7. QUALITY
INDICATORS
Neither observation equations nor normal equations are
formed in the least squares matching by search.
Therefore the variance-covariance matrix of unknown
parameters is not directly available for accuracy estima-
tion. This drawback of the method could be circumvented
by forming the normal equations explicitly in the goal
state. Direct analysis of the texture in the match windows
would be an alternative for quality analysis. The issue
requires further studies.
8. OTHER CRITERIA FOR OPTIMUM
Least squares matching by search uses, as defined here,
the sum of squared residuals as the object function. This
criterion could be replaced by any other function of the
. residuals. Use of the sum of absolute values of residuals
(L,-norm) could be suitable. It would be less sensitive on
large residuals which can be interpreted as blunders in the
gray level values. The robust estimation methods and
weight reduction methods used for blunder detection
could also be implemented in a very efficient way.
9. ON COMPUTER IMPLEMENTATIONS
The numerical methods for making the search efficient
where treated in Section 4. Regarding computer
implementation of many numerical algorithms, the
innermost loop is the most critical for speed. All 'tricks' for
making it efficient should be regarded if the speed is a
bottle neck or an obstacle for use. In our problem the
innermost loop deals with the resampling of the gray level
values and some rather simple computations on them.
Use of methods like integer arithmetics instead of floating
points arithmetics, multithreaded programming, or even
assembly level programming could be justified here.
10. CONCLUSIONS
Least squares matching by search is based on the well
established theory on object space least squares
matching. The implementation is rigorous and straight-
forward because the linearization of the observation
equations is not necessary. Use of case-dependent
knowledge on geometry makes it possible to keep
dimensionality of the search space moderate. Further
reduction of the search space is possible by reducing the
range of unknown variables hierarchically when the
corresponding step size is decreased. The principle for
reaching subpixel accuracy is similar compared to the
original formulation of least squares matching, although
the numerical realization is very different. Further study is
proposed for developing other quality criteria to replace
the use of the variance-covariance matrix of unknown
parameters. The effect of using other norms in the object
function should be investigated, to be able to compensate
radiometric disturbances on the gray level values.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
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