For the last two decades, different aspects of visualization have been
very popular area of research. A great variety and volume of journal papers
has resulted from the research work conducted by scientists and engineers
around the world. A major portion of this work
has concerned visualization of volume data sets in general,
and isosurface extraction in particular.
We summarize some of the currently used algorithms and approaches
in this field, and their efficiency issues in first few chapters.
We attempt to show in this dissertation that
the direction of past and present research has been
designed to meet the increasing visualization demands of the late twentieth
century in medicine and science,
and to produce
practical, usable results for scientists. Certainly, the effort of the visualization specialists
has been successful in
pushing the boundaries of both quality and applicability, and raising scientific expectations.
Many more issues remain unresolved, particularly when visualizing
large volume data sets, such as the bottleneck induced by excessive I/O operations.

We present an algorithm for organizing the discrete scalar volume data on external storage
with important application to out-of-core visualization of extremely large data sets. The
application include extraction isosurfaces in a manner that minimizes both I/O
and disk seek time, topologically correct isosurface simplification and producing a visual
atlas of all topologically distinct objects in the data set, with the range of scalar
isovalues that reveal each. The segmentation algorithm computes the region of space called
topological zone components, so that any isosurface component is completely contained in
a zone component and all contours contained in a zone component are homeomorphic. The
algorithm also develops a search structure called criticality tree as by-product
and both of these computation is carried out in space efficient manner. The algorithm is very
generic in nature. It does not assume any specific structure of the input data or any specific
interpolates and can be extended to data sets with non-unique values. Towards the end
we give a simple, efficient and provably correct algorithm for constructing isosurfaces.
Finally we present the results obtained by various experiments that justifies our assumption.