D2D4D7D6D5D6D3D4D6D6
 D5D8D6D8D8DCE1DAD4DAD8D6D6D5D4D8D5D6D6D4D3D4D4D7D5D6D6D4D1D5D3D6D7D6D4D6
 D7D9D6D4D4D4CFD4D2CFD3D5D0D2CDCDCCCBC8C7C9D1CCC7CACDCED3D0CECCCBC6CAC6C6
 C8C8C6C5C0C5C2C1C2C2BEC0BEC2C4CACAC8C4C8C8CAC9CBC7C7C4C3C3C3C1C2C3C4C4C5
 C6C4C1C4C2C1C0C0BBC2C2BBBBBFBCBEBEC0C0BDBCC1C0C2C3C6C6C4C0C7C9C6C5C5C3C6
 C6C7C3C5C8C7C4C6C4C4C4C5C2C5C4C4C4C4C0C1C1C5C1BEC0C1BCBFBDBBBAB9B6B4B2B2
 B1B2B1AFACAEADACABACAAB0AFAEABAAC7C1BAC2C5C6C2C4C2C4C3C5C5C7C6C4C4CAC9CB
 C9CACDCAC8CDCACCCFCFD0D0CED2D1D1D2D4D0D2CFCFCED2D4D6D3D5D4D3D5D8D5D8D7D5
 D6D6D4D9D7D6D8D7D6DDDBD8D9D9D8D8D6D8D8D8D8D9D7D8D4D5D6D3D4D9D7D8D8D5D4D4
 D1D6D7D5D4D5D5D6D7D8D3D1D1D5D2D3D3D0CDCECACBC8C8C9C8C9CBC7C9CCCBCCD0CCCD
 CECDCBCCC7CACCCACBCAC8CBC8C9C7C4C4C9C8CDCCC9C8CAC7C9CBCECDC8C4C5C2C1C2C4
 C2C5C4C7C7C2C0C2BEBFBFBFBFC1BFBFBCBDBCBCBDC0BBBFC0C2C2C2C1C4C5C6C5C9CCCC
 C5C4C4C6C5C3C2C7C6C5C4C4C4C7C6C7C5C3C2C5C3C4C4C2C1C1BFC2BFBFC0BEBCBCB8B9
 B8B3B0B3B2B2B1B2B1ADAAAEACADAFAEADAFABAAC2C3C4C5C4C8C6C5C4C5C5C7C3C6C7C6
 C7C9C7CAC8CACDCDCBD0CDCCCED1D1D2D0D3D1D0D2D4D2D2CFD1D3D6D6D5D3D4D3D2D6D8
 D6D8D4D4D7D8D5D8D6D6DAD8D4D8D6D7D7D6D6D9D6D6D5D6DADBD6D9D6D6D9D8D7DCDAD9
 D9D8D8DAD6D9D8D6D5D6D3D5DCDDD0D2D4D7D5D4CFCECFCECBCDCBC9C9CBCAC9C5C7C8CB
 CACBC8C8C9CACBCCC8CCCCCBCCCDCACECBCBCAC9CBCEC8CCCCC9C4C7CBCFC8C7C8C6C4C7
 C4C6C6C6C8C7C1C3C4C3C3C5C3C4BFBDBEC3C2C0BCBDBCBDBEC0BABEC1C3C4C2BFC3C4C4
 C6C8CAC9C4C7C7C7C8C8C5C8C6C5C6C5C5C9C5C5C4C4C4C4C3C5C2C2C4C4C0C3C1BFBFBE
 BCBDBBBBB8B4B2B4B3B5B4B4B3B2ADAEAEAFADAFAFAFACACBFC1C0C5C7C6C6C5C3C8C6C6
 CACCC9C8C6C9C8C8C9CCC7CACECEC9CBCBCFCECED0D2D1D2CED1D1CFCFD2CFD6D8D4D2D5
 D2D4D5D4D4D4D3D6D4DADBD5D4DCDAD7D6D6D6D8D6D5D4D6D8D7D6DAD8D8D7D6D7DCD9D4
 D4DBDBD8D7D9D6D8DADBDAD9D6D7D5D4DADBD3D6D4D3D4D1CDD0CDCDCBCACCCEC9CCCDCA
 C6C6C4CFCAC6C9C8C7CBC7C8C8C8CACEC9C8C9C8C6C9C6C6C2C6CAC9C7CBC9C8CACACBCE
 C6C5C8C9C5C4C4C7C6C5C2C2C0C3C0C4C4C4C3C0BDC2C2BEBCBFBEBFBBBCBEBEBDC4C3C0
 C0C2C3C4C0C5C7C5C4C5C6CAC6C4C7C8C7CAC7C9C6C4C6C8C5C4C1C1C3C3C1C4C3C4C5C6
 C4C2BEC0BDBABCBDBABBB7B5B5B5B3B6B4B2B0B0B0B1B0B2AEAFAFB0C1C2C2C6C8C7C6C7
 C4C6C6CBCED0CCCBC8CAC8C8CCCFCDD0D0CFCFCECDD2CFD0D2D2CED1D0D0D0D0D0D4D5D9
 D6D4D6D6D5D5D2D4D7D5D3D6D7DCDCD7D7DAD7D7D6D5D6D6D6D9D6D9DAD8D6DAD6D6D8D7
 D8DCDAD8D5D6D9D9D6D8D7DADCDBD9D9D8DBD8D5D6D6D4DAD6D3D4D3CED2CFCFD0CECDCE
 C9CCCCCAC7CACCD4CDC6C8C9C7CBC8CAC9C8C9CBC5C5C5C3C4C5C1C5C6C6C6C8C6C9C6CA
 CBCBCCCBC3C4C6C7C6C5C4CACBC6C3C5C4C5C2C6C6C5C3C1BFC5C3BDBCBFBCBEBEBFBEC0
 C2C4C2C4C3C6C8C8C2C7CAC5C3C6C7CAC8C9C9C8C7CAC7C9C6C6C6C7C3C6C4C4C2C2C2C3
 C2C6C7C7C8C6C1C3BFBDBDBEBCBBBAB8B4B4B6BAB3B4B4B3B3B6B3B4B1B2B1B3C4C2C0C3
 C5C7C3C6C7C2C1C8C8CCCAC8CACCC8CCCDCCCCCECDCFCCCECECDCFD2D0D1D0CFD0D1CFD2
 D1D3D6D5D4DBD5D5D6D4D2D6D4D6D5D5D7DAD6D7D7D6D5D5D6D8D5D7DAD9DADBD6D7D7D8
 D8D8D8DCD9D9DAD6D6DAD7D6D7D8D7DAD9DCD9D7D8D7D5D6D4D5D7D6D2D5D4D2CDD2D1CF
 CDD0CECECDCDC9CBC9CACECDC5C6C7C8C6C5C8CAC5C6C6C6C7C6C4C8C6C5C6C4C2C6C6C8
 C7C8CACAC8C9C8C8C8C8C7CBC9C6C6C8C8C9C6C6C4C5C5C5C4C5C1C4C6C8C6BDBABFBFC0
 BFC0BDC1C2C2C4C4C2CACAC6C8CCCAC4C1C8C9CACBC9C4C6C6C7CCCAC5C8C4C4C5C3C2C5
 C2C4C3C4C3C6C6C8C5C4C2C0BDBFBAB9BCBCBBBAB6B5BAC2BFB9B5B9B5B5B6B6B4B5B4B6
 BFBEC0C3C1C5C4C5C5C4C3C7C8C9C7C6CACAC9CCCBCAD0D1CDD2D0CECCCFD3D6D0CECFCF
 D2D4D2D4D1D2D4D4D6DEDCD8D6D4D4D6D4D5D2D2D7D8D3D6D4D4D6D7D6D8D6D8D8DADADE
 DDDCD7D6D8DAD6D9D7D7D8D8D8DAD6D8D6D4D7D8D7DDD8D5D7D8D4D8D6D6D6D5D2D4D0D2
 D1D0D1D1CED0CECECCCAC8CBC9CACBCAC8CBCACCC8C6CACAC4C5C6C8C7C6C6C8C5C5C4C3
 C6CAC6C9CAC7C8CAC5CAC9C9CBCBCACAC6C8C9C6C6C8C6C5C4C5C6C5C4C8C5C4C5CACAC3
 BCC0C0BEBEC2C0C2C2C3C4C5C5CDCCC9C8C8C9CAC5C9CBCACACCC7C6C9CDCDCDCACAC5C5
 C2C2C3C6C2C3C2C2C2C4C2C2C0C4C2BFBDBEBCBEBCBBBABBB7B6BCC5C7C2BABCB9B7B6B5
 B4B6B5B7BCBFC0C2C4C6C6C6C5C7C5C6C8CAC9CDCAC6C9CBC9CCC8C8CDD6D2CDCFD2CED1
 D0D0D1D5D2D4D3D2D2D4D1D4D7DBDAD6D3D6D4D4D4D3D2D8D6D9D8D6D5D6D3D4D6D7D6D8
 D7DAD7D9DEDDD7D8D4D6D6D6D6D8D6D9D8D7D8D6D4D9D6D7D9D9D8DAD6D7D6D5D8D7D1D4
 D3D1D2D0CCCFCDCDCFCDCCCFCACCCBCACBCDC9CAC6C8CFCCC6CACBCBC6C4C6CCCBCAC7C7
 C8C8C6C9C6C5C7CAC8C9CACAC9C9CACCC8CBCAC8C8C7C5C7C2C3C5C6C4C6C4C5C3C5C4C6
 C4C9C8C4C1C1BFC2BFC0C2C4C3C5C5C8C6C7CACAC7CACBCAC9CBC9CBC8C8C7C6C8CCCCD2
 D0CDC9C7C2C4C0C2C4C3C2C6C3C3C0C0C4C7BFC1C2BDBCBFBCBDBDBBB7B6B7BDC0BFB9B8
 B8BAB6B8B6B5B7B7BFC2C2C5C4C4C7CAC8CAC7C8CBCAC9CDCCCBCCCCCCCCC8CED2D6D4D0
 CED3D2D0D1D1CED2D2D4D1D0D2D4D0D5D6D7D5D4D3D6D4D6D7D6D4D6D6DCD9D5D6D8D2D7
 DDDBD7D6D4D9D8D9DCDDD9D9D5D8D7D6D8DAD7DADADAD8D8D7DAD8DADBD9D8DAD6D9D8D5
 D4D6D3D5D4D3D2D0CDCECDCFCFCECDCFC8CACDCCCED2CDCAC8CCD3D4CCC9C8CAC9C8C9CC
 C9C9C8C7C8CAC7CAC8C9CACAC9CBC9CDCBC9C9CBC6C9CAC9C8CAC8CAC8CBCCC8C6C9C6C8
 C8C5C4C6C4C6C6C6C4C2C1C4C2C5C6C2C4C8C4C6C8CACCCDC8C8C8C8C7C9C8CBC7C9C6C4
 C6CDCCCECCD2D0C8C2C4C0C2C4C5C4CACCC8C1C2C3C5C3C5C3C0C0C1BCBFBCBAB9B6B2B6
 B7B9BBBAB9BCB9B8B6B5B4B6C4C5C5C4C2C5C5C6C8C9C7CBC8CBCDCCCBCCC8CAC9C9CACA
 CAD3D0CFD0D3D4D4CDCED0D1D3D3CDD2D5D4D2D2D4DAD4D2D4D4D1D6D5D5D5D5D5D9D4D5
 D5D5D5D9DBDBD7D6D6D7D9DCD8DAD9D9D9D9D6D9D7D7D7D7D7DAD5D4D7DADBDBD8DCD9D8
 D9D9D6D9D6D4D6D2D1D5D2D2D0CDCED0CDD2CECDCFCECCCED0D5D2CECBCED1D8D3C9C9CC
 C8CAC8C8CACAC7CECBC9CBC9C6C8C7CACAC8CACCC8CBCBCACBCAC8CAC8CACBCACACDC9CA
 C9C3C5C9C4C5C4C6C6C6C6C7C5C6C4C3C4C6C1C5C4C4C5C6C5CBCACBCBCAC8CACACCC9C8
 C9C7BEC3C8CACCCFCCD2CEC8C5C4C2C5C5C8C5C8CFCBBEC0C4C4C2C3C0C1C0BFBFBEBFBE
 B8BAB9B7B8B7B6BAB9B9BAB9B5B5B4B5C4C4C6C8C6C8C5C7CACAC8CAC7CAC9C9CACACACC
 CCCACBCDCBCFD0D1D0D2D6D5CDD0D2D3D6D7D4DADDD6CFD3D6D6D4D6D4D3D2D4D5D5D2D2
 D4D7D1D4D4D4D3D8D8DAD8D8D7D6D6DAD7D9D9D8D8DBD6D8D4D6D6D6D6D9D6D9D7D6D6D8
 D5DAD9D6D6D8D6D8D4D5D6D8D5D5D1D5D3D0CFD0CED4D1CFCDCFD0CFCDD0CECCCDD1CFD4
 D3CBCACCC9CACACACBC8C8CDCBCACCCBC9CAC9CBCACACDCDC9CDCCCACAC9CCCDC9CACBCA
 CACDC8CBCCCAC8C8C5C7C5C6C6C6C7C8C7C5C2C3C4C8C4C5C4C5C4C6C8CDCBCACACACACD
 C9CDCDCBCBCDC9C8C9CDCECECDCECACAC8C4C4C8C5C6C7C9CAC8C1C3C2C3C1C0BFBFBDBE
 BDBDBEC1BBBDBCB8B7B9BABBB8BBB9B8B6B9B4B8C4C4C4C5C6C7C6CAC8C9CAC8C8C8C6CA
 C8C8CCCECCCECCD0CECDCFCFCED4D2D1D2D4D5DAD7D5D8D9DADCD4D5D4D6D6D7D3D6D3D4
 D9D9D5D8D6D5D6D5D2D5D3D6D6D6D7D7D4D8D4D5D6D6D6D9D6D9D7D7D6D7D5D5D4D7DAD7
 D4D9D6D6D6D6D8DDD8D7D7D6D6D6D4D8D4D0D2D3CED1CFCFCECECED2CECED0D0CFCECACB
 C9CACFD1D2D2CAC8C9C5C6CCC9C9C9CBCDCBC9CDCBC9CACACACDCBCBCBCACCCDC9CDD0CF
 CDCAC8CCCAC8CACCCCCFC9C9CACAC8C8C7C9C6C6C9CCC5C5C4C3C4C7C6C6C6CAC8CACBCA
 C8CCCBCACCCAC6CCCAC7C8C9C8C9C9D0D0CCC9C9C4C5C4C5C6C8C6C6C4C5C3C2C3C4C1C4
 C0BDBCBEBCC0BFBDBABABABCB9B6B5B6B8BAB6BBBAB6B5B7C8C8C6C7C8C8C6CAC8CCCCCC
 CCCAC8CCCACACCCCCACCCDD4D1CDCECDCBD1D1D0D3D6D4D8DBDAD4D4D5D7D5D8D5D4D6D6
 D6D8D5D6DCDBD8DAD6D7D7D3D3D6D3D9D8D7D9DAD8DBD8D8D9D9D6D8D6DBD9D7D7DAD6DA
 DADADCDAD8DCD8D8D8DCDDDFD8DBD8D5D5D7D3D6D5D2D3D6D2D3D2D4D2CECDD1CDD0D2D2
 CFCDCACCCCCDCFD0D1D0CBCBC9C9CCCEC9CACBC8CACAC7CACCCCCACACCCFCCCDCECFCFCE
 CBCFD2D0CCCCCACDCCCDCCCDCFD2CDCDCACACBCAC8CAC9CACCCDC7C6C3C4C6C8C7CAC9CA
 CACCCDCDC9CDCCCCCCCDCDCEC8CACCCBCBCCC7CDCCC9C8C8C4C4C2C5C6C6C5C7C2C5C4C5
 C4C4C0C2BFBEBFBFBCBFBDBFBBB7B7BAB6BABBB9B7BBB9BCBBB6B3B8CECECBCCCCCFCBCA
 C7CACDCECACCCECDCCCDCCCDCACBCDCECBCFCECDCDCFCED2CFD3D4D6D8D8D4D8D5D5D7D6
 D4D7D5D6D6D5D6D8D5D9D9D8D7D8D4D4D4D6D7D6D5D9D8DCDDDCD9D8D6DADAD9DADAD7DA
 D8D8D8D8D8DCDBDDDAD8D8DAD6D9E1DEDAD9D7D9D7D6D8D7D5D9D7D9D7CFD0D6CFCCCCCF
 D1D2CFD2D1D0CFCECDCFCED0CFCDCCCCC9CCCCCDCECCC9CACACCCCCBCBCDC8CCD0D5D4D0
 CBCECECDCDCFD0D1CBCDCCCBCBCCC9D0CFCACBCDCBCCCACBCBC9C6CACACCC9C6C5C6C4C9
 CAC9CACCCACFD0CFCCCDCCCECCCECDCAC8CAC6C9C8C9CAC9C8CBC8C7C7C5C4C7C3C5C4C4
