Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Electronics and Communication Sciences Unit (ECSU-Kolkata)


Majumdar, Dwijesh Dutta (ECSU-Kolkata; ISI)

Abstract (Summary of the Work)

Digital topology provides a sound mathematical basis for object classification, counting and labeling, border tracking, contour filling, thinning, segmentation and many other image processing applications. An important characteristic of topo- logical properties is that they are invariant under translation, rotation, and more generally under any elastic deformation. The analysis of three dimensional (3D) digital images has generated increasing interest with the rapid growth of 3D image processing applications including computer vision. 3D digital images are common input/output media in the several application domains of image processing, pattern recognition and computer vision among which 3D medical imaging is of particular interest. In medical imaging, applications like Computed Tomography (CT), Mag- netic Resonance Imaging (MRI), Positron Emission Tomography (PET), Ultrasound Echography (UE), Single Photon Emission Computed Tomography (SPECT), Digital Subtraction Angiography (DSA) are widely used in producing 3D digital images that carry many important information about organs interior to the human body. These images are routinely used by the doctors both for diagnosis of abnormalities in the structure and function of organs and also for therapeutic treatment planning. Lee and Rosenfeld [65) pointed out the fact that many organs are highly flexible and change shapes due to external forces or due to their own functions. For example, the heart always changes its shape with heart beats. However, these deformations generally follow elastic deformation rules. This phenomenon gives importance to topological features such as the numbers of components, tunnels, cavities etc. in the 3D digital images of interior organs. These are invariant under elastic deformation. These topological numbers, useful for organ identification, may also be used for diagnosis and therapeutic planning. For example, the usual number of passage- ways through the heart is used as a pathology. Udupa (136] discussed about the applications of digital topology in three-dimensional medical imaging.This thesis is devoted to the study of topological properties in three dimensional dig- ital space and their applications to image processing. Rosenfeld and Kak (105] and Chaudhuri and Dutta Majumder (22] among others discussed about the importance of geometrical and topological properties in digital image analysis and recognition. A well-developed theory of topological properties of 3D digital images may be found in [96]. A survey on digital topology was reported by Kong and Rosenfeld 51]. In general, digital topology deals with binary images (although some works [98,103) were reported on the topology of gray-tone images). In a binary digital image a point is either a black (object) point or a white (non-object) point. We mainly consider binary images and in the remaining part of the thesis image will refer to "binary image unless stated otherwise.The black points in an image may be grouped as a set of connected components. A component may contain tunnels and cavities. A cavity is a 3D analog of 2D hole where white points generate a bounded component. A tunnel on the other hand, does not generate a component of white points.


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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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