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C00002 00002 {≥G⊂CαLOCUS SOLVINGλ30P109JUFA}
C00006 00003 {P114JUFA}⊂9.4 Sun Locus Solving: A Simple Solar Ephemeris.⊃
C00010 00004 ⊂9.5 Related and Future Locus Solving Work.⊃
C00011 ENDMK
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⊂9.3 Object Locus Solving: Silhouette Cone Intersection.⊃
After the camera location, orientation and projection are
known; 3-D object models can be constructed. The silhouette cone
intersection method is a conceptually simple form of wide angle,
stereo reconstruction. The idea arose out of an original intention to
do "blob" oriented visual model acquisition, however a 2-D blob came to
be represented by a silhouette polygon and a 3-D blob consequently
came to be represented by a polyhedron. The present implementation
requires a very favorably arranged viewing environment (white objects
on dark backgrounds or vice versa); application to more natural
situations might be possible if the necessary hardware (and software)
were available for extracting depth discontinuities by bulk
correlation. Furthermore, the restriction to turntable rotation is
for the sake of easy camera solving; this restriction could be lifted
by providing stronger feature tracking for camera calibration.
Figure 9.3 shows four video images and the corresponding
silhouette contours of a baby doll on a turn table. Figure 9.4 is an
overhead view of the four silhouette cones that were swept from the
contours, the circle in the middle of Figure 9.4 is the turntable.
Figure 9.5 gives three views (cross eyed stereo pairs) of the
polyhedron that resulted by taking the intersection of the four
silhouette cones. Like in the joke about carving a statue by cutting
away everything that does not look like the subject, the approximate
shape of the doll is hewed out of 3-D space by cutting away
everything that falls outside of the silhouettes. A second example of
silhouette cone intersection is depicted in Figure 9.6; the model was
made from three silhouettes of the horse facing to the left which can
be compared with an initial video image and a final view of the
result of the horse facing to the right - a plausible (maximal)
backside has been constructed that is consistent with the front
views.
The silhouette cone intersection method does indeed construct
concave objects and even objects with holes in them - what are missed
are concavities with a full rim, that is points on the surface of the
object whose tangent plane cuts the surface in a loop that encloses
the point.{Q}
{P114;JUFA}⊂9.4 Sun Locus Solving: A Simple Solar Ephemeris.⊃
The location of the sun is useful to a robot vehicle vision
system both for sophisticated scene interpretation and for avoiding
the blunder of burning holes in the television vidicon. The
approximate position of the sun in the sky is readily computed from
the time, date and latitude using circular approximations. The
longitude is implicitly used to compute Local Solar Time, since the
Stanford A.I. Lab is 122 degrees 10 minutes west of the Greenwich
meridian, Local Solar time is 8 minutes, 44 seconds earlier than
Pacific Standard Time (120 degrees west). The orientation of the
earth with respect to the sun follows from remembering that the sun
is highest at noon. The tilt of the earth with respect to its orbit
is 23.45 degrees, so in earth centered coordinates the sun appears to
circle the earth counterclockwise crossing the plane of the equator
from south to north on the spring equinox, March 21.
The SUNLOCUS procedure given below computes the local azimuth
and altitude of the sun in the sky, given the number of days since
March 21, the time in seconds since midnight and the latitude in
radians.
{λ10;JAF3;}
PROCEDURE SUNLOCUS (REAL DAY,TIME,LAT; REFERENCE REAL SUNAZM,SUNALT);
BEGIN
REAL RHO,PHI,TMP,ECLIPTIC,NORTH,EAST,ZENITH;
COMMENT POSITION OF THE SUN ON THE ECLIPTIC IN THE CELESTIAL SPHERE;
ECLIPTIC← ((23+27/60)*PI);
RHO ← 2*PI*DAY/365.25;
EAST ← SIN(RHO)*COS(ECLIPTIC);
NORTH ← SIN(RHO)*SIN(ECLIPTIC);
ZENITH ← COS(RHO);
COMMENT LOCAL SOLAR TIME, OVER THE MAST AT NOON;
TIME ← TIME - (8*60 + 44);
PHI ← PI*(1-TIME/(12*3600)) - ATAN2(EAST,ZENITH);
TMP ← ZENTITH*COS(PHI) - SIN(PHI)*EAST;
EAST ← EAST*COS(PHI) + SIN(PHI)*ZENITH;
ZENITH ← TMP;
COMMENT ROTATE CLOCKWISE IN THE NORTH/ZENITH PLANE TO LOCAL LATITUDE;
TMP ← COS(LAT)*ZENITH + SIN(LAT)*NORTH;
NORTH ← COS(LAT)*NORTH - SIN(LAT)*ZENITH;
ZENITH ← TMP;
CONVERT TO ANGULAR MEASURES;
SUNAZM ← ATAN2(NORTH,EAST); COMMENT AZIMUTH FROM DUE EAST;
SUNALT ← PI/2 - ACOS(ZENTIH); COMMENT ALTITUDE ABOVE HORIZON;
END "SUNLOCUS";
{λ30;JUFAQ;}
⊂9.5 Related and Future Locus Solving Work.⊃
The camera solving problem is discussed in Roberts (63),
Sobel (70) and Quam (71). I have always disliked the many dimensional
hill climbing approach to camera solving and have sought more
geometric and intuitive solutions to the problem. Although the bulk
of this chapter concerned camera solving using one view of three
points the multi view camera calibration is probably more important
to continuous image processing.