 C4C5C0C3C4C2BFC1BEC0BEBFBFBEBFC0BABAB9B7B8BBBABBB8B8BCBEBCBBB7B6D1D2D3D4
 D2D2D1D1CFD0D1D2CFD2D2D2D3D2CBCFCFCED0D4D3D4D2D2D0CED0D3D2D6D4D3D6D8D6D8
 D6D6D7DCDCDAD5D7D7D7D9DBD6D9DAD5D5D9D6D7D8DBD8D9DBDCD8DCDAD9DADBD9DBD9D7
 D8DBD8D9D7D8D8D6D8DDD8DDDDDADAD9D6DADCDAD7D7D7DAD8D7D7D8DADED7DADBD2D0D5
 D2D2D2D3D2D2CECECFD4D4CFD0D4D2D2CFCFCFCFCDCECCCDCECDCDCECBCDCCCACACECCCF
 D5E0D7CACAD0CECFCFCFCFD0CCCDCCCBCCCECBCECDCBCCCECDD0CCCCCAC7C8CCCACDCCC9
 C6C9C8C8C9CAC9CBC9CBCFD2CDC9CBCFCCCDCBCAC9C9C9CAC7C9CACBCCCEC9C9CAC8C4C7
 C7C6C4C8C7C6C6C7C6C8C6C0BEC1BEBFC0BEBDBFBDBDBBBAB8B7BBBFBABDC0BDB9BAB6B7
 CCD1D0CECCCED0D1CED2D3D3D2D2D6DFD9D4D2D4D3D3D4D6D3D4D6D4D0D4D4D2D4D6D3D5
 D2D5D7D6D5D6D6D9D6D3D5D6D3D7D8D8DBDDD9DAD9DAD9D9DADAD7DBDAD8D9DBD8D8D8DA
 DCDCD8DCDADBDCDAD9DBD7D9D7D9DCDEDCDCDADCDCD9D9DDDBDBDAD9DADCD9DDDCD9D6D9
 D5D5D6D6D5D0D2D8D3D4D3D2D3D5D0D2D1D0D0D1CFD1CCCCCECFCED2D0D1D0CCCDD0CCCD
 CAC9CCCDCED9D4CDCCCECFD0D2D4D2CFCDD0CDCDCCCFCFCECECFCCCFCFCDCCD0CFCFCACA
 CCCECCCBC4C5C7C7CACDC8CACACACDCFCBCBCBCFCFCECDCECCCDCBC9CBCECACCCECDCCCD
 CCCCC9C9C8C7C5C8C7C9C6C5C7CAC3C2C2C0BFBEBDC2C0C1BFBDBDBDB6B7BDBDB9BDBBBB
 BBBBB8B8CCD0CBCECECBCCCECED2D0D0D1D4D6D9D4D3D4D5D5D7D6D8D7D7D5D7D5D8D6D8
 D8D8D4D5D4D5D4D4D4D4D2D6D6D5D2D6D5D8D6D6E1E6DDDAD7DCDAD7DADBDBDED8D7D9DA
 D6D7D7D8D9DCDDDCD8DCDDDAD9DAD5D7D8D9DBDDD9DAD9DCDCDCDCDCDADBDAD8DADBD7D9
 D7D9DAD6D2D8D7D6D6D5D6D9D4D4D5D4D4D6D2D1D0D2D0CDCED2CCCDCDCECFD3D1D2D0CB
 CBD2D3CECACDD0D0D0D5D2D0CDCECFD2D0D2CDCDCFD1CFD1CDCFD1CFCCCFCACDCECECED1
 CFD0CDCCCDCECDCEC9CACDCDCACECCCDCECECED0CDCECBCDD1D0D1D2CFCECED0D1D0CBCC
 CBCACCCDCACAC8C8C8C7C6C9C6C6C5C8C8C4BEC2C1C2C2C4C3C3BCBCC0BEBCBEB9BAB9BA
 B8B9BBBCBABAB9BAC8C5C9CBC8CBCBCDCFCEC9CCCCCECECFCFD0D0D4D4D7D9D8D4D5D4D5
 D5D5D5D6D4D6D5D7D8D6D5DBDAD6D6D8D7D7D5D7D7D7D7DBE4E4DCDDDDDBD8D8D7DADFDE
 D4D6D5D7D6D6D7DAD8DDDDDADADBD8D9D8D9D8D9D7D8E0E5D6D2D8DAD6DADBDADCDCD7D9
 D8DAD8D4D3DAD3D0D4D6D5D6D3D6D2D2D1D3D2D4D2D4D4D0D0D3CDD0D2D0CDD0CDD0CDCE
 D0D2D0CFCCD5D7CECCD5D6D4D2D4D8D8D2D2D1D2D4D4CFD2D0D0D1D0D0D2CFD1D2D2CDCD
 CDCFCDCFCFD0D0D1CDCFD0CECACECCCBCCCFCDCDCED2CDCBCDCCCACFD0CED3D6CECBCCCF
 CECCCCCBCACBCACCC7C6C8CAC4C4C6C6C4C3C0C2C2C3C5C4C0C3C2C1BFBFBDBFBCBDBBBC
 B9B9B6B7B6B8BBB8B6B9B7B9C8C8C7C8C8CCC9CDCDCCCBCCC9CCCCCACBD0CDCED0D4D4D3
 D2D4D3D6D5D4D4D6D6D8D6D6D8D8D7E2DED7D7D9DBDBD4D6D7D8D8DADDDFDADCDEE0DAD8
 D9E0E4DFDADEDAD9D9D8D9DAD9DDDAD9D8D9DADCD9D9DAD8D8DBE1E6DAD2D7DAD6DADCDC
 DCDBD9DCDAD9D9D5D7DDD7D5D5D3D4D4D3D6D4D3D3D2D1D4D0D2D4D2D0D2CFD3D4D2D2D4
 D0D1D0D0D2D2D0D2D0D6D6CCCCDDE1D8D2D7DED9D3D6D2D6D8D7D3D6D1D2D4D2D0D6D3D2
 D2D2D0CFD1D4CFD2D4D4D0D1CECECECFCDCFCCCDCDCECECFD1D9D2CECECFCFD5D4D0CFD2
 CFCECECECACACCCBC9CCCACBC9C6C6C8C6C7C7C6C3C2C2C5BEC0C7C7C2C5C2C2C0C0BFC0
 BDBFBDBDBCBABABDB8B9BAB7B6B8B6B9C9CCC9C7C6C7C9CBC9CCCBCACCCBC8CDCCCDCED0
 D1D6D4D4D2D2D4D5D0D1D4D3D3D5D4D9D6D5D6DCDBD9D7D9D9D7D6D6D5D8DAD9DADAD8DF
 E2E4DAD6DFE9EAE4DDDFE1DFDADADADAD9DAD7D9DADCDDDBDCDDD6D9D8D6DCE2DAD8D8DA
 D7DCDEDFDCDEDDDCDEDED8DBD9D9D9D8D4D6D5D6D7DADADAD6D8D6D2D1D4D2D5D4D2D0D5
 D6D6D4D5D5D2D1D4D1D4D4D2D2D8D4D5D3D6DBD3D0D8D7D8D9D5CFD4D6DAD5D3D2D4D3D4
 D3D2D1D2D2D4CFD1D3D2D2D4D1D4D3D0CFCFCED2D0CECBCACACFCCCFD4DAD6CFCCCFCED0
 D4CFCCCFCCCCCCCBCBCCCACDCECCCCCDC9C8C8CAC9C4C3C7C5C4C2BFBDC1C2C6C6C5C1C0
 BFC3BFBEBEC1C0C1BCBEBDBBB9BAB7B9B9B8B8BBC8C9C6CACCCAC8C9C9CECBC9CCCFCCCF
 CDCCCCD0D1D5D0D3D3D1D0D3D0D4D2D2D3D4D3D6D5D6D5D7D8D6D4D8D8D7D6D5D6DEDCDA
 DADBDADDE0E1D6D6DFE6E6E2DCE0E0E0DDDDDADADBDDDBDCD8DCDCDADBDED8D9DADCDDDE
 DCDDDADADDE2E0E2DEDDDCDDDFDED8DCDCDDDCD9D7DAD6D7DCE5E1D8D6DAD8D2CED0CFD2
 D2D5D6D4D5D7D6D8D7D5D3D4D3D5D5D6D4D6D4D4D3D5D3D0D1D5D2D4D6D4D3D5D4D7D4D2
 D1D3D3D4D0D2D3D2D1D4CECFD0D0D2D5D2D3D0D0D0D0CED2D1D1D0CECDD2D0D4D4D4D4D0
 CCD0CFCFCFCFCCCDC9CCCECCC8CAC9CDCECCCDCDCACAC8CBC8C4C4C7C1C2C3C1C0C3C4CB
 C9C5C1C0C0C2BEBFC0C0C1C0BEBEBEBDBABBBABAB9BABCBCCAC8C6C9CACECCCBCCCCCBCD
 CCCBCBCCCBCDCCD0CECECECFCFD0CDCFD0D1D2D6D3D2D2D5D6D6D1D6D8D5D8DDDAD8D2CF
 DAE4DFD9D6D8DADCE1E0D8D9D9DCDDDBD7DADDE0DCD9DADBD8DBD9DADCDDD8DADADCDCD8
 D9DDDADCDCDCDDDDDADFDFE2E2DED9E1E2DBD9DAD8DBD8D8D8D7D5D4D5E2DDD6DADBDADA
 D0D1D3D4D2D3D0D4D4D4D7D9D1D4CECFDCDCD0D2D0D4D4D2D3D5CFD0D2D2D2D5D3D5D2D4
 D6D6D3D4D0D3DCDBD4D3CDD1D2D0CFCFCDCFD0D3D5D4D0D1CDCFD0CECED4CDCBCED2D1D1
 D0D1D0D0CECFD0D1CECFCFCCC9CACACDCAC9CACBCCCFCCCCCBCAC8CAC7C7C6C6C4C4C0C3
 C0C1C1C7C8C6BFC0C0C0C0C2BEC0C0BFBCBFBABABBBCB8B6B9BDB8B9C8C9C9CBCBCCCDCF
 CCCCCDCFCDCFCFCECED0D0D4CECDCFD4D3D2CFD1D1D3D4D6D5D6D6D5D6D6D6D9D6D2DAE5
 E0DBD3D7E2E6DCD9D7DADADCE2E4DAD8D7D8D9DADCDEE0E2DBDADCDBD8DBD6D7D9D9D6D9
 D9DADBDADFE1DCDCDCDDDFDDD8DDE0E1E0E0DFE2DFDDDAD8D9DEDAD7D7D6D6D6D7DDDCDA
 E0E2DEDED9D8D6D4D4D6D3D4D2D4D7D9D6D6CECEDBDDD3D2D0D3D6D3D1D6D2D4D4D6D5D8
 DADAD6D6D6D5D5D6D0D5DFDCD3D5D0D1D1D2D3D2D0D1D0D6DCD6D0CECDD0CFCDCED2D1D1
 CED2D2D2D2D2CFD0D0CECED4CFCFD2D0CDCFCDCFCDCECDCDCCCECCCBCACCCAC9C8C9C6C4
 C2C1C0C4C1C1C2C5C4C5C2C4C2C0C1C1BDBEBFC1C1C0BFC2C1BFBFBCBABEB9B8CCCCCACC
 CBC9CDD2CED0D0CECECDCDD4CDCDD3D5D3D4D0D3D1CDCFD2D1D4D4D5D4D4D3D6D4D5D6D5
 D6DAD8DFDED6D3D9DCE0DBD8DADAD9DEDFE0DBD8D9DCD9DDD8D6DDE0DADBDADADADAD7DB
 DBDDDCDADBDFDADCDDDCDCDEDCDDDCDBD9DADCE0DCE0E0DCDBDED8D9D8DADBD9D8DBD8D8
 D9D9D6D8DDE5DFDAD8DAD4D2D2D4D3D5D2D4D8DDD7D2D1D2D5DAD7D4D2D5D4D4D3D4D3D4
 D4D7D2D5DBDBD2D1D0D5D6D4D3D3D6DAD5D1CECFD1D4D3D5D6D5D2D3D6DAD8D4D2D2CFD0
 CFD1D0D0D0D1CECFCFD0CFD0D0D4D1D1D3D4D3D4D0D1CFCCCBCFCCCECFCECCCDC9CBCCCD
 CAC7C5C7C3C2C1C1C2C3C0C2C2C3C2C4C3C3C2C3C0BEBDC2BFC0BEBDBCBEBCBBB7B9B8B8
 CBCBC8CBCCCDCDD0CED0CFCDCCCED4DACCCDD3D4D2D3D1D3D1D1D1D4D4D6D4D4D4D6D6D7
 D2D6D7D4D6DAD6D6D8D6D6D9D8DCD9D9D9D9D9DBD9DADCDBDBDDDADBDBDADAD9D9DBD9D9
 DADBDADCD9DCDBD8D9DBD9DADADDDCDBDBDFDCD9D9DBDCE0DBDBDDDAD9DDD8D9D8DBDAD8
 D9DDDAD6D6D8D8DAD9DDD9D6D6D6D6D7D4D6D8D8D5D8D9DCD8D5D4D4D2D7D5D4D6D6D4D4
 D2D5D6D5D4D7D5D6D6D8D6D8D4D4D2D3D3D4D1D4D0D1D4D4D2D6D6D7D6D4D4D4D4D9D6D6
 D2D1CFD0D0D1D2D2D1D2D0D2D2D2D1D2D2D4D1D1D3D4D2D2D0D0D0D0CECFCDCECFD0D0CF
 CCCCCACACCCBC9C8C2C4C7C6C6C6C1C2C2C5C5C5C4C5C1C2C2C0BFC1BCBDBCBDBCBDBABA
 B6B6B7B9CCC8C8CDCCCDCCCFD0CCCCCFCBCED9D9CECFD0D2D1D2D4D5D2D4D0D4D8D6D4D8
 D4D5D6D9D9D8D4D5D5D7D8D8D6D9D4D6DBDAD7D9D6D8D9D9DADBDADCDCDCDADBDADBD8DA
 DCDBDADCDBDCDADADADBD8DAD9DBDCDAD9DBD9DBDEDFDDDCD8DAE2E4DCDADBDCD7D9DAD6
 D5DAD7D7DADAD8D8D7DBDAD8DADBD7D9D7D7D7D6D4D6D3D5D5D6D8DAD7D9D6D5D6D8D6DA
 D6D6D7D5D3D6D5D6D6D4D4D6D6D9D6D7D6D4D3D6D2D1D4D6D2D4D2D3D2D4D7D8D6D9D4D2
 D2D4D6D7D0D0D1D2D0CFCFD1CFD1D2D2D2D4D0D2D2D2D2D4D2D4D2D2D1D2CCCFCECECFCF
 CDCFCDCECDCBCBCDCBCAC8C8C6C5C6C7C5C6C5C3C2C4C3C4C4C1C2C6C1BDBCBEBDBDB9BC
 BAB9BABAB7B9B8B7CBC8C9CDCED2D0D2D2D0D0D2CED2D6D4CFD0D0D0D2D2D4D4D4D6D2D4
 D6D6D6D8D3D6D7DADBD8D4D6D6D7D7D6D6DAD5D7DAD9D8DAD7DADAD7D6D6D7DAD8DADADA
 DADCD7D8DCDCDCDEE0E3DCDADADBDBDDD9DBDCDAD8DCDDDDDDDEDCDDDADDE2E4DCD9DBDD
 D8D9DAD9D7DCD8DADADAD9DBDCE0DCD9DCE0DADAD7D8D7D6D5D6D3D6D6D9D7D7D6D9D7DA
 DAD9D7DAD7D8D7D6D6D8D6D6D6D4D4D8D4D6D6D7D7D5D2D7D4D5D4D4D3D5D2D5D4D4D6D8
 D7D9D6D5D4D4D3D5D2D3D2D2D2D2D0D2D1D1D2D4D4D4D0D2D5D4D2D5D4D6D5D6D4D3D0D1
 CECFD0CECDD0CDCECFCDCBCBCBCDC9C8C5C4C2C9CAC8C6C6C4C4C2C4C1C1C2C2BFBFBCBD
 BDBBB9BEBCBCBEBFBABAB7B9C7CDCCCDD0D2CDD1CDCECECECFD1D0D0CDCFCECECED2D0D4
 D2D2D2D4D2D3D3D4D0D2D2D7D6D6D6D7D6D6D3D4D4D5D3D6D7DCD8D5D7DBDAD9D4D4D5D7
 D8DAD6D8D7D6D8DADADDDADBDEE0E1DFD9E0E2D9D9DDDADAD8DADADCDCDDD8D8D9DADCDC
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0)
)
>

