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minimizing the norm (1284) (1285) where b is the baseline in stereo coordinates, and rl and rr are the left and right rays rotated into stereo coordinates To solve the ray intersection problem, differentiate with respect to tl and tr and set the result equal to zero Solve the equations for tl and tr and plug the solution values for the parameters into the ray equations (Equation 1282 and 1283) to obtain the point on each ray that is closest to the other ray A verage the two point locations to obtain the depth estimate The stereo point measurements are in the coordinate system of the stereo system, either the left or right camera, or a neutral coordinate system If the algorithm for relative orientation presented in Section 124 was used to determine the baseline, then the measurements are in a unitless system of measurement If the rigid body transformations between the left and right cameras and another coordinate system for the stereo hardware were obtained by solving the exterior orientation problem (Section 128) or by other means, then the stereo point measurements are in the units that were used for the calibration points Regardless of how the stereo system was calibrated, we have to transform the point measurements into an absolute coordinate system for the scene We can convert the measurements into a system of units appropriate to the scene at the same time by solving the absolute orientation problem with a scale factor

Freq*

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The formulation of the absolute orientation problem in Section 123 does not allow transformations that include a scale change; the transformation between coordinate systems is a rigid body transformation which includes only rotation and translation Scale changes occur, for example, in binocular stereo when the baseline between the stereo cameras is unknown or incorrect or between range cameras with different measurement units The absolute orientation problem, presented in Section 123, can be extended to include scale changes The solution to this extended problem will be a transformation that includes rotation and translation to align the viewpoint to an absolute coordinate system and includes a scale factor to convert camera-specific measurement units to the common system of units Consider a point P with coordinates PI = (Xl, YI, Zl) in one coordinate system and coordinates P2 = (X2' Y2, Z2) in another coordinate system The transformation between coordinates is (1286) where s is the scale change This increases the number of parameters in the absolute orientation problem to seven: three parameters for rotation, three parameters for translation, and the scale factor The scaling transformation is uniform scaling: the coordinates of each axis are scaled by the same amount The input to the absolute orientation problem is a set of n conjugate pairs for the first and second views: {(PI ,i' P2 ,in The regression problem is to find the rotation R, translation Po, and scale s that minimize

(P2,i - SRPl,i - Po)

(1287)

MSJC and IBC agree that the lowest level of quality assurance effort applies to prescriptively designed masonry in non-essential facilities A moderate level of effort is required for prescriptively designed masonry in essential facilities and for engineered masonry in non-essential facilities The most extensive effort is required only for engineered masonry in essential facilities Quality assurance efforts required by IBC and MSJC are defined by two types of requirements: necessary tests and submittals and necessary inspection (called special inspection by IBC) Submittals

The solution requires at least three points to get nine equations for the seven unknowns In practice, more points are used to provide better accuracy Ignore for the moment that the correspondence between points is known and imagine that the two sets of points (the set of points in the first coordinate system and the set in the second system) are two clouds of points in absolute coordinate space Compute the centroid of each cloud of points:

f the project problem is chronic and important to the organization, the Champion should have no problem supporting the Black Belt in solving it If the problem is not worth the time, then the wrong problem has been chosen

(1288)

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