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Title: Variational Models in Image Segmentation Using Fuzzy Set Theory
Authors: Ahmad, Ali
Keywords: Mathematics
Issue Date: 2019
Publisher: University of Engineering & Technology Peshawar
Abstract: Computer vision is an important field in which techniques are developed to study and understand the properties and structure of a 3D scene present in a digital image (2D scene) and output is just some descriptive information. While an intermediate step to computer vision is field of image processing in which input and output are both images and has five main components, i.e image segmentation, detection, tracking, registration and shape analysis. Image segmentation is main concern of this research work in context of the theory of fuzzy sets [97]. The key to fuzzy sets is fuzzy membership (FMB) u obeys the constraint 0 6 u 6 1. Level set method (LSM) [66] which naturally handles splitting and merging of the evolving curve C, is a well established technique for performing image segmentation. In this thesis, to solve a partial differential equation numerically, a pseudo level set expression [38] relied on u alike LSM is used and the curve C is considered as pseudo zero level set of u. Fuzzy set is generalization to crisp set and is more generalized approach towards image domain classification based on idea of partial membership of belonging described by a FMB function. Therefore, in many real situations in images, issues like poor contrast, limited spatial resolution, overlapping intensities, noise and inhomogeneities produces fuzziness in the object boundaries and hence fuzzy set theoretic approach is an ultimate option to utilize. Utilizing such approach, we have developed five models for segmentation of variety of images. First model (see Chapter 4) is developed for segmenting images having multiobjects with variable intensities and background having maximum, minimum, average or cluttered intensities. For such achievements generalized averages are merged in kernel metric and FMB is utilized as region descriptor. Second model (see Chapter 5) developed uses approximate image in kernel metric obtained by multi scale filtering technique to ensure segmentation of images consisting of less or severe inhomogeneity. To tackle more complicated task of segmenting images having noise, texture and inhomogeneity at the same time our third model (see Chapter 6) is developed utilizing idea of measure of relative variability i.e coefficient of variation (COV), which is further extended to multiphase image segmentation model (see Chapter 7). Extraction of particular features in medical images is another very challenging task, to solve we have developed our selective segmentation model (SSM) (see Chapter 8) by utilizing idea of multi scale difference image with COV. Overall in this thesis, our main focuss is on the development of variational models in fuzzy sets framework. Evaluation of the proposed approach on a number of datasets and benchmark validate its superiority over other existing models in terms of accuracy and efficiency.
Gov't Doc #: 19347
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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