<Row,"Row">

<Cell>

<"CellBody">

          (a) frame 25 of approach to two <SR>
chairs
<Cell>

<"CellBody">

(b) frame 35
<Row,"Row">

<Cell>

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       Width = 2.559 Inches,
       Height = 2.559 Inches,
       Size Contents to Width = Yes, 
       Size Contents to Height = Yes, 
       No Border = Yes,
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 B4B4B4B4B5B5B5B5B1B1B1B1B3B3B3B3F0F0F0F0B9B9B9B9B9B9B9B9B9B9B9B9BABABABA
 BABABABABABABABABABABABABABABABABABABABABBBBBBBBBABABABAC2C2C2C2D2D2D2D2
 AAAAAAAAB1B1B1B1B3B3B3B3BBBBBBBBB6B6B6B6BFBFBFBFC0C0C0C0C0C0C0C0BEBEBEBE
 BEBEBEBEBDBDBDBDBEBEBEBEBEBEBEBEBEBEBEBEBBBBBBBBC5C5C5C5CECECECECECECECE
 C9C9C9C9C9C9C9C9CCCCCCCC373737373737373737373737373737373737373737373737
 3737373737373737B6B6B6B6BCBCBCBCBDBDBDBDBABABABABABABABAB8B8B8B8B4B4B4B4
 BCBCBCBCC2C2C2C2C1C1C1C1A7A7A7A7A7A7A7A7A7A7A7A7A8A8A8A8A8A8A8A8A9A9A9A9
 A9A9A9A9B4B4B4B4B5B5B5B5B1B1B1B1B3B3B3B3F0F0F0F0B9B9B9B9B9B9B9B9B9B9B9B9
 BABABABABABABABABABABABABABABABABABABABABABABABABBBBBBBBBABABABAC2C2C2C2
 D2D2D2D2AAAAAAAAB1B1B1B1B3B3B3B3BBBBBBBBB6B6B6B6BFBFBFBFC0C0C0C0C0C0C0C0
 BEBEBEBEBEBEBEBEBDBDBDBDBEBEBEBEBEBEBEBEBEBEBEBEBBBBBBBBC5C5C5C5CECECECE
 CECECECEC9C9C9C9C9C9C9C9CCCCCCCC3737373737373737373737373737373737373737
 373737373737373737373737B6B6B6B6BCBCBCBCBDBDBDBDBABABABABABABABAB8B8B8B8
 B4B4B4B4BCBCBCBCC2C2C2C2C1C1C1C1A7A7A7A7A7A7A7A7A7A7A7A7A8A8A8A8A8A8A8A8
 A9A9A9A9A9A9A9A9B4B4B4B4B5B5B5B5B1B1B1B1B3B3B3B3F0F0F0F0B9B9B9B9B9B9B9B9
 B9B9B9B9BABABABABABABABABABABABABABABABABABABABABABABABABBBBBBBBBABABABA
 C2C2C2C2D2D2D2D2AAAAAAAAB1B1B1B1B3B3B3B3BBBBBBBBB6B6B6B6BFBFBFBFC0C0C0C0
 C0C0C0C0BEBEBEBEBEBEBEBEBDBDBDBDBEBEBEBEBEBEBEBEBEBEBEBEBBBBBBBBC5C5C5C5
 CECECECECECECECEC9C9C9C9C9C9C9C9CCCCCCCC37373737373737373737373737373737
 37373737373737373737373737373737B6B6B6B6BCBCBCBCBDBDBDBDBABABABABABABABA
 B8B8B8B8B4B4B4B4BCBCBCBCC2C2C2C2C1C1C1C1A7A7A7A7A7A7A7A7A7A7A7A7A8A8A8A8
 A8A8A8A8A9A9A9A9A9A9A9A9B4B4B4B4B5B5B5B5B1B1B1B1B3B3B3B3F0F0F0F0B9B9B9B9
 B9B9B9B9B9B9B9B9BABABABABABABABABABABABABABABABABABABABABABABABABBBBBBBB
 BABABABAC2C2C2C2D2D2D2D2AAAAAAAAB1B1B1B1B3B3B3B3BBBBBBBBB6B6B6B6BFBFBFBF
 C0C0C0C0C0C0C0C0BEBEBEBEBEBEBEBEBDBDBDBDBEBEBEBEBEBEBEBEBEBEBEBEBBBBBBBB
 C5C5C5C5CECECECECECECECEC9C9C9C9C9C9C9C9CCCCCCCC373737373737373737373737
 3737373737373737373737373737373737373737B6B6B6B6BCBCBCBCBDBDBDBDC0C0C0C0
 C0C0C0C0C1C1C1C1C1C1C1C1C5C5C5C5C8C8C8C8C8C8C8C8C5C5C5C5A8A8A8A8C7C7C7C7
 C4C4C4C4C2C2C2C2ACACACACB2B2B2B2BABABABAB8B8B8B8B5B5B5B5BABABABAD3D3D3D3
 C8C8C8C8BFBFBFBFBEBEBEBEBDBDBDBDBFBFBFBFBABABABABABABABABABABABABABABABA
 BCBCBCBCBCBCBCBCC3C3C3C3CFCFCFCFD2D2D2D2BEBEBEBEBFBFBFBFC2C2C2C2C0C0C0C0
 C4C4C4C4C8C8C8C8C6C6C6C6C0C0C0C0BFBFBFBFBFBFBFBFBFBFBFBFBFBFBFBFBFBFBFBF
 BDBDBDBDCDCDCDCDD0D0D0D0CFCFCFCFCACACACACACACACACECECECE3737373737373737
 373737373737373737373737373737373737373737373737B6B6B6B6BCBCBCBCBDBDBDBD
 C0C0C0C0C0C0C0C0C1C1C1C1C1C1C1C1C5C5C5C5C8C8C8C8C8C8C8C8C5C5C5C5A8A8A8A8
 C7C7C7C7C4C4C4C4C2C2C2C2ACACACACB2B2B2B2BABABABAB8B8B8B8B5B5B5B5BABABABA
 D3D3D3D3C8C8C8C8BFBFBFBFBEBEBEBEBDBDBDBDBFBFBFBFBABABABABABABABABABABABA
 BABABABABCBCBCBCBCBCBCBCC3C3C3C3CFCFCFCFD2D2D2D2BEBEBEBEBFBFBFBFC2C2C2C2
 C0C0C0C0C4C4C4C4C8C8C8C8C6C6C6C6C0C0C0C0BFBFBFBFBFBFBFBFBFBFBFBFBFBFBFBF
 BFBFBFBFBDBDBDBDCDCDCDCDD0D0D0D0CFCFCFCFCACACACACACACACACECECECE37373737
 37373737373737373737373737373737373737373737373737373737B6B6B6B6BCBCBCBC
 BDBDBDBDC0C0C0C0C0C0C0C0C1C1C1C1C1C1C1C1C5C5C5C5C8C8C8C8C8C8C8C8C5C5C5C5
 A8A8A8A8C7C7C7C7C4C4C4C4C2C2C2C2ACACACACB2B2B2B2BABABABAB8B8B8B8B5B5B5B5
 BABABABAD3D3D3D3C8C8C8C8BFBFBFBFBEBEBEBEBDBDBDBDBFBFBFBFBABABABABABABABA
 BABABABABABABABABCBCBCBCBCBCBCBCC3C3C3C3CFCFCFCFD2D2D2D2BEBEBEBEBFBFBFBF
 C2C2C2C2C0C0C0C0C4C4C4C4C8C8C8C8C6C6C6C6C0C0C0C0BFBFBFBFBFBFBFBFBFBFBFBF
 BFBFBFBFBFBFBFBFBDBDBDBDCDCDCDCDD0D0D0D0CFCFCFCFCACACACACACACACACECECECE
 3737373737373737373737373737373737373737373737373737373737373737B6B6B6B6
 BCBCBCBCBDBDBDBDC0C0C0C0C0C0C0C0C1C1C1C1C1C1C1C1C5C5C5C5C8C8C8C8C8C8C8C8
 C5C5C5C5A8A8A8A8C7C7C7C7C4C4C4C4C2C2C2C2ACACACACB2B2B2B2BABABABAB8B8B8B8
 B5B5B5B5BABABABAD3D3D3D3C8C8C8C8BFBFBFBFBEBEBEBEBDBDBDBDBFBFBFBFBABABABA
 BABABABABABABABABABABABABCBCBCBCBCBCBCBCC3C3C3C3CFCFCFCFD2D2D2D2BEBEBEBE
 BFBFBFBFC2C2C2C2C0C0C0C0C4C4C4C4C8C8C8C8C6C6C6C6C0C0C0C0BFBFBFBFBFBFBFBF
 BFBFBFBFBFBFBFBFBFBFBFBFBDBDBDBDCDCDCDCDD0D0D0D0CFCFCFCFCACACACACACACACA
 CECECECE3737373737373737373737373737373737373737373737373737373737373737
 B2B2B2B2B2B2B2B2BCBCBCBCBFBFBFBFC0C0C0C0C2C2C2C2C6C6C6C6C9C9C9C9CCCCCCCC
 CCCCCCCCCDCDCDCDA7A7A7A7C8C8C8C8C5C5C5C5C6C6C6C6BEBEBEBEBDBDBDBDBFBFBFBF
 BBBBBBBBB7B7B7B7BBBBBBBBC1C1C1C1C1C1C1C1BFBFBFBFBFBFBFBFBEBEBEBEC1C1C1C1
 BCBCBCBCBBBBBBBBBBBBBBBBBABABABABDBDBDBDBDBDBDBDC3C3C3C3CDCDCDCDD0D0D0D0
 D1D1D1D1C3C3C3C3CFCFCFCFD0D0D0D0CCCCCCCCD1D1D1D1D0D0D0D0C2C2C2C2C0C0C0C0
 C0C0C0C0C1C1C1C1C1C1C1C1C3C3C3C3C1C1C1C1D4D4D4D4D3D3D3D3D2D2D2D2D1D1D1D1
 CFCFCFCFD1D1D1D137373737373737373737373737373737373737373737373737373737
 37373737B2B2B2B2B2B2B2B2BCBCBCBCBFBFBFBFC0C0C0C0C2C2C2C2C6C6C6C6C9C9C9C9
 CCCCCCCCCCCCCCCCCDCDCDCDA7A7A7A7C8C8C8C8C5C5C5C5C6C6C6C6BEBEBEBEBDBDBDBD
 BFBFBFBFBBBBBBBBB7B7B7B7BBBBBBBBC1C1C1C1C1C1C1C1BFBFBFBFBFBFBFBFBEBEBEBE
 C1C1C1C1BCBCBCBCBBBBBBBBBBBBBBBBBABABABABDBDBDBDBDBDBDBDC3C3C3C3CDCDCDCD
 D0D0D0D0D1D1D1D1C3C3C3C3CFCFCFCFD0D0D0D0CCCCCCCCD1D1D1D1D0D0D0D0C2C2C2C2
 C0C0C0C0C0C0C0C0C1C1C1C1C1C1C1C1C3C3C3C3C1C1C1C1D4D4D4D4D3D3D3D3D2D2D2D2
 D1D1D1D1CFCFCFCFD1D1D1D1373737373737373737373737373737373737373737373737
 3737373737373737B2B2B2B2B2B2B2B2BCBCBCBCBFBFBFBFC0C0C0C0C2C2C2C2C6C6C6C6
 C9C9C9C9CCCCCCCCCCCCCCCCCDCDCDCDA7A7A7A7C8C8C8C8C5C5C5C5C6C6C6C6BEBEBEBE
 BDBDBDBDBFBFBFBFBBBBBBBBB7B7B7B7BBBBBBBBC1C1C1C1C1C1C1C1BFBFBFBFBFBFBFBF
 BEBEBEBEC1C1C1C1BCBCBCBCBBBBBBBBBBBBBBBBBABABABABDBDBDBDBDBDBDBDC3C3C3C3
 CDCDCDCDD0D0D0D0D1D1D1D1C3C3C3C3CFCFCFCFD0D0D0D0CCCCCCCCD1D1D1D1D0D0D0D0
 C2C2C2C2C0C0C0C0C0C0C0C0C1C1C1C1C1C1C1C1C3C3C3C3C1C1C1C1D4D4D4D4D3D3D3D3
 D2D2D2D2D1D1D1D1CFCFCFCFD1D1D1D13737373737373737373737373737373737373737
 373737373737373737373737B2B2B2B2B2B2B2B2BCBCBCBCBFBFBFBFC0C0C0C0C2C2C2C2
 C6C6C6C6C9C9C9C9CCCCCCCCCCCCCCCCCDCDCDCDA7A7A7A7C8C8C8C8C5C5C5C5C6C6C6C6
 BEBEBEBEBDBDBDBDBFBFBFBFBBBBBBBBB7B7B7B7BBBBBBBBC1C1C1C1C1C1C1C1BFBFBFBF
 BFBFBFBFBEBEBEBEC1C1C1C1BCBCBCBCBBBBBBBBBBBBBBBBBABABABABDBDBDBDBDBDBDBD
 C3C3C3C3CDCDCDCDD0D0D0D0D1D1D1D1C3C3C3C3CFCFCFCFD0D0D0D0CCCCCCCCD1D1D1D1
 D0D0D0D0C2C2C2C2C0C0C0C0C0C0C0C0C1C1C1C1C1C1C1C1C3C3C3C3C1C1C1C1D4D4D4D4
 D3D3D3D3D2D2D2D2D1D1D1D1CFCFCFCFD1D1D1D137373737373737373737373737373737
 37373737373737373737373737373737B5B5B5B5B6B6B6B6BFBFBFBFBDBDBDBDBFBFBFBF
 C5C5C5C5CBCBCBCBCBCBCBCBCFCFCFCFCFCFCFCFD3D3D3D3A7A7A7A7CBCBCBCBC8C8C8C8
 C9C9C9C9C1C1C1C1C0C0C0C0C7C7C7C7C3C3C3C3BBBBBBBBC5C5C5C5CBCBCBCBCBCBCBCB
 C9C9C9C9CACACACAC7C7C7C7CACACACAC7C7C7C7C2C2C2C2C3C3C3C3C1C1C1C1C8C8C8C8
 CACACACACECECECED0D0D0D0D1D1D1D1D1D1D1D1D2D2D2D2D0D0D0D0D1D1D1D1CFCFCFCF
 CCCCCCCCD2D2D2D2CCCCCCCCCBCBCBCBCACACACAC9C9C9C9CACACACACACACACAC6C6C6C6
 D8D8D8D8DADADADADBDBDBDBD8D8D8D8D3D3D3D3DADADADA373737373737373737373737
 3737373737373737373737373737373737373737B5B5B5B5B6B6B6B6BFBFBFBFBDBDBDBD
 BFBFBFBFC5C5C5C5CBCBCBCBCBCBCBCBCFCFCFCFCFCFCFCFD3D3D3D3A7A7A7A7CBCBCBCB
 C8C8C8C8C9C9C9C9C1C1C1C1C0C0C0C0C7C7C7C7C3C3C3C3BBBBBBBBC5C5C5C5CBCBCBCB
 CBCBCBCBC9C9C9C9CACACACAC7C7C7C7CACACACAC7C7C7C7C2C2C2C2C3C3C3C3C1C1C1C1
 C8C8C8C8CACACACACECECECED0D0D0D0D1D1D1D1D1D1D1D1D2D2D2D2D0D0D0D0D1D1D1D1
 CFCFCFCFCCCCCCCCD2D2D2D2CCCCCCCCCBCBCBCBCACACACAC9C9C9C9CACACACACACACACA
 C6C6C6C6D8D8D8D8DADADADADBDBDBDBD8D8D8D8D3D3D3D3DADADADA3737373737373737
 373737373737373737373737373737373737373737373737B5B5B5B5B6B6B6B6BFBFBFBF
 BDBDBDBDBFBFBFBFC5C5C5C5CBCBCBCBCBCBCBCBCFCFCFCFCFCFCFCFD3D3D3D3A7A7A7A7
 CBCBCBCBC8C8C8C8C9C9C9C9C1C1C1C1C0C0C0C0C7C7C7C7C3C3C3C3BBBBBBBBC5C5C5C5
 CBCBCBCBCBCBCBCBC9C9C9C9CACACACAC7C7C7C7CACACACAC7C7C7C7C2C2C2C2C3C3C3C3
 C1C1C1C1C8C8C8C8CACACACACECECECED0D0D0D0D1D1D1D1D1D1D1D1D2D2D2D2D0D0D0D0
 D1D1D1D1CFCFCFCFCCCCCCCCD2D2D2D2CCCCCCCCCBCBCBCBCACACACAC9C9C9C9CACACACA
 CACACACAC6C6C6C6D8D8D8D8DADADADADBDBDBDBD8D8D8D8D3D3D3D3DADADADA37373737
 37373737373737373737373737373737373737373737373737373737B5B5B5B5B6B6B6B6
 BFBFBFBFBDBDBDBDBFBFBFBFC5C5C5C5CBCBCBCBCBCBCBCBCFCFCFCFCFCFCFCFD3D3D3D3
 A7A7A7A7CBCBCBCBC8C8C8C8C9C9C9C9C1C1C1C1C0C0C0C0C7C7C7C7C3C3C3C3BBBBBBBB
 C5C5C5C5CBCBCBCBCBCBCBCBC9C9C9C9CACACACAC7C7C7C7CACACACAC7C7C7C7C2C2C2C2
 C3C3C3C3C1C1C1C1C8C8C8C8CACACACACECECECED0D0D0D0D1D1D1D1D1D1D1D1D2D2D2D2
 D0D0D0D0D1D1D1D1CFCFCFCFCCCCCCCCD2D2D2D2CCCCCCCCCBCBCBCBCACACACAC9C9C9C9
 CACACACACACACACAC6C6C6C6D8D8D8D8DADADADADBDBDBDBD8D8D8D8D3D3D3D3DADADADA
 3737373737373737373737373737373737373737373737373737373737373737BCBCBCBC
 BFBFBFBFC8C8C8C8C2C2C2C2C8C8C8C8BFBFBFBFDBDBDBDBD0D0D0D0D3D3D3D3D5D5D5D5
 DADADADAD3D3D3D3C5C5C5C5C3C3C3C3C8C8C8C8BFBFBFBFBCBCBCBCC7C7C7C7C8C8C8C8
 C4C4C4C4C9C9C9C9CCCCCCCCCCCCCCCCCBCBCBCBCBCBCBCBCACACACACACACACAC9C9C9C9
 C7C7C7C7C8C8C8C8C6C6C6C6CBCBCBCBCDCDCDCDCFCFCFCFD1D1D1D1D1D1D1D1D1D1D1D1
 D2D2D2D2D1D1D1D1D1D1D1D1D0D0D0D0CECECECEDBDBDBDBD2D2D2D2D1D1D1D1D0D0D0D0
 D0D0D0D0D0D0D0D0CFCFCFCFCECECECEDEDEDEDEE2E2E2E2E5E5E5E5DDDDDDDDDBDBDBDB
 E3E3E3E33737373737373737373737373737373737373737373737373737373737373737
 BCBCBCBCBFBFBFBFC8C8C8C8C2C2C2C2C8C8C8C8BFBFBFBFDBDBDBDBD0D0D0D0D3D3D3D3
 D5D5D5D5DADADADAD3D3D3D3C5C5C5C5C3C3C3C3C8C8C8C8BFBFBFBFBCBCBCBCC7C7C7C7
 C8C8C8C8C4C4C4C4C9C9C9C9CCCCCCCCCCCCCCCCCBCBCBCBCBCBCBCBCACACACACACACACA
 C9C9C9C9C7C7C7C7C8C8C8C8C6C6C6C6CBCBCBCBCDCDCDCDCFCFCFCFD1D1D1D1D1D1D1D1
 D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1D0D0D0D0CECECECEDBDBDBDBD2D2D2D2D1D1D1D1
 D0D0D0D0D0D0D0D0D0D0D0D0CFCFCFCFCECECECEDEDEDEDEE2E2E2E2E5E5E5E5DDDDDDDD
 DBDBDBDBE3E3E3E337373737373737373737373737373737373737373737373737373737
 37373737BCBCBCBCBFBFBFBFC8C8C8C8C2C2C2C2C8C8C8C8BFBFBFBFDBDBDBDBD0D0D0D0
 D3D3D3D3D5D5D5D5DADADADAD3D3D3D3C5C5C5C5C3C3C3C3C8C8C8C8BFBFBFBFBCBCBCBC
 C7C7C7C7C8C8C8C8C4C4C4C4C9C9C9C9CCCCCCCCCCCCCCCCCBCBCBCBCBCBCBCBCACACACA
 CACACACAC9C9C9C9C7C7C7C7C8C8C8C8C6C6C6C6CBCBCBCBCDCDCDCDCFCFCFCFD1D1D1D1
 D1D1D1D1D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1D0D0D0D0CECECECEDBDBDBDBD2D2D2D2
 D1D1D1D1D0D0D0D0D0D0D0D0D0D0D0D0CFCFCFCFCECECECEDEDEDEDEE2E2E2E2E5E5E5E5
 DDDDDDDDDBDBDBDBE3E3E3E3373737373737373737373737373737373737373737373737
 3737373737373737BCBCBCBCBFBFBFBFC8C8C8C8C2C2C2C2C8C8C8C8BFBFBFBFDBDBDBDB
 D0D0D0D0D3D3D3D3D5D5D5D5DADADADAD3D3D3D3C5C5C5C5C3C3C3C3C8C8C8C8BFBFBFBF
 BCBCBCBCC7C7C7C7C8C8C8C8C4C4C4C4C9C9C9C9CCCCCCCCCCCCCCCCCBCBCBCBCBCBCBCB
 CACACACACACACACAC9C9C9C9C7C7C7C7C8C8C8C8C6C6C6C6CBCBCBCBCDCDCDCDCFCFCFCF
 D1D1D1D1D1D1D1D1D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1D0D0D0D0CECECECEDBDBDBDB
 D2D2D2D2D1D1D1D1D0D0D0D0D0D0D0D0D0D0D0D0CFCFCFCFCECECECEDEDEDEDEE2E2E2E2
 E5E5E5E5DDDDDDDDDBDBDBDBE3E3E3E33737373737373737373737373737373737373737
 373737373737373737373737F6F6F6F6F8F8F8F8E9E9E9E9CBCBCBCBD7D7D7D7F5F5F5F5
 F1F1F1F1D3D3D3D3D6D6D6D6D6D6D6D6CFCFCFCFD1D1D1D1C9C9C9C9C9C9C9C9CBCBCBCB
