PE&RS May 2016 - page 380

pixel), the reference image coordinates are first transformed to
object space using the datum/projection parameters to obtain
latitude and longitude, followed by extracting corresponding
height value from SRTM/ASTER for the computed latitude and
longitude. The points thus obtained become the checkpoints.
GA-based GCP Selection
The accuracy of the ortho product depends on only few good
quality GCP s as compared to a large number of not so accurate
GCPs, which is shown by Reinartz et al. (2006) and Fraser et
al. (2009). The checkpoints identified in the previous section
could contain a mix of error points, not so accurate points,
as well as good quality GCP s. The task of GCP selection is to
identify the best combination of minimal checkpoints among
the given set which is consistent with the given RSM/RFM.
Subsequently the same GCP s are used to refine RSM/RFM and
compute model error at all the checkpoints.
Genetic Algorithms (Michalewicz, 1992) and Genetic
Programming (Koza et al., 1992) are a set of artificial intelli-
gence search algorithms based on evolutionary theory and are
applied in optimization problems. GA represents the solution
to a problem as an individual (chromosome) in the popula-
tion pool, and evolves the chromosomes across generations
using genetic operations such as crossover and mutation. The
evolution processes reproduce a new set of chromosomes and
carry the individuals with the best fitness to the next genera-
tion. Crossover ensures the diversity and the genetic fitness of
the population, while mutation improves diversity as well as
prevents it from being trapped in the local optimal solution.
The genetic modeling involves two crucial factors: first indi-
vidual representation and genetic operations, i.e., crossover,
mutation, and individual selections for next generations, and
second, modeling of fitness function. This section describes
genetic modeling adopted for the task of selecting good GCPs
consistent with the RSM/RFM from a large pool of checkpoints.
Population and Genome Representation and Genetic Operations
A population P in GA consists of several individuals g rep-
resenting chromosomes/genomes. If n represents the total
number of checkpoints for GCPs identified by SIFT (as previous-
ly explained), and m represents the desired number of GCPs
for the RSM/RFM refinement, then two possible representations
of the individual for the problem can be possible as shown in
Figure 3. The first is a true binary representation as shown in
Figure 3a, where the length of the genome is the same as that
of the total number of checkpoints and the individual gene is
either ‘0’ or ‘1’ indicating whether the corresponding check-
point is selected as GCP or not. The other representation can be
an integer representation as shown in Figure 3b, correspond-
ing to a tuple of m elements (g1, g2, …., gm), where each ele-
ment in the tuple is a gene gk Є {1,…., n} for k= 1,…,m, where
n is the total number of checkpoints and m is the number of
GCPs desired for RSM/RFM refinement. The value of m is gov-
erned by the model based on factors such as mission/imaging
complexity, terrain, and length of the scene etc.
The integer representation is chosen in this work, as it has
been found to be more computationally optimal in both space
and time. There are two major implementations of GA, i.e.,
Simple GA and Steady State GA. Simple GA as described by
Goldberg (1989) uses non overlapping populations. In each
generation an entirely new population of chromosomes are
created, and forwards the best individual (based on fitness
value) from the current generation to the next generation.
Steady State GA implements overlapping populations, for-
warding the user specified set of best individuals in each gen-
eration to the next generation. Here, we propose to use Steady
State GA with larger overlap percent at around 50 percent for
the following reasons.
• SIFT generates good checkpoints and reference data-
sets are reasonably accurate (at least at 50 percent of
points); hence if reference images are reasonably accu-
rate and the RSM/RFM if modeled accurately, we expect
more chromosomes clustered near the optimal solution.
Hence, the crossover between the chromosomes would
provide further refinement.
• The number of GCP s required is far fewer compared
to the number of candidate points, i.e., 6 to 12 GCPs
Figure 2. SIFT-based checkpoint identification for VHR images using coarser HR images.
Figure 3. (a) Binary, and (b) integer chromosome.
380 May 2016 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING