2 research outputs found
Toward Parallel Computation of Dense Homotopy Skeletons for nD Digital Objects
An appropriate generalization of the classical notion of
abstract cell complex, called primal-dual abstract cell complex (pACC
for short) is the combinatorial notion used here for modeling and analyzing
the topology of nD digital objects and images. Let D ⊂ I be a set of
n-xels (ROI) and I be a n-dimensional digital image.We design a theoretical
parallel algorithm for constructing a topologically meaningful asymmetric
pACC HSF(D), called Homological Spanning Forest of D (HSF
of D, for short) starting from a canonical symmetric pACC associated
to I and based on the application of elementary homotopy operations
to activate the pACC processing units. From this HSF-graph representation
of D, it is possible to derive complete homology and homotopy
information of it. The preprocessing procedure of computing HSF(I) is
thoroughly discussed. In this way, a significant advance in understanding
how the efficient HSF framework for parallel topological computation of
2D digital images developed in [2] can be generalized to higher dimension
is made.Ministerio de EconomÃa y Competitividad TEC2016-77785-PMinisterio de EconomÃa y Competitividad MTM2016-81030-
Parallel Image Processing Using a Pure Topological Framework
Image processing is a fundamental operation
in many real time applications, where lots of parallelism
can be extracted. Segmenting the image into different
connected components is the most known operations, but
there are many others like extracting the region adjacency
graph (RAG) of these regions, or searching for features
points, being invariant to rotations, scales, brilliant
changes, etc. Most of these algorithms part from the basis
of Tracing-type approaches or scan/raster methods. This
fact necessarily implies a data dependence between the
processing of one pixel and the previous one, which
prevents using a pure parallel approach. In terms of time
complexity, this means that linear order O(N) (N being the
number of pixels) cannot be cut down. In this paper, we
describe a novel approach based on the building of a pure
Topological framework, which allows to implement fully
parallel algorithms. Concerning topological analysis, a first
stage is computed in parallel for every pixel, thus
conveying the local neighboring conditions. Then, they are
extended in a second parallel stage to the necessary global
relations (e.g. to join all the pixels of a connected
component). This combinatorial optimization process can
be seen as the compression of the whole image to just one
pixel. Using this final representation, every region can be
related with the rest, which yields to pure topological
construction of other image operations. Besides, complex
data structures can be avoided: all the processing can be
done using matrixes (with the same indexation as the
original image) and element-wise operations. The time
complexity order of our topological approach for a m×n
pixel image is near O(log(m+n)), under the assumption that
a processing element exists for each pixel. Results for a
multicore processor show very good scalability until the
memory bandwidth bottleneck is reached, both for bigger
images and for much optimized implementations. The
inherent parallelism of our approach points to the
direction that even better results will be obtained in other
less classical computing architectures.1Ministerio de EconomÃa y Competitividad (España) TEC2012-37868-C04-02AEI/FEDER (UE) MTM2016-81030-PVPPI of the University of Sevill