 C2C2C2C2C2C2C2C2CCCCCCCCCDCDCDCDC8C8C8C8C9C9C9C9CCCCCCCCCDCDCDCDCCCCCCCC
 CCCCCCCCCBCBCBCBCBCBCBCBCCCCCCCCCBCBCBCBCACACACAC9C9C9C9CDCDCDCDCECECECE
 CFCFCFCFD0D0D0D0D0D0D0D0D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1D1D1D1D1D0D0D0D0
 E1E1E1E1D5D5D5D5D4D4D4D4D3D3D3D3D2D2D2D2D2D2D2D2D1D1D1D1D2D2D2D2E2E2E2E2
 E4E4E4E4E7E7E7E7E5E5E5E5E5E5E5E5E7E7E7E737373737373737373737373737373737
 37373737373737373737373737373737F6F6F6F6F8F8F8F8E9E9E9E9CBCBCBCBD7D7D7D7
 F5F5F5F5F1F1F1F1D3D3D3D3D6D6D6D6D6D6D6D6CFCFCFCFD1D1D1D1C9C9C9C9C9C9C9C9
 CBCBCBCBC2C2C2C2C2C2C2C2CCCCCCCCCDCDCDCDC8C8C8C8C9C9C9C9CCCCCCCCCDCDCDCD
 CCCCCCCCCCCCCCCCCBCBCBCBCBCBCBCBCCCCCCCCCBCBCBCBCACACACAC9C9C9C9CDCDCDCD
 CECECECECFCFCFCFD0D0D0D0D0D0D0D0D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1D1D1D1D1
 D0D0D0D0E1E1E1E1D5D5D5D5D4D4D4D4D3D3D3D3D2D2D2D2D2D2D2D2D1D1D1D1D2D2D2D2
 E2E2E2E2E4E4E4E4E7E7E7E7E5E5E5E5E5E5E5E5E7E7E7E7373737373737373737373737
 3737373737373737373737373737373737373737F6F6F6F6F8F8F8F8E9E9E9E9CBCBCBCB
 D7D7D7D7F5F5F5F5F1F1F1F1D3D3D3D3D6D6D6D6D6D6D6D6CFCFCFCFD1D1D1D1C9C9C9C9
 C9C9C9C9CBCBCBCBC2C2C2C2C2C2C2C2CCCCCCCCCDCDCDCDC8C8C8C8C9C9C9C9CCCCCCCC
 CDCDCDCDCCCCCCCCCCCCCCCCCBCBCBCBCBCBCBCBCCCCCCCCCBCBCBCBCACACACAC9C9C9C9
 CDCDCDCDCECECECECFCFCFCFD0D0D0D0D0D0D0D0D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1
 D1D1D1D1D0D0D0D0E1E1E1E1D5D5D5D5D4D4D4D4D3D3D3D3D2D2D2D2D2D2D2D2D1D1D1D1
 D2D2D2D2E2E2E2E2E4E4E4E4E7E7E7E7E5E5E5E5E5E5E5E5E7E7E7E73737373737373737
 373737373737373737373737373737373737373737373737F6F6F6F6F8F8F8F8E9E9E9E9
 CBCBCBCBD7D7D7D7F5F5F5F5F1F1F1F1D3D3D3D3D6D6D6D6D6D6D6D6CFCFCFCFD1D1D1D1
 C9C9C9C9C9C9C9C9CBCBCBCBC2C2C2C2C2C2C2C2CCCCCCCCCDCDCDCDC8C8C8C8C9C9C9C9
 CCCCCCCCCDCDCDCDCCCCCCCCCCCCCCCCCBCBCBCBCBCBCBCBCCCCCCCCCBCBCBCBCACACACA
 C9C9C9C9CDCDCDCDCECECECECFCFCFCFD0D0D0D0D0D0D0D0D1D1D1D1D2D2D2D2D1D1D1D1
 D1D1D1D1D1D1D1D1D0D0D0D0E1E1E1E1D5D5D5D5D4D4D4D4D3D3D3D3D2D2D2D2D2D2D2D2
 D1D1D1D1D2D2D2D2E2E2E2E2E4E4E4E4E7E7E7E7E5E5E5E5E5E5E5E5E7E7E7E737373737
 37373737373737373737373737373737373737373737373737373737F7F7F7F7F8F8F8F8
 F8F8F8F8F6F6F6F6F4F4F4F4F6F6F6F6F5F5F5F5F6F6F6F6DDDDDDDDDBDBDBDBDADADADA
 D2D2D2D2CECECECECDCDCDCDCDCDCDCDC6C6C6C6C8C8C8C8CECECECED0D0D0D0CBCBCBCB
 C9C9C9C9CBCBCBCBCCCCCCCCCDCDCDCDCCCCCCCCCBCBCBCBCCCCCCCCCDCDCDCDCDCDCDCD
 CCCCCCCCCACACACACDCDCDCDCECECECECECECECECFCFCFCFCFCFCFCFCFCFCFCFD1D1D1D1
 D1D1D1D1D0D0D0D0D1D1D1D1D0D0D0D0E5E5E5E5DCDCDCDCDADADADAD8D8D8D8D8D8D8D8
 DADADADAD9D9D9D9DDDDDDDDE6E6E6E6E7E7E7E7E9E9E9E9F6F6F6F6E7E7E7E7E8E8E8E8
 3737373737373737373737373737373737373737373737373737373737373737F7F7F7F7
 F8F8F8F8F8F8F8F8F6F6F6F6F4F4F4F4F6F6F6F6F5F5F5F5F6F6F6F6DDDDDDDDDBDBDBDB
 DADADADAD2D2D2D2CECECECECDCDCDCDCDCDCDCDC6C6C6C6C8C8C8C8CECECECED0D0D0D0
 CBCBCBCBC9C9C9C9CBCBCBCBCCCCCCCCCDCDCDCDCCCCCCCCCBCBCBCBCCCCCCCCCDCDCDCD
 CDCDCDCDCCCCCCCCCACACACACDCDCDCDCECECECECECECECECFCFCFCFCFCFCFCFCFCFCFCF
 D1D1D1D1D1D1D1D1D0D0D0D0D1D1D1D1D0D0D0D0E5E5E5E5DCDCDCDCDADADADAD8D8D8D8
 D8D8D8D8DADADADAD9D9D9D9DDDDDDDDE6E6E6E6E7E7E7E7E9E9E9E9F6F6F6F6E7E7E7E7
 E8E8E8E83737373737373737373737373737373737373737373737373737373737373737
 F7F7F7F7F8F8F8F8F8F8F8F8F6F6F6F6F4F4F4F4F6F6F6F6F5F5F5F5F6F6F6F6DDDDDDDD
 DBDBDBDBDADADADAD2D2D2D2CECECECECDCDCDCDCDCDCDCDC6C6C6C6C8C8C8C8CECECECE
 D0D0D0D0CBCBCBCBC9C9C9C9CBCBCBCBCCCCCCCCCDCDCDCDCCCCCCCCCBCBCBCBCCCCCCCC
 CDCDCDCDCDCDCDCDCCCCCCCCCACACACACDCDCDCDCECECECECECECECECFCFCFCFCFCFCFCF
 CFCFCFCFD1D1D1D1D1D1D1D1D0D0D0D0D1D1D1D1D0D0D0D0E5E5E5E5DCDCDCDCDADADADA
 D8D8D8D8D8D8D8D8DADADADAD9D9D9D9DDDDDDDDE6E6E6E6E7E7E7E7E9E9E9E9F6F6F6F6
 E7E7E7E7E8E8E8E837373737373737373737373737373737373737373737373737373737
 37373737F7F7F7F7F8F8F8F8F8F8F8F8F6F6F6F6F4F4F4F4F6F6F6F6F5F5F5F5F6F6F6F6
 DDDDDDDDDBDBDBDBDADADADAD2D2D2D2CECECECECDCDCDCDCDCDCDCDC6C6C6C6C8C8C8C8
 CECECECED0D0D0D0CBCBCBCBC9C9C9C9CBCBCBCBCCCCCCCCCDCDCDCDCCCCCCCCCBCBCBCB
 CCCCCCCCCDCDCDCDCDCDCDCDCCCCCCCCCACACACACDCDCDCDCECECECECECECECECFCFCFCF
 CFCFCFCFCFCFCFCFD1D1D1D1D1D1D1D1D0D0D0D0D1D1D1D1D0D0D0D0E5E5E5E5DCDCDCDC
 DADADADAD8D8D8D8D8D8D8D8DADADADAD9D9D9D9DDDDDDDDE6E6E6E6E7E7E7E7E9E9E9E9
 F6F6F6F6E7E7E7E7E8E8E8E8373737373737373737373737373737373737373737373737
 3737373737373737B6B6B6B6F9F9F9F9F7F7F7F7F4F4F4F4F2F2F2F2F4F4F4F4F3F3F3F3
 F4F4F4F4EAEAEAEAE1E1E1E1D9D9D9D9D6D6D6D6D1D1D1D1D0D0D0D0D1D1D1D1CDCDCDCD
 CFCFCFCFD0D0D0D0D0D0D0D0CECECECECBCBCBCBCCCCCCCCCDCDCDCDCDCDCDCDCECECECE
 CECECECECFCFCFCFD0D0D0D0D0D0D0D0D1D1D1D1CFCFCFCFCFCFCFCFD0D0D0D0D0D0D0D0
 D0D0D0D0CFCFCFCFCFCFCFCFD1D1D1D1D1D1D1D1D0D0D0D0D1D1D1D1D1D1D1D1E5E5E5E5
 E2E2E2E2E1E1E1E1DFDFDFDFE0E0E0E0E2E2E2E2E2E2E2E2E6E6E6E6E7E7E7E7E7E7E7E7
 EFEFEFEFF1F1F1F1F3F3F3F3E6E6E6E63737373737373737373737373737373737373737
 373737373737373737373737B6B6B6B6F9F9F9F9F7F7F7F7F4F4F4F4F2F2F2F2F4F4F4F4
 F3F3F3F3F4F4F4F4EAEAEAEAE1E1E1E1D9D9D9D9D6D6D6D6D1D1D1D1D0D0D0D0D1D1D1D1
 CDCDCDCDCFCFCFCFD0D0D0D0D0D0D0D0CECECECECBCBCBCBCCCCCCCCCDCDCDCDCDCDCDCD
 CECECECECECECECECFCFCFCFD0D0D0D0D0D0D0D0D1D1D1D1CFCFCFCFCFCFCFCFD0D0D0D0
 D0D0D0D0D0D0D0D0CFCFCFCFCFCFCFCFD1D1D1D1D1D1D1D1D0D0D0D0D1D1D1D1D1D1D1D1
 E5E5E5E5E2E2E2E2E1E1E1E1DFDFDFDFE0E0E0E0E2E2E2E2E2E2E2E2E6E6E6E6E7E7E7E7
 E7E7E7E7EFEFEFEFF1F1F1F1F3F3F3F3E6E6E6E637373737373737373737373737373737
 37373737373737373737373737373737B6B6B6B6F9F9F9F9F7F7F7F7F4F4F4F4F2F2F2F2
 F4F4F4F4F3F3F3F3F4F4F4F4EAEAEAEAE1E1E1E1D9D9D9D9D6D6D6D6D1D1D1D1D0D0D0D0
 D1D1D1D1CDCDCDCDCFCFCFCFD0D0D0D0D0D0D0D0CECECECECBCBCBCBCCCCCCCCCDCDCDCD
 CDCDCDCDCECECECECECECECECFCFCFCFD0D0D0D0D0D0D0D0D1D1D1D1CFCFCFCFCFCFCFCF
 D0D0D0D0D0D0D0D0D0D0D0D0CFCFCFCFCFCFCFCFD1D1D1D1D1D1D1D1D0D0D0D0D1D1D1D1
 D1D1D1D1E5E5E5E5E2E2E2E2E1E1E1E1DFDFDFDFE0E0E0E0E2E2E2E2E2E2E2E2E6E6E6E6
 E7E7E7E7E7E7E7E7EFEFEFEFF1F1F1F1F3F3F3F3E6E6E6E6373737373737373737373737
 3737373737373737373737373737373737373737B6B6B6B6F9F9F9F9F7F7F7F7F4F4F4F4
 F2F2F2F2F4F4F4F4F3F3F3F3F4F4F4F4EAEAEAEAE1E1E1E1D9D9D9D9D6D6D6D6D1D1D1D1
 D0D0D0D0D1D1D1D1CDCDCDCDCFCFCFCFD0D0D0D0D0D0D0D0CECECECECBCBCBCBCCCCCCCC
 CDCDCDCDCDCDCDCDCECECECECECECECECFCFCFCFD0D0D0D0D0D0D0D0D1D1D1D1CFCFCFCF
 CFCFCFCFD0D0D0D0D0D0D0D0D0D0D0D0CFCFCFCFCFCFCFCFD1D1D1D1D1D1D1D1D0D0D0D0
 D1D1D1D1D1D1D1D1E5E5E5E5E2E2E2E2E1E1E1E1DFDFDFDFE0E0E0E0E2E2E2E2E2E2E2E2
 E6E6E6E6E7E7E7E7E7E7E7E7EFEFEFEFF1F1F1F1F3F3F3F3E6E6E6E63737373737373737
 373737373737373737373737373737373737373737373737F5F5F5F5FAFAFAFAF8F8F8F8
 F5F5F5F5F2F2F2F2F4F4F4F4F4F4F4F4F3F3F3F3DEDEDEDEDADADADAD6D6D6D6D5D5D5D5
 D2D2D2D2D1D1D1D1D1D1D1D1CECECECED0D0D0D0D0D0D0D0D0D0D0D0CFCFCFCFCBCBCBCB
 CDCDCDCDCCCCCCCCCDCDCDCDCECECECECECECECECECECECED0D0D0D0D1D1D1D1D2D2D2D2
 D1D1D1D1D0D0D0D0D1D1D1D1D2D2D2D2D4D4D4D4D2D2D2D2D2D2D2D2D6D6D6D6DADADADA
 DADADADAD7D7D7D7D4D4D4D4DFDFDFDFE8E8E8E8EAEAEAEAE3E3E3E3E4E4E4E4E6E6E6E6
 F3F3F3F3EFEFEFEFEEEEEEEEE8E8E8E8DFDFDFDFE8E8E8E8EDEDEDEDECECECEC37373737
 37373737373737373737373737373737373737373737373737373737F5F5F5F5FAFAFAFA
 F8F8F8F8F5F5F5F5F2F2F2F2F4F4F4F4F4F4F4F4F3F3F3F3DEDEDEDEDADADADAD6D6D6D6
 D5D5D5D5D2D2D2D2D1D1D1D1D1D1D1D1CECECECED0D0D0D0D0D0D0D0D0D0D0D0CFCFCFCF
 CBCBCBCBCDCDCDCDCCCCCCCCCDCDCDCDCECECECECECECECECECECECED0D0D0D0D1D1D1D1
 D2D2D2D2D1D1D1D1D0D0D0D0D1D1D1D1D2D2D2D2D4D4D4D4D2D2D2D2D2D2D2D2D6D6D6D6
 DADADADADADADADAD7D7D7D7D4D4D4D4DFDFDFDFE8E8E8E8EAEAEAEAE3E3E3E3E4E4E4E4
 E6E6E6E6F3F3F3F3EFEFEFEFEEEEEEEEE8E8E8E8DFDFDFDFE8E8E8E8EDEDEDEDECECECEC
 3737373737373737373737373737373737373737373737373737373737373737F5F5F5F5
 FAFAFAFAF8F8F8F8F5F5F5F5F2F2F2F2F4F4F4F4F4F4F4F4F3F3F3F3DEDEDEDEDADADADA
 D6D6D6D6D5D5D5D5D2D2D2D2D1D1D1D1D1D1D1D1CECECECED0D0D0D0D0D0D0D0D0D0D0D0
 CFCFCFCFCBCBCBCBCDCDCDCDCCCCCCCCCDCDCDCDCECECECECECECECECECECECED0D0D0D0
 D1D1D1D1D2D2D2D2D1D1D1D1D0D0D0D0D1D1D1D1D2D2D2D2D4D4D4D4D2D2D2D2D2D2D2D2
 D6D6D6D6DADADADADADADADAD7D7D7D7D4D4D4D4DFDFDFDFE8E8E8E8EAEAEAEAE3E3E3E3
 E4E4E4E4E6E6E6E6F3F3F3F3EFEFEFEFEEEEEEEEE8E8E8E8DFDFDFDFE8E8E8E8EDEDEDED
 ECECECEC3737373737373737373737373737373737373737373737373737373737373737
 F5F5F5F5FAFAFAFAF8F8F8F8F5F5F5F5F2F2F2F2F4F4F4F4F4F4F4F4F3F3F3F3DEDEDEDE
 DADADADAD6D6D6D6D5D5D5D5D2D2D2D2D1D1D1D1D1D1D1D1CECECECED0D0D0D0D0D0D0D0
 D0D0D0D0CFCFCFCFCBCBCBCBCDCDCDCDCCCCCCCCCDCDCDCDCECECECECECECECECECECECE
 D0D0D0D0D1D1D1D1D2D2D2D2D1D1D1D1D0D0D0D0D1D1D1D1D2D2D2D2D4D4D4D4D2D2D2D2
 D2D2D2D2D6D6D6D6DADADADADADADADAD7D7D7D7D4D4D4D4DFDFDFDFE8E8E8E8EAEAEAEA
 E3E3E3E3E4E4E4E4E6E6E6E6F3F3F3F3EFEFEFEFEEEEEEEEE8E8E8E8DFDFDFDFE8E8E8E8
 EDEDEDEDECECECEC37373737373737373737373737373737373737373737373737373737
 37373737E5E5E5E5F6F6F6F6EFEFEFEFEDEDEDEDF1F1F1F1F2F2F2F2F3F3F3F3F3F3F3F3
 DEDEDEDEDDDDDDDDDCDCDCDCD9D9D9D9D8D8D8D8D4D4D4D4D5D5D5D5D1D1D1D1D5D5D5D5
 D6D6D6D6D2D2D2D2D2D2D2D2D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1
 D1D1D1D1D2D2D2D2D2D2D2D2D3D3D3D3D2D2D2D2D2D2D2D2D3D3D3D3D7D7D7D7D9D9D9D9
 D7D7D7D7D6D6D6D6DCDCDCDCDEDEDEDEDDDDDDDDDBDBDBDBD6D6D6D6E5E5E5E5EDEDEDED
 E6E6E6E6E4E4E4E4E5E5E5E5E7E7E7E7E6E6E6E6ECECECECECECECECEAEAEAEAEAEAEAEA
 EEEEEEEEF0F0F0F0F2F2F2F2373737373737373737373737373737373737373737373737
 3737373737373737E5E5E5E5F6F6F6F6EFEFEFEFEDEDEDEDF1F1F1F1F2F2F2F2F3F3F3F3
 F3F3F3F3DEDEDEDEDDDDDDDDDCDCDCDCD9D9D9D9D8D8D8D8D4D4D4D4D5D5D5D5D1D1D1D1
 D5D5D5D5D6D6D6D6D2D2D2D2D2D2D2D2D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1D1D1D1D1
 D1D1D1D1D1D1D1D1D2D2D2D2D2D2D2D2D3D3D3D3D2D2D2D2D2D2D2D2D3D3D3D3D7D7D7D7
 D9D9D9D9D7D7D7D7D6D6D6D6DCDCDCDCDEDEDEDEDDDDDDDDDBDBDBDBD6D6D6D6E5E5E5E5
 EDEDEDEDE6E6E6E6E4E4E4E4E5E5E5E5E7E7E7E7E6E6E6E6ECECECECECECECECEAEAEAEA
 EAEAEAEAEEEEEEEEF0F0F0F0F2F2F2F23737373737373737373737373737373737373737
 373737373737373737373737E5E5E5E5F6F6F6F6EFEFEFEFEDEDEDEDF1F1F1F1F2F2F2F2
 F3F3F3F3F3F3F3F3DEDEDEDEDDDDDDDDDCDCDCDCD9D9D9D9D8D8D8D8D4D4D4D4D5D5D5D5
 D1D1D1D1D5D5D5D5D6D6D6D6D2D2D2D2D2D2D2D2D1D1D1D1D2D2D2D2D1D1D1D1D1D1D1D1
 D1D1D1D1D1D1D1D1D1D1D1D1D2D2D2D2D2D2D2D2D3D3D3D3D2D2D2D2D2D2D2D2D3D3D3D3
 D7D7D7D7D9D9D9D9D7D7D7D7D6D6D6D6DCDCDCDCDEDEDEDEDDDDDDDDDBDBDBDBD6D6D6D6
 E5E5E5E5EDEDEDEDE6E6E6E6E4E4E4E4E5E5E5E5E7E7E7E7E6E6E6E6ECECECECECECECEC
 EAEAEAEAEAEAEAEAEEEEEEEEF0F0F0F0F2F2F2F237373737373737373737373737373737
 37373737373737373737373737373737E5E5E5E5F6F6F6F6EFEFEFEFEDEDEDEDF1F1F1F1
 F2F2F2F2F3F3F3F3F3F3F3F3DEDEDEDEDDDDDDDDDCDCDCDCD9D9D9D9D8D8D8D8D4D4D4D4
 D5D5D5D5D1D1D1D1D5D5D5D5D6D6D6D6D2D2D2D2D2D2D2D2D1D1D1D1D2D2D2D2D1D1D1D1
 D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D2D2D2D2D2D2D2D2D3D3D3D3D2D2D2D2D2D2D2D2
 D3D3D3D3D7D7D7D7D9D9D9D9D7D7D7D7D6D6D6D6DCDCDCDCDEDEDEDEDDDDDDDDDBDBDBDB
 D6D6D6D6E5E5E5E5EDEDEDEDE6E6E6E6E4E4E4E4E5E5E5E5E7E7E7E7E6E6E6E6ECECECEC
 ECECECECEAEAEAEAEAEAEAEAEEEEEEEEF0F0F0F0F2F2F2F2373737373737373737373737
 3737373737373737373737373737373737373737D0D0D0D0F8F8F8F8EEEEEEEEEFEFEFEF
 F2F2F2F2F1F1F1F1F3F3F3F3F2F2F2F2DADADADADBDBDBDBDADADADAD9D9D9D9DCDCDCDC
 D6D6D6D6D6D6D6D6D8D8D8D8DDDDDDDDDEDEDEDED2D2D2D2D2D2D2D2D1D1D1D1D2D2D2D2
 D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D2D2D2D2D3D3D3D3D2D2D2D2
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 37373737373737373737373737373737373737373737373737373737D0D0D0D0F8F8F8F8
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0)
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>

