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The relational distance can be normalized in the range [0; 1], as follows:
RDN(s!: .s; )7 RD(sj s; /NC (6)
where, NC is the total number of components in the stars S? and S.
In an ideal condition, the correspondence (f, f) is compatible when RDN( sf .st )- 0, and the opposite when
RDN( st T )= 1. However, in practical applications, it will be necessary to use a threshold (0«L«1). The
correspondence (f, f) is compatible when RDN( si sh j« L.
233 Self-diagnosis. The self-diagnosis is the last criterion to be evaluated in order to verify whether the
correspondence (f;, f, (or F;)) that is being analyzed is accepted or not. In opposition to the two previous criterion, the
self-diagnosis is a statistical decision. It is only applied if the two previous criteria are satisfied. At this step the state
vector is also filtered using the observed parameters of the straight lines.
Self-diagnosis is based on the data snooping statistical test implemented with the process of space resection using the
IEKF. The photogrammetric model (Tommaselli and Tozzi, 1996) is based on the geometry that is shown in figure 3.
The geometry of the figure 3 is modeled by the following
equation:
a= -
(7) |
L3, Ix t 755 .Dy + [35.02 d= |m
b =fr.- n
D, Ix * D.ny + 3-1
where Az Sn F
e ng -n(Y,-Y)tm(Z,-Zj [PC-C] r n
e ny n(X,-X) * £.(Z, - Zi
. n; -m.(X, - Xi) * l (Yo = Yi
e X, Y,, Z, are the object-space coordinates of the
perspective center (PC) of the camera;
e Xi, Y, Z, are the object-space coordinates of a
known point on the object straight line; & x
e Í[, m, n are the components of the direction X 21
vector d of the object-space straight line;
® 1; 1<i<3 and 1<j<3, are the elements of a
rotation matrix, defined by the matrix product Figure 3. Interpretation plane and normal vectors
M,(K ) M,(£ ).M,(W ), where k, £, w are
orientations angles of the camera, i. e., the rotation angles between the image-space and object-space reference
systems;
e fis the focal length; and
* à, b are the linear and angular parameters of the image-space straight line, which are extracted by using a
feature extraction process.
EN
However, when the image straight line are close to vertical, the representation y=a.x+b is unstable. In other words,
equation 7 can not be used. This problem can be solved using another representation for image straight line, i. e., X=
a*.y+b*. Taking into account this representation, the equation 8 can be written:
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 209
