19-04-2014, 11:02 AM
Morphological image sequence processing
Abstract
We present a morphological multi-scale method
for image sequence processing, which results in a truly cou-
pled spatio-temporal anisotropic diffusion. The aim of the
method is not to smooth the level-sets of single frames but
to denoise the whole sequence while retaining geometric fea-
tures such as spatial edges and highly accelerated motions.
This is obtained by an anisotropic spatio-temporal level-set
evolution, where the additional artificial time variable serves
as the multi-scale parameter. The diffusion tensor of the evo-
lution depends on the morphology of the sequence, given by
spatial curvatures of the level-sets and the curvature of trajec-
tories (=acceleration) in sequence-time. We discuss different
regularization techniques and describe an operator splitting
technique for solving the problem. Finally we compare the
new method with existing multi-scale image sequence pro-
cessing methodologies.
Introduction
During the last decade scale-space methods have proven to be
useful in image processing, including image denoising, edge
enhancement and shape recovery from noisy data [1,25,33,
38]. A given image is thereby considered as initial data to
some suitable evolution problem. The artificial time param-
eter acts as the scale parameter, which guides the user from
noisy fine scale representations to enhanced and coarse scale
representations of the original image.
Discretization and numerical solution
Up to now we have considered image-sequences to be suffi-
ciently smooth in space and time . Since in the applications
image-sequences arise as a finite sequence of single images
(the frames) consisting of arrays of pixels or voxels, we will
discretize the model in an appropriate way. For each single
frame, we interpret the pixel/voxel values as nodal values on
a uniform quadrilateral respectively hexahedral mesh cov-
ering the whole spatial domain . Moreover since typically
the time offset
between successive frames is constant in
image sequences, we introduce an equidistant lattice in the
sequence-time direction. In any coordinate direction, we con-
sider the data to be piece-wise multi-linear.
Comparison to other methods
In this section we would like to compare some of the image-
sequence processing models mentioned in Section 2 with the
new model. We will not discuss any steady-image method-
ology which may be applied to the single frames of the se-
quence, since a model taking into account velocity and accel-
eration of an image sequence clearly gives better correlation
between successive frames of the sequence.
Conclusions
We have presented a new morphological anisotropic smooth-
ing approach for image sequences, which takes into account
temporal and spatial curvature information. The multi-scale
diffusion thereby is truly coupled in sequence-time and space
and the anisotropy directions correspond to the apparent di-
rection of motion in sequence-time and to principal directions
of curvature in space. The diffusivity is decreased in areas of
high curvature which results in a good preservation of spatial
corners and edges as well as highly accelerated motions in
sequence-time.