<Row,"Row">

<Cell>

<"CellBody">

(c) quantized flow (pixel brightness <SR>
indicates image motion magnitude)
<Cell>

<"CellBody">

(d) interpolated flow
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB> 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>An example of the optical flow output of this algorithm is shown in Figure 6. The top <SR>
part of this figure shows two 256x256 pixel images, spaced ten images apart, of a typical <SR>
image sequence resulting from a robot's own forward motion. The bottom of this figure <SR>
shows grey-level images indicating the magnitude of the optical flow vectors at each point; <SR>
brighter pixels correspond to faster motion. Figure 6 (c) shows the output of the quantized <SR>
optical flow algorithm on these ten images (subsampled to 64x64 pixels in size). This can <SR>
be compared to the results of the interpolated optical flow algorithm, seen in Figure 6 (d). <SR>
The quantized optical flow field (Figure 6 (c)) contains a total of only 19 discrete motion <SR>
magnitudes, whereas the interpolated optical flow field (Figure 6 (d)) yields a continuously-valued flow field, which, when qua<SR>
ntized to 8-bits for display, contains 144 separate <SR>
motion magnitudes. Although the original quantization boundaries are still visible in many <SR>
places, this interpolated optical flow algorithm represents a greatly improved motion vector resolution over the quantized opti<SR>
cal flow algorithm and will prove sufficient for our <SR>
purposes. Also, note that in both cases the flow estimates are dense even on the relatively <SR>
weakly-textured laboratory floor.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>When compared to computing flow without interpolation, the use of two one-dimensional interpolations cuts the frame rate appro<SR>
ximately in half: real-valued optical flow can <SR>
be computed on 32x64 images, calculating and interpolating 5 speeds per frame, at 17 <SR>
frames per second on an 80 MHz Themis HyperSPARC 10 computer. In our obstacle- <SR>
avoidance application, the flow is run at only about 4 Hz. This consumes from 20-25% of <SR>
the processor's total time and allows the entire obstacle avoidance system to run comfortably on a single workstation with a co<SR>
nsistent frame rate and about a 20% processor idle <SR>
time to buffer unexpected operating system events.

<"section",
        Font =           F3@Lam,
        Line Spacing =   1.750 lines>

<F13>3<TAB>Spherical Pinhole Camera Model <F3@Lam>


<"body",
        Bottom Margin =  0.000 inches,
        Line Spacing =   1.750 lines>

<TAB><TAB>Most authors assume a simple planar pinhole camera model in deriving equations. We <SR>
will argue that the 
<"body",
        Line Spacing =   1.750 lines>

<TAB> wide-angle camera used in our system more closely approximates <SR>
a spherical pinhole camera model than the traditional planar pinhole model. The local area <SR>
at any point 
<"body",
        Line Spacing =   1.750 lines>

<TAB> on the spherical imaging surface can be approximated by a tangent planar surface with 
<"body",
        Line Spacing =   1.750 lines>

<TAB> at the tangent point. In the next section, we will exploit this <SR>
observation to use properties of image flow divergence which hold at 
<"body",
        Line Spacing =   1.750 lines>

<TAB> in a <SR>
planar pinhole imaging model. This tangent planar surface approximation extends the results for 
<"body",
        Line Spacing =   1.750 lines>

<TAB> in a planar pinhole coordinate system to all points 
<"body",
        Line Spacing =   1.750 lines>

<TAB> in a spherical pinhole coordinate system, as long as all calculations performed are limited to a local <SR>
area around the given 
<"body",
        Line Spacing =   1.750 lines>

<TAB>.    

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 7 <Ref, Page #, Tag = "27754">  Wide-angle Optics <F3@Lam>



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(a) Actual wide-angle image.
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(b) Same image warped to a planar image <SR>
assuming that the wide-angle camera <SR>
approximates a spherical pinhole camera <SR>
model. 
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<"body",
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<TAB><TAB>An image from the 
<"body",
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<TAB> wide-angle camera appears in Figure 7 (a). This image is visibly distorted, as expected with a wide-angle camera. To show that<SR>
 the wide-angle camera <SR>
more closely approximates a spherical pinhole camera model, we warp the wide-angle image into a planar pinhole camera image und<SR>
er the spherical pinhole camera assumption. If <SR>
this assumption is true, the warped image should appear relatively flat and undistorted. 

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<F13>Figure 8 <Ref, Page #, Tag = "16492">  Spherical projection camera model <F3@Lam>



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<Cell>

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<Cell>

<"CellBody">

(a) Above left: warping a spherical <SR>
pinhole camera retina to a planar pinhole camera retina as a function of <SR>
equal angle from the center of projection 
<Cell>

<"CellBody">

(b) Above right: uniformly mapping <SR>
a spherical pinhole camera image to <SR>
a flat image as a function of equal <SR>
linear distance from the center of the <SR>
imaging surface 
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB>

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>There are two steps to this process. First, we transform a spherical pinhole camera retina into a planar pinhole camera retina<SR>
, <F14@Lam>i.e.<F3@Lam>, we warp an image created from a spherical <SR>
pinhole camera into an equivalent image as it would appear if it were created from a traditional planar pinhole camera; this is<SR>
 shown in Figure 8 (a). However, we are not given <SR>
true spherical retinas as imaging surfaces. We are given flat, distorted images. Thus, prior <SR>
to this transformation, we must convert the flat, distorted image into its equivalent spherical retinal representation, as show<SR>
n in Figure 8 (b). Note that this latter mapping is uniform and is equivalent to simply rolling" a flat planar representation o<SR>
nto a spherical retina. Thus, the complete sequence involved to map a spherical pinhole model image (presented in the form of a <SR>
flat, distorted image) is to take its spherical imaging surface <SR>
equivalent (shown in Figure 8 (b)) and map it to its planar imaging surface equivalent <SR>
(shown in Figure 8 (a))

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The result of this mapping/warping process on Figure 7 (a), using a focal length equivalent of 150 pixels (given an image widt<SR>
h of 256 pixels), results in Figure 7 (b), which is <SR>
clearly much less distorted than the former image. From experiments such as these, we <SR>
conclude that our 115-degree wide-angle camera is better approximated by a spherical pinhole camera model than a more tradition<SR>
al planar pinhole camera model. As described previously, this fact is exploited in the next section. 

