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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