Dariusz Małyszko

Adaptive multilevel rough entropy evolutionary thresholding

Abstract In this study, comprehensive research into rough set entropy-based thresholding image segmentation techniques has been performed producing new and robust algorithmic schemes. Segmentation is the low-level image transformation routine that partitions an input image into distinct disjoint and homogenous regions using thresholding algorithms most often applied in practical situations, especially when there is pressing need for algorithm implementation simplicity, high segmentation quality, and robustness. Combining entropy-based thresholding with rough set results in the rough entropy thresholding algorithm. The authors propose a new algorithm based on granular multilevel rough entropy evolutionary thresholding that operates on a multilevel domain. The MRET algorithm performance has been compared to the iterative RET algorithm and standard k-means clustering methods on the basis of β -index as a representative validation measure. Performance in experimental assessment suggests that granular multilevel rough entropy threshold based segmentations – MRET – present high quality, comparable with and often better than k-means clustering based segmentations. In this context, the rough entropy evolutionary thresholding MRET algorithm is suitable for specific segmentation tasks, when seeking solutions that incorporate spatial data features with particular characteristics.

Standard and Fuzzy Rough Entropy Clustering Algorithms in Image Segmentation

Clustering or data grouping presents fundamental initial procedure in image processing. This paper addresses the problem of combining the concept of rough sets and entropy measure in the area of image segmentation. In the present study, comprehensive investigation into rough set entropy based thresholding image segmentation techniques has been performed. Segmentation presents the low-level image transformation routine concerned with image partitioning into distinct disjoint and homogenous regions with thresholding algorithms most often applied in practical solutions when there is pressing need for simplicity and robustness. Simultaneous combining entropy based thresholding with rough sets results in rough entropy thresholding algorithm. In the present paper, new algorithmic schemes Standard RECA(Rough Entropy Clustering Algorithm) and Fuzzy RECAin the area of rough entropy based partitioning routines have been proposed. Rough entropy clustering incorporates the notion of rough entropy into clustering model taking advantage of dealing with some degree of uncertainty in analyzed data. Both Standard and Fuzzy RECAalgorithmic schemes performed usually equally robustly compared to standard k-means algorithm. At the same time, in many runs yielding slightly better performance making possible future implementation in clustering applications.

Adaptive Rough Entropy Clustering Algorithms in Image Segmentation

High quality performance of image segmentation methods presents one leading priority in design and implementation of image analysis systems. Incorporating the most important image data information into segmentation process has resulted in development of innovative frameworks such as fuzzy systems, rough systems and recently rough - fuzzy systems. Data analysis based on rough and fuzzy systems is designed to apprehend internal data structure in case of incomplete or uncertain information. Rough entropy framework proposed in [12,13] has been dedicated for application in clustering systems, especially for image segmentation systems. We extend that framework into eight distinct rough entropy measures and related clustering algorithms. The introduced solutions are capable of adaptive incorporation of the most important factors that contribute to the relation between data objects and makes possible better understanding of the image structure. In order to prove the relevance of the proposed rough entropy measures, the evaluation of rough entropy segmentations based on the comparison with human segmentations from Berkeley and Weizmann image databases has been presented. At the same time, rough entropy based measures applied in the domain of image segmentation quality evaluation have been compared with standard image segmentation indices. Additionally, rough entropy measures seem to comprehend properly properties validated by different image segmentation quality indices.

Rough Entropy Based k-Means Clustering

Data clustering algorithmic schemes receive much careful research insight due to the prominent role that clustering plays during data analysis. Proper data clustering reveals data structure and makes possible further data processing and analysis. In the application area, k-means clustering algorithms are most often exploited in almost all important branches of data processing and data exploration. During last decades, a great deal of new algorithmic techniques have been invented and implemented that extend basic k-means clustering methods. In this context, fuzzy and rough k-means clustering presents robust modifications of basic k-means clustering that are aimed at better apprehension of data structure that advantageously incorporate notions from fuzzy and rough set theories. In the paper, an extension of rough k-means clustering into rough entropy domain has been introduced. Experimental results suggest that proposed algorithm outperforms standard k-means clustering methods applied in the area of image segmentation.