<"section",
        Font =           F3@Lam,
        Line Spacing =   1.750 lines>

<F13>4<TAB>Divergence for Obstacle Avoidance<F3@Lam>


<"body",
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<TAB><TAB>Process 2 (Figure 1) computes flow divergence. Divergence of flow can be used to estimate time-to-contact (<F14@Lam>T<F14@B@Lam>c<F3@B@Lam><F3@Lam>). Both theory an<SR>
d implementation are discussed here as well as <SR>
considerations for employing 
<"body",
        Line Spacing =   1.750 lines>

<TAB> for obstacle detection by a moving robot.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The equations for the 
<"body",
        Line Spacing =   1.750 lines>

<TAB> and 
<"body",
        Line Spacing =   1.750 lines>

<TAB> components of optical flow 
<"body",
        Line Spacing =   1.750 lines>

<TAB> due to general <SR>
camera motion (arbitrary translation and rotation) in a stationary environment given a planar projection coordinate system are 

<"equation">

<TAB><F2@Lam><TAB>(2)
<"equation">

<TAB> 

<"equation">

<TAB><TAB>(3)
<"equation">

<TAB>

<"body",
        Line Spacing =   1.750 lines>

<TAB><F3@Lam><TAB>where 
<"body",
        Line Spacing =   1.750 lines>

<TAB> is the depth of the object in the environment relative to the camera, and <SR>

<"body",
        Line Spacing =   1.750 lines>

<TAB> and 
<"body",
        Line Spacing =   1.750 lines>

<TAB> are the translational and rotational motion of the environment relative to the camera [35]. This camera frame is a right-hande<SR>
d coordinate system <SR>
centered behind the image plane with the positive<F14@Lam><F14@Lam> <F3@Lam><F14@Lam><F14@Lam>X<F3@Lam><F14@Lam><F14@Lam> <F3@Lam>direction extending leftward, positive <F14@Lam><F14@Lam> <F3@Lam> <SR>
<F14@Lam><F14@Lam>Y<F3@Lam> upward, and positive <F14@Lam><F14@Lam>Z<F3@Lam> forward. The divergence of an optical flow field (parameterized <SR>
by image coordinates 
<"body",
        Line Spacing =   1.750 lines>

<TAB> is defined as: 

<"equation">

<TAB><F2@Lam><TAB>(4)<Ref, Page #, Tag = "67406">
<"equation">

<TAB>.

<"Body">

Note that 

<"equation">

<TAB><F2@Lam><TAB>(5)
<"equation">

<TAB>

<"equation">

<TAB><TAB>(6)<Ref, Page #, Tag = "97341">
<"equation">

<TAB>

<"Body">

where 
<"Body">

 = 
<"Body">

. From equations (4) through (6), at 
<"Body">

:

<"equation">

<TAB><F2@Lam><TAB>(7)<Ref, Page #, Tag = "15540">
<"equation">

<TAB>.

<"body",
        Line Spacing =   1.750 lines>

<TAB><F3@Lam>This can be rewritten in terms of the gradient 
<"body",
        Line Spacing =   1.750 lines>

<TAB> as 

<"equation">

<TAB><F2@Lam><TAB>(8)
<"equation">

<TAB> <Index, "equation 8">

<"equation">

<TAB><TAB>(9)<Ref, Page #, Tag = "22940">
<"equation">

<TAB> 

<"Body">

where 
<"Body">

 is the surface gradient [10]. As stated, this equation holds for a <SR>
<F14@Lam>planar<F3@Lam> coordinate system at 
<"Body">

. Because we are modeling our wide-angle <SR>
camera using a spherical coordinate system, the spherical imaging surface at every point <SR>

<"Body">

 can be approximated by a tangent planar surface with 
<"Body">

 in that tangent <SR>
plane's local coordinate system. A precise derivation of the consequences of this assumption is future work. The local <F14@Lam><F14@Lam>Z<F3@Lam> axis i<SR>
s the ray through the point 
<"Body">

. Equation (9) now <SR>
holds for every point in the image of the wide-angle camera that is well-approximated by <SR>
a spherical pinhole camera model. From equation (9), 

<"equation">

<TAB><F2@Lam><TAB>(10)<Ref, Page #, Tag = "46696">
<"equation">

<TAB>

<"Body">

whenever the imaged surface is perpendicular to the local <F14@Lam>Z<F3@Lam> axis, or<F14@Lam> <F3@Lam>the gradient of the <SR>
surface, 
<"Body">

, is perpendicular to the transverse velocity 
<"Body">

, or the transverse velocity <SR>
is zero. 

<"Body">

As will be explained below, we use relatively large image masks for computing divergence. In our lab experiments, these masks, w<SR>
hen projected out into the 3-D scene, usually cover a scene area 1 to 4 square meters. There are often many surfaces, at differe<SR>
nt <SR>
orientations, in such an area in our scenes. We believe that when the surface gradients, expressed in the local camera coordina<SR>
te system, are averaged in such an area, the average <SR>
gradient tends to be very small. Given two (nearly planar) surface segments of the same <SR>
size in 3-D space, the segment with large gradient (i.e., steep slope in the local coordinate <SR>
system) will project into a much smaller area of the image than the segment with small <SR>
gradient (i.e., which is nearly perpendicular to the line of sight). Therefore, surfaces with <SR>
small gradients should tend to contribute more to the average surface gradient" within <SR>
the mask area than surfaces with large gradients. Because of these effects, the first term in <SR>
the right-hand-side of equation (9) usually dominates the second term. For surfaces near <SR>
the direction of motion, 
<"Body">

 is small. This further reinforces the domination of the <SR>
first term.Therefore, we can estimate time-to-contact directly from equation (10).

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Divergence is a particularly useful measure for obstacle avoidance during visual navigation because it is invariant under the <SR>
rotational motion of the sensor that is inevitable <SR>
due to imperfect stabilization. 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 9 <Ref, Page #, Tag = "40488">  Flow divergence templates <F3@Lam>



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<Row,"Row">

<Cell>

<"CellBody">

(a) 
<Cell>

<"CellBody">

(b) 
<Cell>

<"CellBody">

(c) 
<Cell>

<"CellBody">

(d) 
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB>

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Equation (10) suggests that <F14@Lam>divergence <F3@Lam>has only time as its dimension. The values of <SR>
<F14@Lam>divergence <F3@Lam>over any significant area represent the inverse of time-to-contact, i.e., the time <SR>
needed to reach an object at depth 
<"body",
        Line Spacing =   1.750 lines>

<TAB> with velocity 
<"body",
        Line Spacing =   1.750 lines>

<TAB> in the 
<"body",
        Line Spacing =   1.750 lines>

<TAB> direction. A family of simple fixed flow divergence templates can be applied to any image sequence to estimate divergence [28]<SR>
. Each template is symmetrically divided into positive and negative halves <SR>
(Figure 9). Flow divergence is calculated by convolving the template with a window in the <SR>
flow image and computing the sum of the optical flow derivatives in perpendicular directions. In particular, the convolution of<SR>
 the first two such templates may be performed extremely quickly using a <F14@Lam><F14@Lam>box filter <F3@Lam>as described in [7][8]. In order to improve <SR>
the consistency of the divergence estimates, we apply temporal and spatial median filters to the individual divergence values (p<SR>
rocess 3 in Figure 1).

<"section",
        Font =           F3@Lam,
        Line Spacing =   1.750 lines>

<F13>5<TAB>Simple Robust Filters<F3@Lam>


<"body",
        Bottom Margin =  0.000 inches,
        Line Spacing =   1.750 lines>

<TAB><TAB>Median filtering performed on dense two-dimensional data can use fast running-histogram methods such as in [19] if the dynamic<SR>
 range of the data and desired quantization <SR>
resolution of the median value can be specified. The algorithm described in [19] was intended for finding the true median and r<SR>
educes an <F14@Lam><F14@Lam>O(nm)<F3@Lam> complexity algorithm to approximately <F14@Lam><F14@Lam>O(n)<F3@Lam> per pixel for an 
<"body",
        Line Spacing =   1.750 lines>

<TAB> filtering window, where 
<"body",
        Line Spacing =   1.750 lines>

<TAB>. It can, however, be <SR>
generalized to the separable median [26] which approximates a two-dimensional true median filter by the successive application <SR>
of two orthogonal one-dimensional median filters: <SR>
first the median of each row of a two-dimensional window is computed, and then, the median of these row-medians is returned as <SR>
the separable median. This transformation reduces the time complexity from <F14@Lam><F14@Lam>O(n)<F3@Lam> for the running-histogram method alone to approx<SR>
imately constant time for the combined method. To the authors' knowledge, this is the first time <SR>
that this combined, approximately constant time median filtering algorithm has been used <SR>
in image analysis. Because of this, its utility will be explored further.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Exploiting this combined approach assumes that there are only a limited number of <SR>
histogram bins, which would not be the case with floating-point data. In that case one <SR>
could modify the algorithm to first quantize the data into a histogram of 256 bins (for example). The true median could then be<SR>
 found by performing a quicksort-partitioning [30] <SR>
on that bin which contains the midpoint of the histogram for that pixel's local window. In <SR>
our case, however, the divergence data are already quantized to 8-bit values (necessary in <SR>
order to reduce the data bandwidth in the previous system's implementation [11]) so this <SR>
extension is not necessary.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Although the separable median filter is not guaranteed to find true median values, it <SR>
reduces noise almost as well as a true median filter [26]. By definition, the true median is <SR>
greater than or equal to half the data in the data set and less than or equal to the other half <SR>
of the data. The separable median, however, is greater than or equal to all points less than <SR>
or equal to those row-medians which are less than or equal to the separable median. By <SR>
definition, the separable median is greater than or equal to 50% of the row medians, therefore, the separable median is greater<SR>
 than or equal to 25% of the data. Similarly, the separable median is guaranteed to be less than or equal to 25% of the data. It<SR>
s relationship to <SR>
the rest of the data is unknown.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The breakpoint" of an estimator is defined as the smallest fraction (or percent) of contamination of a data set that can resu<SR>
lt in an arbitrarily incorrect value [32]. In the case of <SR>
least-sum-of-squares (a non-robust estimator), that percent tends to 0% for large 
<"body",
        Line Spacing =   1.750 lines>

<TAB> (i.e., a <SR>
single outlier can cause an arbitrarily incorrect result). In the case of the true median filter, <SR>
that percent is 50%. In the case of the separable median filter, that percent is 25%, given <SR>
our arguments above. Although this means that the separable median filter is not as robust <SR>
as the true median filter, it still performs extremely well in most cases.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The current system first performs an 
<"body",
        Line Spacing =   1.750 lines>

<TAB> (height by width) spatial median filter <SR>
on the divergence estimates (The filter's proportions roughly paralleled the proportions of <SR>
the 
<"body",
        Line Spacing =   1.750 lines>

<TAB> image field). Because our robot operates in a 2-D world (<F14@Lam>i.e.,<F3@Lam> its motion is <SR>
constrained to two degrees of freedom: speed and steering), we use the 
<"body",
        Line Spacing =   1.750 lines>

<TAB> filter to <SR>
produce a single horizontal array of divergence values, which is centered on the middle <SR>
row of each image. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The 1-D divergence arrays are stored in a history buffer of 1-D arrays of spatially-filtered divergence estimates. The dimensi<SR>
ons of the temporal filter are 11 pixels in space <SR>
(horizontally within each array) and 11 frames in time (across arrays). Because of the temporal median filter's width, the filt<SR>
ered divergence information has a latency of 5 frames <SR>
or about 1.25 seconds. This effect is offset, however, by the ability of the system to sense <SR>
obstacles at a range of up to several meters. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Both the separable and true median filters have the desirable property of preserving <SR>
horizontally and vertically aligned edges. This means that unlike many other averaging or <SR>
smoothing filters, these filters have no temporal hysteresis. Unlike the true median filter, <SR>
however, the separable median filter has the additional desirable property of preserving <SR>
corners [26]. Preserving corners can be advantageous in ordinary image processing but is <SR>
especially valuable in our application, because an erosion of an object's full spatial or temporal extent could create the illu<SR>
sion of an open space and cause a collision. This corner <SR>
preservation can also prevent distinct objects from blurring together [29], which could be <SR>
equally undesirable because some valid pathways may otherwise falsely appear to be <SR>
blocked.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>When performing the separable temporal median filter, the order of the two 1-D median operations can make a difference in some<SR>
 cases [29]. By performing the spatial 1-D <SR>
median filter first, we slightly emphasize spatial coherence over temporal continuity.

<"section",
        Font =           F3@Lam,
        Line Spacing =   1.750 lines>

<F13>6<TAB><Ref, Page #, Tag = "16151">Driving Control<F3@Lam>


<"body",
        Bottom Margin =  0.000 inches,
        Line Spacing =   1.750 lines>

<TAB><TAB>Processes 4 and 5 (Figure 1) control driving and gaze. The robot's task is to avoid obstacles while achieving mobility goals. <SR>
In general, such goals might be specified by coordinates in a map, features that uniquely identify a location, or simply feature<SR>
s that satisfy <SR>
a precondition required for the next subtask (<F14@Lam>e.g.<F3@Lam>, the mobility goal might be positioning <SR>
the robot to pick up an object.) Ideally, the robot would survey the visual data to identify <SR>
the direction nearest its desired path that is also a safe direction in which to travel. 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 10 <Ref, Page #, Tag = "29240">  Body control automaton <F3@Lam>



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halt signal 


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or 


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communications 


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time-out

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turn 


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away

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halt

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<TAB><TAB>In these experiments, the goal is to maneuver without collision using only flow divergence to sense the environment. The robot<SR>
's behavioral goal is simply to drive forward, <SR>
steering away from obstacles in its path, and to stop and turn when it senses that collision <SR>
is imminent. The robot drives at up to 20 cm/s. Speed is regulated to keep visual data (<F14@Lam><F14@Lam>i.e.<F3@Lam>, <SR>
flow and divergence estimates) within measurable ranges and to avoid detrimental behavior that results when high rates of speed<SR>
 and steering occur simultaneously. The steering <SR>
policy uses the sensed flow divergences to steer around obstacles while attempting to steer <SR>
toward the provided goal direction. (In these experiments, the goal direction was always <SR>
straight ahead for simplicity.) Indication of imminent collision in the central quarter of the <SR>
camera's divergence data causes the robot to stop, turn away and resume wandering. This <SR>
sequencing is implemented with a finite state automaton, with a command associated with <SR>
each state (Figure 10). Some state transitions are triggered by sensed events, and others <SR>
merely provide command sequencing. For instance, the system remains in the refractory <SR>
state until visual motion lingering from the brisk turn is no longer seen by the visual system. An interesting consequence of t<SR>
his behavior is that the robot in the refractory state <SR>
will remain still while a person moves in its view. 

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<F13>Figure 11 <Ref, Page #, Tag = "29048">  Trace of Robot's View <F3@Lam>



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<"CellBody">

(b)   Trace of <SR>
median-filtered <SR>
flow divergence <SR>
maps (brighter <SR>
intensity indicates larger <SR>
divergence).
<Cell>

<"CellBody">

(c)   Trace of <SR>
hazard maps <SR>
with selected <SR>
goal direction <SR>
highlighted in <SR>
white.
<Cell>

<"CellBody">

(d)   XY path trace beginning at (0,0).
<End Table>

<"body",
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<TAB> 

<"body",
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<TAB><TAB>The robot steering and collision detection improve when the robot turns relatively <SR>
slowly for two reasons: (1) temporal consistency of the spatial locus of samples for divergence estimation is improved, and (2)<SR>
 accuracy of motion estimates themselves is improved. Therefore, the behavior and motor control systems are designed to reduce r<SR>
otation <SR>
of the cameras. This is accomplished by stabilizing the cameras with active motor commands and by limiting rotation of the body<SR>
 so the gaze stabilization system is not overstressed. Despite these precautions, gaze stabilization is imperfect and some data <SR>
are contaminated. However, the edge-preserving spatio-temporal median filtering effectively discards intermittent unusable data

<"body",
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<TAB><TAB>The steering policy is implemented using hazard maps derived from flow divergence, <SR>
the desired goal direction, and the target heading 
<"body",
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<TAB>that was previously selected by the <SR>
steering policy. Each hazard map is a 1-dimensional horizontal array that encodes the <SR>
risk" associated with each possible steering direction. Traces of median-filtered flow divergence maps and composite hazard ma<SR>
ps are shown in Figure 11 (b) and (c). The target <SR>
heading selected in each hazard map is highlighted in white. The path of the robot in this <SR>
trial appears in (d) for the gauntlet of office chairs seen in (a) from the robot's viewpoint <SR>
before the trial began. 

