TY - JOUR

T1 - Replicator Dynamics in the Iterative Process for Accurate Range Image Matching

AU - Liu, Yonghuai

N1 - Liu, Y. (2009). Replicator Dynamics in the Iterative Process for Accurate Range Image Matching. International Journal of Computer Vision, 83 (1), 30-56

PY - 2009/6/1

Y1 - 2009/6/1

N2 - Iterative algorithms are often used for range image
matching. In this paper, we treat the iterative process of
range image matching as a live biological system: evolving
from one generation to another. Whilst different generations
of the population are regarded as range images captured at
different viewpoints, the iterative process is simulated using
time. The well-known replicator equations in theoretical
biology are then adapted to estimate the probabilities of
possible correspondences established using the traditional
closest point criterion. To reduce the effect of image resolutions
on the final results for efficient and robust overlapping
range image matching, the relative fitness difference
(rather than the absolute fitness difference) is employed in
the replicator equations in order to model the probability
change of possible correspondences being real over successive
iterations. The fitness of a possible correspondence is
defined as the negative of a power of its squared Euclidean
distance. While the replicator dynamics penalize those individuals
with low fitness, they are further penalised with a
parameter, since distant points are often unlikely to represent
their real replicators. While the replicator equations assume
that all individuals are equally likely to meet each other and
thus treat them equally, we penalise those individuals competing
for the same points as their possible replicators. The
estimated probabilities of possible correspondences being
real are finally embedded into the powerful deterministic
annealing scheme for global optimization, resulting in the
camera motion parameters being estimated in the weighted
least squares sense. A comparative study based on real range
images with partial overlap has shown that the proposed algorithm
is promising for automatic matching of overlapping
range images.

AB - Iterative algorithms are often used for range image
matching. In this paper, we treat the iterative process of
range image matching as a live biological system: evolving
from one generation to another. Whilst different generations
of the population are regarded as range images captured at
different viewpoints, the iterative process is simulated using
time. The well-known replicator equations in theoretical
biology are then adapted to estimate the probabilities of
possible correspondences established using the traditional
closest point criterion. To reduce the effect of image resolutions
on the final results for efficient and robust overlapping
range image matching, the relative fitness difference
(rather than the absolute fitness difference) is employed in
the replicator equations in order to model the probability
change of possible correspondences being real over successive
iterations. The fitness of a possible correspondence is
defined as the negative of a power of its squared Euclidean
distance. While the replicator dynamics penalize those individuals
with low fitness, they are further penalised with a
parameter, since distant points are often unlikely to represent
their real replicators. While the replicator equations assume
that all individuals are equally likely to meet each other and
thus treat them equally, we penalise those individuals competing
for the same points as their possible replicators. The
estimated probabilities of possible correspondences being
real are finally embedded into the powerful deterministic
annealing scheme for global optimization, resulting in the
camera motion parameters being estimated in the weighted
least squares sense. A comparative study based on real range
images with partial overlap has shown that the proposed algorithm
is promising for automatic matching of overlapping
range images.

KW - Replicator dynamics

KW - Iterative process

KW - Accurate matching

KW - Overlapping range images

KW - Fitness

KW - Probability of a possible correspondence being real

U2 - 10.1007/s11263-009-0210-8

DO - 10.1007/s11263-009-0210-8

M3 - Article

SN - 0920-5691

VL - 83

SP - 30

EP - 56

JO - International Journal of Computer Vision

JF - International Journal of Computer Vision

IS - 1

ER -