Rough entropy hierarchical agglomerative clustering in image segmentation

In data clustering there is a constant demand on development of new algorithmic schemes capable of robust and correct data handling. This demand has been additionally highly fueled and increased by emerging new technologies in data imagery area. Hierarchical clustering represents established data grouping technique with a wide spectrum of application, especially in image analysis branch. In the paper, a new algorithmic rough entropy framework has been applied in the hierarchical clustering setting. During cluster merges the quality of the resultant merges has been assessed on the base of the rough entropy. Incorporating rough entropy measure as the evaluation of cluster quality takes into account inherent uncertainty, vagueness and impreciseness. The experimental results suggest that hierarchies created during rough entropy based merging process are robust and of high quality, giving possible area for future research applications in real implementations.

Probabilistic rough entropy measures in image segmentation

In numerous data clustering problems, the main priority remains a constant demand on development of new improved algorithmic schemes capable of robust and correct data handling. This requirement has been recently boosted by emerging new technologies in data acquisition area. In image processing and image analysis procedures, the image segmentation procedures have the most important impact on the image analysis results. In data analysis methods, in order to improve understanding and description of data structures, many innovative approaches have been introduced. Data analysis methods always strongly depend upon revealing inherent data structure. In the paper, a new algorithmic Rough Entropy Framework - (REF, in short) has been applied in the probabilistic setting. Crisp and Fuzzy RECA measures (Rough Entropy Clustering Algorithm) introduced in [5] are extended into probability area. The basic rough entropy notions, the procedure of rough (entropy) measure calculations and examples of probabilistic approximations have been presented and supported by comparison to crisp and fuzzy rough entropy measures. In this way, uncertainty measures have been combined with probabilistic procedures in order to obtain better insight into data internal structure.

Subspace entropy maps for rough extended framework

Dynamic increase in development of data analysis techniques that has been strengthened and accompanied by recent advances witnessed during widespread development of information systems that depend upon detailed data analysis, requiremore sophisticated data analysis procedures and algorithms. In the last decades, deeper insight into data structure has been more many innovative data analysis approaches have been devised in order to make possible. In the paper, in the Rough Extended Framework, SEM - a new family of the rough entropy based image descriptors has been introduced. The introduced rough entropy based image descriptors are created by means of introduced k-Subspace notion. The Subspace Entropy Maps analysis seems to present potentially robust medium during detailed data analysis. The material has been presented by examples of the introduced solutions as image descriptors

Fuzzified Probabilistic Rough Measures in Image Segmentation

Recent advances witnessed during widespread development of information systems that depend upon detailed data analysis, require more sophisticated data analysis procedures and algorithms. In the last decades, deeper insight into data structure has been made more precise by means of many innovative data analysis approaches. Rough Extended (Entropy) Framework presents recently devised algorithmic approach to data analysis based upon inspection of the data object assignment to clusters. Data objects belonging to clusters contribute to cluster approximations. Cluster approximations are assigned measures that directly make possible calculation of cluster roughness. In the next step, total data rough entropy measure is calculated on the base of the particular roughness. In the paper, in the Rough Extended (Entropy) Framework, a new family of the probabilistic rough (entropy) measures has been presented. The probabilistic approach has been extended into fuzzy domain by fuzzification of the probabilistic distances. The introduced solution seems to present promising area of data analysis, particulary suited in the area of image properties analysis.

Generalized Hypersphere d-Metric in Rough Measures and Image Analysis

Dynamic advances in data acquisition methods accompanied by widespread development of information systems that depend upon them, require more sophisticated data analysis tools. In the last decades many innovative data analysis approaches have been devised in order to make possible deeper insight into data structure. Rough Extended Framework - REF - presents recently devised algorithmic approach to data analysis based upon inspection of the data object assignment to clusters. In the paper, in the Rough Extended Framework, a new family of generalized hypersphere d-metrics has been presented. The introduced hypersphere d-metrics have been applied in the rough clustering (entropy) measures setting. The combined analysis based upon hypersphered d-metric type and rough (entropy) measures is targeted as a robust medium for development of image descriptors.

Fuzzy Rough Entropy Clustering Algorithm Parametrization

Image processing represents active research area that requires advanced and sophisticated methods capable of handling novel emerging imagery technologies. Adequate and precise capture and image interpretation is primarily based on proper image segmentation. Advances in correct image partitioning are still embracing new research areas such as fuzzy sets, rough sets and rough fuzzy sets. Present research concentrates on new rough entropy clustering algorithm Fuzzy RECA Rough Entropy Clustering Algorithm and extension relative to distance threshold and fuzzy threshold, namely its parameters having impact on rough entropy calculation. Different rough entropy measures are calculated and incorporated into Fuzzy RECA based clustering algorithm on satellite image data set. Presented results suggest that proposed fuzzy thresholds capture properly image properties and it is possible to take advantage of these characteristics in real image processing applications.