Image Processing Reference
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significance to predominant impact on further image data analysis. Segmentation presents
the low-level image transformation routine concerned with image partitioning into distinct
disjoint and homogenous regions. Clustering or data grouping describes distinct key proce-
dure in image processing and segmentation. Rough sets have been employed during image
analysis routines, see for example (Borkowski and Peters, 2007). The presented research is
based on combining the concept of rough sets and entropy measure in the area of image
segmentation by means of Rough Entropy Clustering Algorithm.
In the previous work (Malyszko and Stepaniuk, 2008), new algorithmic scheme RECA in
the area of rough entropy (Pal, Shankar, and Mitra, 2005) based partitioning routines has
been proposed. Proposed entirely novel rough entropy clustering algorithm incorporates
the notion of rough entropy into clustering model taking advantage of dealing with some
degree of uncertainty in analyzed data. Given predefined number of clusters, with each
cluster lower and upper cluster approximations are associated. Image points that are close
to the cluster contribute their impact by increasing lower and upper cluster approximation
value in case of their proximity only to that cluster or distribute uniformly their impact on
some number of upper cluster approximations otherwise. After lower and upper approxi-
mation determination for all clusters, their roughness and rough entropy value calculation
proceeds. On the base of entropy maximization law, the best segmentation is achieved in
case of maximal entropy value. For this purpose, an evolutionary population of separate so-
lutions is maintained with solutions with predefined number of cluster prototypes. For each
solution, respective rough entropy measure is calculated and subsequently, new populations
are created form parental solutions with high values of this fitness measure.
Additionally, an extension of Standard Crisp-Crisp Difference RECA - CCD RECA al-
gorithm into fuzzy domain has been elaborated in the form of Fuzzy RECA algorithms -
Fuzzy-Crisp FCD RECA, Fuzzy-Fuzzy Threshold FFT RECA and Fuzzy-Fuzzy Difference
FFD RECA. In Fuzzy RECA algorithm setting, the impact of each image point on upper
cluster approximations of su
ciently close clusters is not constant and depends upon their
distance from these clusters. Upper cluster approximations are increased by fuzzy measure
for all image points that are su
ciently close to more than one cluster center relative to
distance threshold
dist
or fuzzy threshold
f uzz
.
Present research deals with in-depth analysis of RECA algorithm schemes performance
relative to algorithm parameters defining boundary regions on the final image clustering and
type of fuzziness. The important factor in RECA algorithm setting is the type of fuzziness
that is employed in the algorithm. This experimental research has been concentrated on the
different type of fuzziness and their parameters and generated by means of these parameters
different rough entropy measures. Calculated entropy measures are subsequently compared
with image segmentation quality indices. On this basis some conclusions could be drawn
on type of fuzziness parameters that are the best correlated with other quality measure.
In the experiments, selected number of algorithm parameters have been chosen. During
experimental phase, relevant RECA routines have been employed in CCD RECA, FCD
RECA, FFT RECA and FFD RECA setting. Finally, image clustering quality has been
assessed by means of β-index, mean square error measure as employed in k -means algorithm
and other standard validity indices as Dunn index and Davies-Bouldin index. These stan-
dard and rough factors interdependence has been assessed giving answer on the question
how rough entropy measure is related to other segmentation quality indexes.
Next important factors in RECA algorithm impact assessment are the imagery inher-
ent characteristics.
The above mentioned experiments have been carried out on several
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