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<TAB><TAB>A hazard map is derived from the divergence map. During each steering control cycle <SR>
it encodes not only the present divergence data, but also the past steering choices of the <SR>
robot to help the robot commit to passing an obstacle on one side without switching back <SR>
and forth. The hazard map is a 64-element wide map per sample interval that indicates obstacles and also encodes the cost of cr<SR>
ossing local maxima in the divergence map, starting <SR>
from the previously selected heading. Imagine the divergence map as a cross-section of a <SR>
topographic map, such as the divergence map trace of Figure 11(b). Obstacles are indicated by hills and open spaces by valleys.<SR>
 In the previous cycle, the steering policy selected <SR>
a heading value and committed to one of the valleys in the divergence map. In the present <SR>
cycle, a different valley may appear deeper, but the cost of changing course to pass on the <SR>
other side of an obstacle that has not yet been cleared is represented by the cost of crossing <SR>
the hill to reach the valley on the other side.

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<TAB><TAB>Similarly, another hazard map is derived from the desired goal direction and the previously selected heading (accounting for t<SR>
he gaze angle). This map appears roughly as a <SR>
shallow trough centered midway between the previously selected heading and the goal <SR>
heading, which has the effect of drawing the selected heading back to the goal direction in <SR>
the absence of obstacles in this path. 

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<TAB><TAB>These hazard maps are combined into a single hazard map by summing the component <SR>
hazard maps. The steering policy chooses the direction of minimum hazard in the composite hazard map, with a preference for dir<SR>
ections nearest the previously selected heading in <SR>
case of a tie. The result in general is that if <F14@Lam>any<F3@Lam> sensing mode shows strong evidence of <SR>
danger in some direction, it is unlikely that direction will be chosen. 

<"body",
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<TAB><TAB>Summarizing, the image-based heading 
<"body",
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<TAB> is a heading angle in image space, the gaze <SR>
angle 
<"body",
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<TAB> is relative to the robot's current heading 
<"body",
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<TAB>, and from these the new target heading <SR>

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<TAB> is calculated. 

<"equation">

<TAB><F2@Lam><TAB>(11)
<"equation">

<TAB>

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<TAB><F3@Lam><TAB>When a new desired heading 
<"body",
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<TAB> is chosen, the robot steers smoothly to it with saturated <SR>
negative feedback controls [13]. Desired change in heading, 
<"body",
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<TAB>, is simply the difference <SR>
between the desired heading and current heading.

<"equation">

<TAB><F2@Lam><TAB>(12)
<"equation">

<TAB>

<"Body">

The steering control policy uses a saturated steering velocity proportional to the desired <SR>
heading.

<"equation">

<TAB><F2@Lam><TAB>(13)
<"equation">

<TAB>

<"Body">

The gain 
<"Body">

 (usually <<1) determines how quickly the steering is servoed to the desired <SR>
heading. Time is normalized to seconds by dividing by the body control cycle time, 
<"Body">

. <SR>
Thus angular velocity is expressed in degrees/s rather than degrees/cycle. For instance, <SR>
setting 
<"Body">

 will command a velocity that would reduce the error by 30% in the next <SR>
control cycle (assuming nearly instantaneous acceleration of the steering motor). The angular velocity is saturated at 
<"Body">

 <F14@Lam><F14@Lam>deg/s<F3@Lam> (<F14@Lam><F14@Lam>e.g.<F3@Lam>, 6 <F14@Lam><F14@Lam>deg/s<F3@Lam>) to limit the peak rotation rate to reasonable levels. There are three reasons for this limit. First, the <SR>
latency of robot command <SR>
execution is quite large, and the command cycle is not entirely uniform. Therefore, it is <SR>
possible to overshoot the desired heading if the rotational velocity is too high, because the <SR>
controller might not be able to stop steering at the right time. Second, motion estimation <SR>
suffers if the camera rotates too fast, because our computation of flow is based on a correlation method which limits motion to<SR>
 less than one pixel per frame. Poor flow measurements degrade divergence estimates. This impacts the quality of steering and st<SR>
opping. <SR>
Third, slower steering improves the temporal consistency of flow data for divergence estimation. Although the median filtering <SR>
is quite robust to disturbances, cleaner data produce smoother estimates over time. The second and third issues would be of no c<SR>
oncern if <SR>
gaze were perfectly stabilized, but stabilization is not perfect, and the residual camera rotation is correlated with the steer<SR>
ing rate. 

<"body",
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<TAB><TAB>Like steering, the robot's speed is regulated to maintain all systems within their operating ranges. The robot's top speed is <SR>
set at 20 cm/s based on empirical trials in showing <SR>
that divergence estimation was compromised at faster driving speeds when the robot <SR>
steered at the rates necessary to negotiate the lab. (The crash tests reported later in this paper were run at speeds up to 80 <SR>
cm/s, but these tests used no steering.) Impairment of divergence estimation was proportional to steering rate. Below the top sp<SR>
eed, the robot attempts to keep visual data within measurable ranges. Robot speed is increased when observed flows are too near <SR>
noise levels, and speed is decreased when flows are too large for <SR>
the estimation system to observe. Specifically, the speed is increased to keep the maximum <SR>
observed flow estimate above a set value (50% of the maximum flow estimate that can be <SR>
detected by the system). This ensures that most flows are large enough to be within the <SR>
operating range of the flow estimator. Similarly, robot speed is decreased when too many <SR>
flow estimates (50%) are saturated (have the maximum value the estimator can detect).

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<F13>7<TAB><Ref, Page #, Tag = "30806">Gaze Control <F3@Lam>

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<F13>Figure 12 <Ref, Page #, Tag = "34718">  Gaze control automaton <F3@Lam>



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body stops 


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to turn

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halt signal 


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or 


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communications 


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time-out

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halt

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center 


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gaze

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gaze angle 


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exceeds limit

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saccade and 


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stabilize

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stabilize 


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infinity

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init

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<F13> <F3@Lam>


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<TAB><TAB>The nonlinear gaze control is a <F14@Lam>nystagmus<F3@Lam>, a repetitive eye motion of slow phase rotations punctuated by quick phase rapid ret<SR>
urns. It is also implemented as a finite state automaton (Figure 12). The camera is rotated at velocity 
<"body",
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<TAB> to counter the body rotation and stabilize the camera images. The gaze control also checks the deviation of the <SR>
gaze angle, 
<"body",
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<TAB>, from the robot's heading and snaps the camera back to the heading if the <SR>
limit is exceeded (limit = 12<F3@T@Lam><F3@T@Lam>o<F3@Lam>). 

<"body",
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<TAB><TAB>The nystagmus quick phase that returns gaze to the vehicle's heading turns the gaze <SR>
beyond the current heading in the direction the robot is turning: <F2@Lam>
<"body",
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<TAB><F3@Lam>. This heuristic <SR>
attempts to reduce the number of quick phases required by putting gaze a little bit ahead <SR>
of the vehicle heading, rather than always lagging behind it<F2@Lam>. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><F3@Lam><TAB>The saccades that perform the quick-phase return to realign gaze with the robot's heading briefly produce extremely large opti<SR>
cal flows. These large flows often are encountered <SR>
by the flow estimator. Although the resulting divergence estimates are unusable, the edge- <SR>
preserving spatio-temporal median filtering effectively discards them, providing only the <SR>
divergences observed preceding and following the saccade. 

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<F13>8<TAB>Experiments and Results<F3@Lam>


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<TAB><TAB>Experiments with the obstacle avoidance system were performed in a laboratory containing office furniture, robot, and computin<SR>
g equipment. Furniture and equipment lined <SR>
the walls, and free space was roughly 7 m by 4 m in the center of the lab. Office chairs <SR>
provided obstacles. In addition, there was some space leading to doors in two corners of <SR>
the lab. In all experiments, a single camera with a 
<"body",
        Line Spacing =   1.750 lines>

<TAB> field of view was used. Only the <SR>
half height band in the center of the image was processed. (See Figure 11 (a) for an example of the robot's view of the lab.) T<SR>
hree sets of experiments were performed: (1) crash <SR>
tests" evaluated the system's ability to detect obstacles and warn of imminent collision; <SR>
(2) the robot was forced to run a gauntlet bristling with office chairs to evaluate its ability <SR>
to avoid obstacles while traveling through the room; (3) wandering trials tested the robot's <SR>
ability to move about for extended periods of time.

<"subsection",
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        Line Spacing =   1.166 lines>

<F13>8.1<TAB>Crash tests <F3@Lam>

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<F13>Figure 13 <Ref, Page #, Tag = "40657">  Frames from a 20 cm/s approach to chairs 4 meters distant <F3@Lam>



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(c) frame 60 
<Cell>

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(d) frame 70 
<End Table>



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<TAB><F3@Lam><TAB>Initial experiments tested the robot's ability to detect obstacles and warn of imminent <SR>
collision. To test the robot's ability to detect objects across the wide visual field, a row of <SR>
chairs was placed across the far end of the lab. The robot drove straight toward the chairs <SR>
at fixed speeds (see Figure 13). The system should not only detect obstacles at a reasonable <SR>
distance, but should also continue to detect obstacles as they are approached until they are <SR>
no longer visible in the bottom of the image. To evaluate this property, the robot did not <SR>
attempt to stop to avoid collision, but rather drove into the chairs until the bumper triggered the systems to shut down due to<SR>
 collision. 

<"FigureTableTitle",
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<F13>Figure 14 <Ref, Page #, Tag = "17173">  Frame 64 of a 20 cm/s approach to chairs 4 m distant <F3@Lam>



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(a) intensity frame 64: original 256x512 <SR>
pixel image, taken from a 
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 wide- <SR>
angle lens, subsampled to 128x256 pixels 
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(b) optical flow needle" plot: calculated <SR>
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original image, with the needle diagram <SR>
itself subsampled to 16x32 for clarity 
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0)
)
>

<Cell>

<Row,"Row">

<Cell>

<"CellBody">

(d) median-filtered divergence: the same <SR>
divergence plot but median filtered in <SR>
time (11 frames) as well as in space (11 <SR>
pixels). This filtered 1-D map of divergence estimates is used at each frame to <SR>
control the robot's steering. 
<Cell>

<"CellBody">

(c) divergence plot (top row is current): <SR>
time-space plot of the 1-D divergence <SR>
estimates, median-filtered in space <SR>
(11x17 pixel window centered on the <SR>
middle row of each image). Brighter <SR>
areas indicate higher divergence and thus <SR>
closer objects (automatically contrast- <SR>
adjusted for better clarity). 
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB> 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 15 <Ref, Page #, Tag = "40343">  Frame 49 of a 30 cm/s approach to chairs 4 m distant <F3@Lam>



<Table, "Table", 
        Columns = 2,
        Column 1 Width = 2.900 Inches ,
        Column 2 Width = 3.000 Inches >

<Master Row, "Row">

<Cell><"Table:Cell">

<Cell><"Table:Cell">
<Row,"Row">

<Cell>

<"CellBody">

(a) intensity frame 49 
<Cell>

<"CellBody">

(b) optical flow needle" plot 
<Row,"Row">

<Cell,
Straddle = 2>

<Frame,
       Placement = At Anchor,
       Width = 5.688 Inches,
       Height = 2.843 Inches,
       Size Contents to Width = Yes, 
       Size Contents to Height = Yes, 
       No Border = Yes,
       Diagram = 



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0)
)
>

<Cell>

<Row,"Row">

<Cell>

<"CellBody">

(d) median-filtered divergence 
<Cell>

<"CellBody">

(c) divergence plot (top row is current) 
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB> 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 16 <Ref, Page #, Tag = "20076">  Frame 36 of a 40 cm/s approach to chairs 4 m distant <F3@Lam>



<Table, "Table", 
        Columns = 2,
        Column 1 Width = 2.900 Inches ,
        Column 2 Width = 3.000 Inches >

<Master Row, "Row">

<Cell><"Table:Cell">

<Cell><"Table:Cell">
<Row,"Row">

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<"CellBody">

(a) intensity frame 36 
<Cell>

<"CellBody">

(b) optical flow needle" plot 
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<Cell,
Straddle = 2>

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       Width = 5.688 Inches,
       Height = 2.843 Inches,
       Size Contents to Width = Yes, 
       Size Contents to Height = Yes, 
       No Border = Yes,
       Diagram = 



V11,
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0)
)
>

<Cell>

<Row,"Row">

<Cell>

<"CellBody">

(d) median-filtered divergence 
<Cell>

<"CellBody">

(c) divergence plot (top row is current) 
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB> 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 17 <Ref, Page #, Tag = "39966">  Frame 30 of a 50 cm/s approach to chairs 4 m distant <F3@Lam>



<Table, "Table", 
        Columns = 2,
        Column 1 Width = 2.900 Inches ,
        Column 2 Width = 3.000 Inches >

<Master Row, "Row">

<Cell><"Table:Cell">

<Cell><"Table:Cell">
<Row,"Row">

<Cell>

<"CellBody">

(a) intensity frame 30 
<Cell>

<"CellBody">

(b) optical flow needle" plot 
<Row,"Row">

<Cell,
Straddle = 2>

<Frame,
       Placement = At Anchor,
       Width = 5.688 Inches,
       Height = 2.843 Inches,
       Size Contents to Width = Yes, 
       Size Contents to Height = Yes, 
       No Border = Yes,
       Diagram = 



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>

<Cell>

<Row,"Row">

<Cell>

<"CellBody">

(d) median-filtered divergence 
<Cell>

<"CellBody">

(c) divergence plot (top row is current) 
<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB> 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Examples are shown in Figure 14 (20 cm/s), Figure 15 (30 cm/s), Figure 16 (40 cm/s), <SR>
and Figure 17 (50 cm/s), all beginning at a distance of 4 m from the chairs. The upper left <SR>
quarter (a) of each frame is the original 256x512 pixel image, taken from a 
<"body",
        Line Spacing =   1.750 lines>

<TAB> wide- <SR>
angle lens, subsampled to 128x256 pixels. Results of processing the image are shown <SR>
clockwise (b-d). The upper right quarter (b) shows the optical flow needle" plot calculated from a 32x64 subsampled version of<SR>
 the original image with the needle diagram itself <SR>
subsampled to 16x32 for clarity. The lower right quarter (c) of each frame shows a time- <SR>
space plot of the 1-D divergence estimates, median-filtered in space (11x17 pixel window <SR>
centered on the middle row of each image) but not in time. In these plots, brighter areas <SR>
indicate higher divergence and thus closer objects (each individual plot is automatically <SR>
contrast-adjusted for better clarity). In these plots, time moves upward. Thus, the 1-D divergence map for the current frame is<SR>
 found at the top of the sub-image with the 31 previous frames displayed in addition. The lower left quarter (d) of each frame s<SR>
hows the same <SR>
divergence plot but median filtered in time (11 frames) as well as in space (11 pixels). The <SR>
second filtered 1-D map of divergence estimates is used at each frame to control the robot's steering. In the examples, the div<SR>
ergence due to imminent collision with the chairs <SR>
can be clearly seen. The divergence due to a nearby stepladder and some cables that were <SR>
suspended from the ceiling on the right side of the lab (visible in Figure 11 and Figure 13) <SR>
can also be seen in the history of the time-space divergence plots. Because of the temporal <SR>
median filter's width, the filtered divergence information has a latency of 5 frames or <SR>
about 1.25 seconds. As shown in the figures, however, this effect is offset by the ability of <SR>
the system to sense objects well in advance. 

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 18 <Ref, Page #, Tag = "32762">  Space collision threshold as a function of robot speed <F3@Lam>



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        Column 1 Width = 6.000 Inches >

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>

<End Table>

<"body",
        Line Spacing =   1.750 lines>

<TAB>

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The system is able to detect objects (at divergence estimates above the noise level) at <SR>
ranges up to 6 m (the maximum testable in the lab) at forward speeds ranging from 0.1 to <SR>
0.8 m/s. The divergence estimate arising from an object rises reasonably smoothly as the <SR>
object is approached, and the object continues to be visible until the robot is very near to <SR>
it. These results represent a considerable improvement in both range and persistence of detection over the results reported in <SR>
[11], in which objects were detected in the narrow range <SR>
of 1 to 2.5 m from the vehicle. Based on these trials, an imminent collision function was <SR>
derived for robot speeds up to 0.8 m/s (Figure 18). 

