oint 9 
b- 
S d N; 1. f 8; } f Si 
6) (s, 5] | | (6,1) Tm 
Macs clit L 
22] E 
(3,950 Ce SY (5,1; 
which in turn is generated exclusively by the pair of projective equations 
corresponding to the image of point j on photo Z. These elements in (5) are 
defined by the expressions 
e 
we 
e 
e 
i8 BI. ql 5B. Ll. Co. BZ Wi.c. , 
tj 2d A 43 ij 1j. Ad AS 
— A T ee 
(6) 0 Bt 
N lI n T. LJ . Be . e. e. = n . . . . . 
Nig B Warts st epg Bir Ws ed 
in which W;; is the inverse of the covariance matrix the measured plate 
coordinates xi py and the remaining matrices are defined directly by the 
linearized pair of projective equations generated by XL pL namely: 
(7) Ver % Bu $% + Bu 46 = £j - 
(25, 1) (2,6) (6,1) fa, 3 juifs, 1) (2,1) 
As it stands, the general system of normal equations (3) applies 
implicitly to the situation wherein all measured points appear on all photos, 
as may occur in typical terrestrial applications. By contrast, in the case 
of the typical aerial block a given point will appear on only a relatively 
small number of photos, usually no more than six for normal side overlap of 
less than 50 percent. Here, most of the NZj submatrices will be null matrices, 
for N7j is nonzero only when the jt point appears on the zth photo (this also 
applieS to the submatrices Ki i61 p67)- Accordingly, for the normal 
aerial block the overall a will tend to be sparse, as is illustrated 
in Figure 1 which depicts the coefficient matrix of the general system of 
normal equations generated by the 4x5 photo block illustrated in Figure 2. 
It is this characteristic sparseness of N coupled with the block diagonality 
of N+W and N+W that makes it ultimately practical to solve the system of 
normal equations for blocks having a moderate to large number of photos. 
APPROACHES TO THE SOLUTION OF THE NORMAL EQUATIONS 
Even when N is not sparse (i.e., most points appear on most photos) 
the general system of normal equations of order (6m+3n)x(6m+3n) can easily be 
reduced to an equivalent system of 6mx6m through the direct elimination of 
the à vector from (1). This leads to the reduced system 
-3—