Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Content Based Image Retrieval Using Low Level Features of Automatically Extracted Regions of Interest

This paper proposes a region based image retrieval system using the local colour and texture features of image sub regions. The regions of interest (ROI) are roughly identified by segmenting the image into fixed partitions, finding the edge map and applying morphological dilation. The colour and texture features of the ROIs are computed from the histograms of the quantized HSV colour space and Gray Level co- occurrence matrix (GLCM) respectively. Each ROI of the query image is compared with same number of ROIs of the target image that are arranged in the descending order of white pixel density in the regions, using Euclidean distance measure for similarity computation. Preliminary experimental results show that the proposed method provides better retrieving result than retrieval using some of the existing methods.

Development of Techniques for the Automatic Extraction and Grade Detection of Glioma Tumors from Conventional Brain Magnetic Resonant Images

Cerebral glioma is the most prevalent primary brain tumor, which are classified broadly into low and high grades according to the degree of malignancy. High grade gliomas are highly malignant which possess a poor prognosis, and the patients survive less than eighteen months after diagnosis. Low grade gliomas are slow growing, least malignant and has better response to therapy. To date, histological grading is used as the standard technique for diagnosis, treatment planning and survival prediction. The main objective of this thesis is to propose novel methods for automatic extraction of low and high grade glioma and other brain tissues, grade detection techniques for glioma using conventional magnetic resonance imaging (MRI) modalities and 3D modelling of glioma from segmented tumor slices in order to assess the growth rate of tumors. Two new methods are developed for extracting tumor regions, of which the second method, named as Adaptive Gray level Algebraic set Segmentation Algorithm (AGASA) can also extract white matter and grey matter from T1 FLAIR an T2 weighted images. The methods were validated with manual Ground truth images, which showed promising results. The developed methods were compared with widely used Fuzzy c-means clustering technique and the robustness of the algorithm with respect to noise is also checked for different noise levels. Image texture can provide significant information on the (ab)normality of tissue, and this thesis expands this idea to tumour texture grading and detection. Based on the thresholds of discriminant first order and gray level cooccurrence matrix based second order statistical features three feature sets were formulated and a decision system was developed for grade detection of glioma from conventional T2 weighted MRI modality.The quantitative performance analysis using ROC curve showed 99.03% accuracy for distinguishing between advanced (aggressive) and early stage (non-aggressive) malignant glioma. The developed brain texture analysis techniques can improve the physician’s ability to detect and analyse pathologies leading to a more reliable diagnosis and treatment of disease. The segmented tumors were also used for volumetric modelling of tumors which can provide an idea of the growth rate of tumor; this can be used for assessing response to therapy and patient prognosis.

Automatic Detection and Classification of Glioma Tumors using Statistical Features

The characterization and grading of glioma tumors, via image derived features, for diagnosis, prognosis, and treatment response has been an active research area in medical image computing. This paper presents a novel method for automatic detection and classification of glioma from conventional T2 weighted MR images. Automatic detection of the tumor was established using newly developed method called Adaptive Gray level Algebraic set Segmentation Algorithm (AGASA).Statistical Features were extracted from the detected tumor texture using first order statistics and gray level co-occurrence matrix (GLCM) based second order statistical methods. Statistical significance of the features was determined by t-test and its corresponding p-value. A decision system was developed for the grade detection of glioma using these selected features and its p-value. The detection performance of the decision system was validated using the receiver operating characteristic (ROC) curve. The diagnosis and grading of glioma using this non-invasive method can contribute promising results in medical image computing