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Table bitset Operations Operation test( pos ) any() none() count() size() [ pos ] flip() flip( pos ) set() set( pos ) reset() reset(pos) Function is pos bit on is any bit on are no bits on number of bits on number of bit elems access pos bit reverse all bits reverse pos bit turn on all bits turn on pos bit turn off all bits turn off pos bit Use atest( 4 ) aany() anone() acount() asize() a[ 4 ] aflip() aflip( 4 ) aset() aset( 4 ) areset() areset( 4 )

m||2 . (7.15)

The problem of representing bitvectors with integral types is the low-level complexity of the expressions that use the bitwise operators to set, reset, and test the individual bits For example, to turn on the 27th bit using our integral type, we write the following:

quiz1 |= 1 27;

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file:///F|/WinDDK/resources/CPPPrimer/c++primerhtm (166 / 1065) [2001-3-29 11:32:04]

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Figure 7.3. Illustration of the warping function W. A point v in image plane is projected onto the surface of the 3D object model. After the pose transformation with p, the point on the surface is back-projected onto the image plane at a new point u. The warping function maps from v R2 to u R2 . The red ellipses show the common part in both frames that the warping function W is de ned upon.

quiz1[ 27 ] = 1;

quiz1set( 27 );

In each iteration, m is updated such that Wpt 1 (u, m) Wpt 1 (u, m) Wpt 1 (u, m) 1 .3 Using the additivity of pose transformation for small m, we obtain Wpt 1 (Wpt 1 (u, m) 1 , m) = Wpt 1 (Wpt 1 (u, m), m) = Wpt 1 (u, m m). Thus, the above update is essentially m m + m. Baker and Matthews [15] proved that for the inverse compositional algorithm to be provably equivalent to the Lucas Kanade algorithm up to the rst order approximation of m, the set of warps {W} must form a group; that is, every warp W must be invertible. If the change of pose is small enough, the visibility for most of the pixels will remain the same; thus W can be considered approximately invertible. However, if the pose change becomes too big, some portion of the object will become invisible after the pose transformation, and W will no longer be invertible (see [17] for more details). Since the GAM along the motion direction is composed of a set of tangent planes at a few discrete poses (see Figure 7.1), the computations for m need to happen only at these poses (called cardinal poses). Thus all frames that are close to a particular pose pj will use the B and C at that pose, and the warp W should be performed to normalize the pose to pj . While most of the existing inverse compositional methods move the expensive update steps out of the iterations for two-frame matching, we go even further and perform these expensive computations only once every few frames. This is by virtue of the fact that we estimate 3D motion. 7.3.1.1 The IC Algorithm on GAMs

(As noted in the previous section, the numbering of bits begins with zero: in practice, bit 27 refers to the 28th bit In our example, we are wasting the first bit so that references to our bits begin with 1) To use the bitset class, we must include its associated header file:

A bitset can be declared in one of three ways In its default definition, we simply indicate how large a bitvector we wish For example:

Consider a sequence of image frames It , t = 0, . . . , N 1. Assume that we know the pose and illumination estimates for frame t 1, that l is, pt 1 and t 1 .

bitset< 32 > bitvec;

declares a bitset object containing 32 bits numbered from 0 to 31 By default, all the bits are initialized to zero To test whether a bitset object has any of its bits set, we use the any() operation; any() returns true if one or more bits of the bitset object are turned on For bitvec, the test

As we can see, the limited scope of each access technology forces the user to gain connectivity through a variety of network technologies. From a user s perspective, this can mean several things:

3 The compositional operator means that the second warp is composed into the rst warp, that is, Wpt 1 (u, m) Wpt 1 (Wpt 1 (u, m) 1 , m).

bool is_set = bitvecany();

evaluates, of course, to false Conversely, the operation none() returns true if all the bits of the bitset object are set to zero For bitvec, the test

bool is_not_set = bitvecnone();

7

evaluates to true Alternatively, the count() operation returns the number of bits that are set:

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