<"subsection",
        Font =           F3@Lam,
        Line Spacing =   1.166 lines>

<F13>8.2<TAB>Gauntlet trials      <F3@Lam>

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 19 <Ref, Page #, Tag = "11721">  Frame 28 of a 20 cm/s obstacle-avoidance test run <F3@Lam>



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        Column 2 Width = 3.000 Inches >

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<Cell><"Table:Cell">
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<Cell>

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(a) intensity frame 28 
<Cell>

<"CellBody">

(b) optical flow needle" plot 
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0)
)
>

<Cell>

<Row,"Row">

<Cell>

<"CellBody">

(d) median-filtered divergence 
<Cell>

<"CellBody">

(c) divergence plot (top row is current) 
<End Table>

<"subsection",
        Font =           F3@Lam,
        Line Spacing =   1.166 lines>

<F13> <F3@Lam>

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 20 <Ref, Page #, Tag = "39342">  Frame 43 of a 20 cm/s obstacle-avoidance test run <F3@Lam>



<Table, "Table", 
        Columns = 2,
        Column 1 Width = 2.900 Inches ,
        Column 2 Width = 3.000 Inches >

<Master Row, "Row">

<Cell><"Table:Cell">

<Cell><"Table:Cell">
<Row,"Row">

<Cell>

<"CellBody">

(a) intensity frame 43 
<Cell>

<"CellBody">

(b) optical flow needle" plot 
<Row,"Row">

<Cell,
Straddle = 2>

<Frame,
       Placement = At Anchor,
       Width = 5.688 Inches,
       Height = 2.843 Inches,
       Size Contents to Width = Yes, 
       Size Contents to Height = Yes, 
       No Border = Yes,
       Diagram = 



V11,
(g9,0,0,
 (i18,1,0,,0,0,7.111,0,0,3.555,0,0,511,255,1,0,7,0,0,7.111,3.555,0,1,511,0,0,255,0,0,511,255,0,0,0,0,0,511,255,8,0,131072
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(d) median-filtered divergence 
<Cell>

<"CellBody">

(c) divergence plot (top row is current) 
<End Table>

<"subsection",
        Font =           F3@Lam,
        Line Spacing =   1.166 lines>

<F13>       <F3@Lam>


<"body",
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        Line Spacing =   1.750 lines>

<TAB><TAB>The robot ran a gauntlet of office chairs to demonstrate the system's ability to avoid <SR>
obstacles while traversing the lab. The lab setup and results for a run are shown in Figure <SR>
11. The robot deflected left to avoid the chairs blocking its path and then continued traversing the room, deflecting to the ri<SR>
ght to avoid the opposite row of chairs. After deflecting right, the robot's path was partially blocked by the end of a desk, as<SR>
 shown in Figure <SR>
19, causing the robot to deflect left. After the robot deflected left, its closest obstacle was <SR>
a chair as shown in Figure 20. The robot then deflected right and headed toward the door <SR>
(the robot's complete path is shown in Figure 11 (d)). In these trials, the robot traveled at <SR>
20 cm/s and steered at a maximum rate of 8 degrees. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Gaze stabilization contributed considerably to the effectiveness of the system by reducing the magnitude of the optical flows <SR>
while the robot was steering. In control trials <SR>
without gaze stabilization, analysis of the data showed that optical flows observed while <SR>
the robot was steering routinely exceeded the range of the flow estimation system. The resulting corrupted data rendered obstac<SR>
les invisible," and the robot consequently failed to <SR>
continue seeing obstacles as executed evasive maneuvers. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>The simple memory of the steering policy, together with the spatio-temporal edge-preserving median filtering of divergence and<SR>
 assigning a cost to crossing ridges" in the divergence data (discussed in Section 6), served to commit the robot to a single c<SR>
ourse <SR>
around an obstacle until it was cleared. In control trials without these features, the robot <SR>
was sometimes lured back toward an obstacle by lower hazard estimates on the far side of <SR>
the obstacle. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>An MPEG video of an example test run may be found in the <F14@Lam><F14@Lam>hypertext portion of this <SR>
<F14@Lam>paper<F3@Lam>. It demonstrates the relationships between the image, the optical flow, the divergence estimates, and the time-filtered d<SR>
ivergence estimates which control the robot's <SR>
steering behavior.

<"subsection",
        Font =           F3@Lam,
        Line Spacing =   1.166 lines>

<F13>8.3<TAB>Wandering trials <F3@Lam>

<"FigureTableTitle",
        Font =           F3@Lam>

<F13>Figure 21 <Ref, Page #, Tag = "21492">  Wandering trial paths: x-y plots <F3@Lam>



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0)
)
>

<Row,"Row">

<Cell>

<"CellBody">

(a) Trial 0, 7.67 minutes 
<Cell>

<"CellBody">

(b) Trial 9, 7.22 minutes 
<Row,"Row">

<Cell>

<Frame,
       Placement = At Anchor,
       Width = 2.756 Inches,
       Height = 2.756 Inches,
       Size Contents to Width = Yes, 
       Size Contents to Height = Yes, 
       No Border = Yes,
       Diagram = 



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<Row,"Row">

<Cell>

<"CellBody">

(c) Trial 12, 6.75 minutes 
<Cell>

<"CellBody">

(d) Trial 1, last 8 of 26 minutes 
<End Table>

<"subsection",
        Font =           F3@Lam,
        Line Spacing =   1.166 lines>

<F13>     <F3@Lam>


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<TAB><TAB>The third set of experiments tested duration. In the wandering trials, the robot was permitted to wander about the relatively <SR>
uncluttered lab one day while the authors prepared a <SR>
report of the present work. Throughout the day, the authors ran 13 trials and collected data. <SR>
In these trials, the robot was started toward open space from various locations in the lab. <SR>
The longest trial lasted 26 minutes. The path of the robot in the final 8 minutes of this trial <SR>
is shown in Figure 21 (d). Three moderate length paths of about 7 minutes are shown entirely in Figure 21 (a-c). The mean trial<SR>
 length was roughly 7.1 minutes and the median <SR>
length was 6.75 minutes. While the robot generally drove back and forth along similar <SR>
paths, it also often worked its way out of such limit cycles. These results were achieved <SR>
with extremely simple behavior control. More sophisticated behavior control making use <SR>
of various mechanisms (<F14@Lam>e.g.<F3@Lam>, an explicit notion of segmented objects, adaptation) to derive <SR>
or interpret hazard maps can be expected to shorten the time to escape such situations. The <SR>
robot also covered a considerable fraction of the lab's open space in the longer trials. The <SR>
failure modes that most commonly terminated these trials with collision are discussed in <SR>
Section 9. While this performance falls far short of the ideal of limitless collision-free <SR>
(however crude) mobility as a base of competence, it is promising enough to be considered <SR>
as a low-level competence in a goal-directed mobile robot system.

<"section",
        Font =           F3@Lam,
        Line Spacing =   1.750 lines>

<F13>9<TAB>Discussion <Ref, Page #, Tag = "14562: Heading1: Discussion">  <F3@Lam>


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<TAB><TAB>Some researchers [20][33][34] have proposed using divergence or flow derivatives for <SR>
visual cues, but did provide real-time implementations of these ideas. Nelson and Aloimonos [27][28] used directional flow dive<SR>
rgence for stop-and-look obstacle avoidance <SR>
(not real-time smooth driving). Their environments were simplified, and they did not demonstrate extensive robust behavior over<SR>
 extended periods of time. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Duchon, <F14@Lam><F14@Lam>et al.<F3@Lam> [14][15][16] demonstrated flow and flow-derived time-to-contact for <SR>
free wandering at 5 cm/s for as long as 5 minutes. In a second implementation, speeds of <SR>
up to 30 cm/s have been achieved, and unrecorded trials have lasted up to 25 minutes without collision. Their most robust steer<SR>
ing strategy was balancing peripheral flows, <F14@Lam>i.e.,<F3@Lam> comparing left and right peripheral flows to steer the robot down a conceptua<SR>
l corridor (referred to as corridor-following, flow-balancing, centering, <F14@Lam><F14@Lam>etc.<F3@Lam>). However, the corridor- <SR>
following" technique is not well-suited to goal-oriented behavior. In [16] target chasing <SR>
and flow balancing are combined by summing the egocentric heading changes dictated by <SR>
both systems. It is possible for this strategy of combining behaviors to result in taking a <SR>
heading that is dangerous because there is no way for behaviors to eliminate all dangerous <SR>
headings from consideration. 

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<TAB><TAB>Coombs, <F14@Lam>et al<F3@Lam>.[11][12] also used flow to implement corridor-following" and used divergence to detect imminent collision. The <SR>
present work achieves similar results using divergence alone and is, therefore, not limited to corridor-following." The present<SR>
 system <SR>
supports goal-directed behavior while providing local obstacle avoidance. The method of <SR>
estimating optical flow described in this paper has been shown to detect obstacles as far <SR>
away as 6 meters under good conditions. On the other hand, the flow returned from the <SR>
PIPE image processing computer used in [11][12] was limited to a range of about 1 to 2.5 <SR>
meters due to the difficulty of detecting edges of distant surfaces. The range of our system <SR>
is even more remarkable given the coarse resolution (32x64) of the images used. In addition, our system implements both wide-an<SR>
gle and narrow-angle camera functions using <SR>
only one wide-angle camera and a single framegrabber, unlike the two cameras and video <SR>
channels used in [11][12].

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>System performance depends on many factors. Underlying the divergence estimates <SR>
are optical flow measurements. Although divergence is theoretically unaffected by camera <SR>
rotation, rotation contributes directly to optical flow. The system calculates optical flow <SR>
using a correlation method, which, like all techniques, has limited spatiotemporal sensitivity. In particular, large flows are <SR>
underestimated, so fast camera rotation can corrupt the <SR>
optical flow estimates on which the divergence estimates rely. Similarly, differential measures such as flow and divergence are<SR>
 inherently susceptible to noise.

<"body",
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<TAB><TAB>Our system relies on gaze stabilization and robust data filters to cope with these problems. Rotational stabilization of the c<SR>
amera reduces flow magnitudes to manageable levels. The brief disturbances introduced by saccades that re-orient the camera to t<SR>
he robot's <SR>
heading are effectively ignored by the spatial and temporal median filters that also suppress noise (in contrast to a non-robus<SR>
t smoothing filter which would be affected). This <SR>
enables the sensing and behavior modules to complement one another without requiring <SR>
tight coordination among them. 

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        Line Spacing =   1.750 lines>

<TAB><TAB>Optical flow also depends on the field of view and scene texture. Although the optical <SR>
flow algorithm used requires very little texture given adequate lighting [7][8], naturally the <SR>
obstacle must appear in the field of view in order to be detected. Even with a wide-angle <SR>
(
<"body",
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<TAB>) lens, not all obstacles will be visible. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>There are two main causes of collision. The first case involves a collision with an obstacle in one of the lower corners of th<SR>
e full-sized image. Currently, due to real-time requirements, only a central 256-pixel band of the 512-pixel height image is use<SR>
d in calculating flow. Grabbing the bottom 256 rows of the 512 rows available would enable these <SR>
objects to be seen. However, lowering the visual band taken from the full field of view is <SR>
undesirable because this also lowers the top edge of the image and thus limits the maximum visual range of the system. Given th<SR>
at the current image size allows for about a 20% <SR>
idle time to buffer OS events, it is likely that a more refined system (perhaps making use <SR>
of real-time OS facilities) could use this available CPU time to process a larger image.

<"body",
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<TAB><TAB>The second most common cause of collision involves a very narrow object, such as the <SR>
back of a chair-viewed edge-on; such an object does not have enough spatial extent to trigger a reaction from the system. Becau<SR>
se very wide images are being subsampled (from a <SR>
width of 512 pixels down to 64 pixels), these objects may be only a few pixels wide in the <SR>
image and they are therefore difficult to detect. This is especially true given the spatial filtering performed to increase rob<SR>
ustness. 

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        Line Spacing =   1.750 lines>

<TAB><TAB>A sensible extension would be construction of a local map of space to help prevent <SR>
such collisions, though this would introduce new problems, such as maintaining the map's <SR>
integrity. Our hazard maps with the steering policy's limited hysteresis provides a simple <SR>
local spatiotemporal map that has proved sufficient to carry the robot around most obstacles in its path without introducing a <SR>
complex spatial memory or world map. Dealing with <SR>
very narrow objects remains future work. 

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        Line Spacing =   1.750 lines>

<TAB><TAB>It has been argued that there are computational advantages in keeping the search radius <SR>
of the optical flow algorithm as small as one pixel [7][8] and keeping the frame rate high. <SR>
It should be noted that because images are subsampled from a size of 256x512 pixels down <SR>
to 32x64 pixels, a single pixel shift at the new coarser scale is equal to an 8 pixel shift at <SR>
the original resolution. In addition, because sub-pixel flows are detected, a magnitude of <SR>
1/2 pixels per frame corresponds to a 4 pixel shift at the original resolution, 1/4 pixels per <SR>
frame corresponds to a 2 pixel shift, <F14@Lam><F14@Lam>etc<F3@Lam>. Even so, when the robot is rotating, the optical <SR>
flow velocities can be extremely high. (Adding to this effect is the fact that the camera is <SR>
mounted about 30 centimeters in front of the rotational axis; each rotation" of the robot <SR>
results in combination of a rotation and a translation of the camera in inertial space.) In <SR>
this application, we could easily modify the search space to detect faster velocities in only <SR>
the horizontal directions, where the greater flows occur. This would allow the vehicle to <SR>
turn faster without saturating the computed flows, with only a linear increase in the computational time. 

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>In the previous version of the optical flow algorithm [7][8], the correlation match values are not saved as they are calculate<SR>
d, because only the best matching correlation match <SR>
is needed. Instead, as each one is calculated, it is compared with the current best match and <SR>
saved if it is the new best match or discarded if it is not. In the new version described here, <SR>
the correlation match values are interpolated, and thus all match values are saved. Although this only requires 553 KB of memor<SR>
y for current parameters, cache thrashing could <SR>
become a performance bottleneck for higher image and velocity resolutions. Future versions will be streamlined to reduce this e<SR>
ffect.

<"body",
        Line Spacing =   1.750 lines>

<TAB><TAB>Sensorimotor interactions also affect overall performance. There are significant latencies in the sensing, estimation, and con<SR>
trol modules shown in Figure 1. These modules are <SR>
only loosely synchronized. Although in general the latency for each module equals its cycle time, in some cases the latency is <SR>
a bit greater. The modules produce and consume data <SR>
at various rates, and the interactions of the unequal cycle times have considerable consequences. Flow and divergence estimates<SR>
 are produced approximately every 260 ms (just <SR>
under 4 Hz). The robot accepts speed and steering commands at about 3 Hz. At a robot <SR>
velocity of 20 cm/s, visual data become available about every 5 cm of robot travel and <SR>
steering is adjusted about every 7 cm. To avoid losing valuable data, especially time-critical impending-collision indications,<SR>
 the behavior controller runs at 20 Hz, evaluating any <SR>
fresh data and writing appropriate steering and speed commands. These commands are <SR>
only single-buffered, so only the most recent command is read by the robot controller <SR>
when it is ready for a new one. This minimizes the overall latency in the system. However, <SR>
it also means the behavior controller does not know exactly which command is being executed unless the robot controller sends a<SR>
n acknowledgment that identifies the accepted <SR>
command. This condition, coupled with considerable latencies in executing a robot command, means it is difficult for the contro<SR>
l (and sensing) systems to know precisely what <SR>
the robot is doing, short of installing high-speed low-latency feedback sensors. Consequently, the systems are designed to requ<SR>
ire only approximate knowledge of the robot's <SR>
current motion state if they use any at all. Instead, for instance, robust data filters are able <SR>
to ignore momentary noise and artifacts that result from system module interactions, and this enables <SR>
modules to cooperate without delicate synchronization.

<"section",
        Font =           F3@Lam,
        Line Spacing =   1.750 lines>

<F13>10<TAB>Conclusions <F3@Lam>


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        Line Spacing =   1.750 lines>

<TAB><TAB>A robot system is presented that uses only real-time image flow divergence to avoid obstacles <SR>
while driving toward a specified goal direction (straight ahead in this demonstration) in a lab containing office furniture and<SR>
 robot and computing equipment. The robot has wandered around the lab at 20 <SR>
cm/s for as long as 26 minutes without collision. To our knowledge, this is the first such demonstration of real-time smooth wa<SR>
ndering for extended periods of time using only flow divergence. 

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<TAB><TAB>The paper describes how flow divergence is computed in real-time to provide the robot's sense of <SR>
space and also how steering, collision detection, and camera gaze control are used together to avoid <SR>
obstacles while attempting to drive in the specified goal direction. The major contribution is the demonstration of a simple, r<SR>
obust, minimal system that uses flow-derived measures to control steering and <SR>
speed to avoid collision in real time for extended periods. 

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<TAB><TAB>Although image motion has long been considered a fundamental element in the perception of <SR>
space, attempts to use it in real-world mobility tasks have always been hampered by problems such <SR>
as noise, brittleness, and computational complexity. We demonstrate that robust image motion cues <SR>
can be extracted using a single ordinary UNIX workstation to safely move about a complex environment in real-time for extended <SR>
periods.

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<TAB><TAB>These results demonstrate that real-time robot vision and control can be achieved with careful implementations on ordinary com<SR>
puting platforms and environments. Similarly, an extensible framework can combine simple robust components in a manner than mini<SR>
mizes requirements for tight synchronization.

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<F13>11<TAB>References <F3@Lam>


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