05-05-2012, 10:55 AM
Variational Dense Motion Estimation Using the Helmholtz Decomposition
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Introduction
In a number of domains affecting our everyday life, the analysis of image sequences
involving fluid phenomena is of importance. This includes for instance
domains such as visualization in experimental fluid mechanics [1,12], environmental
sciences (meteorology [3,4,11,13,21], oceanography [6]) or medical imaging
[2,7,18]. For all these domains it is of primary interest to extract reliable
velocity fields and to the observed fluid flow. With respect to that goal, image
sensors have considerable advantages compared to dedicated probes. Compared
to these probes, image sensors provide a huge amount of almost continuous
spatio-temporal data in a fast, tireless, reproducible and contact-free way. However,
the sought motion information has then to be extracted from the luminance
function which is not an easy task.
Experimental Results
This section is organized into three parts. First, the quantitative and qualitative
influence of the parameters γ and λ is investigated in Section 3.1. Second, the
proposed method is compared with the method of Corpetti et al. [5] on artificial
motion fields, i.e. with ground truth, in Section 3.2. Finally, results for a real
image sequence are presented.
In all experiments, the Euler-Lagrange equations (31) were solved sequentially
in 3000 iterations using an incomplete CLG solver iterating 50 times in
each (outer) iteration. Two resolution levels (including the original one) have
been used for the experiments in Sections 3.1 and 3.2 and three for those in
Section 3.3.
Parameter Studies
In first experimental studies the influence of the parameters γ and λ were investigated
on synthetic potentials in order to have a ground truth (cf. Figure 1).
The associated synthetic flow field was applied to a real image, i.e. the real image
was mapped using the velocity field to obtain a second image resulting in the
input image pair for the current experiments. Note that the vector field consist
of an exact spatial overlap of the true components we wish to determine and
distinguish.
Comparison with the Approaches of Corpetti et al. and Horn and Schunck
In [5] an approach was presented in which the potential functions were approximated
indirectly by first estimating a motion field using a regularization similar
to (21) and a subsequent integration along the stream lines in order to obtain
the velocity potential and the stream function. Both approaches were compared
in two experiments here based on given synthetic potential functions (cf. Figure
5). In order to have a reference both experiments have been carried out with
a Horn and Schunck estimator also. The parameters of all methods have been
optimized manually. Note that the setting of Comparison Experiment 1 is the
same as for the parameters studies.