Exploiting Numerical Features in Computer Tomography Data Processing and Management by CICT

The impact of high resolution Computer Tomography (HRCT) technology is to generate new challenges associated with the problem of formation, acquisition, compression, transmission, and analysis of enormous amount of data. In the past, computational information conservation theory (CICT) has shown potentiality to provide us with new techniques to face this challenge conveniently. CICT explores, at elementary level, the basic properties and relationships of Q arithmetic to achieve full numeric algorithmic information conservation with strong connections to modular group theory and combinatorial optimization. Traditional rational number system can be regarded as a highly sophisticated open logic, powerful and flexible LTR and RTL formal language of languages, with self-defining consistent words and rules, starting from elementary generators and relations. CICT supply us with optimized exponential cyclic sequences (OECS) which inherently capture the hidden symmetries and asymmetries of the hyperbolic space encoded by rational numbers. Symmetry and asymmetry relations can be seen as the operational manifestation of universal categorical irreducible arithmetic dichotomy (”correspondence” and ”incidence”) at the innermost logical data structure level. These two components are inseparable from each other, and in continuous reciprocal interaction. According to Pierre Curie, symmetry breaking has the following role: for the occurrence of a phenomenon in a medium, the original symmetry group of the medium must be lowered (broken, in today's terminology) to the symmetry group of the phenomenon (or to a subgroup of the phenomenons symmetry group) by the action of some cause. In this sense symmetry breaking, or asymmetry, is what creates a phenomenon. The same dichotomy generates ”pairing” and ”fixed point” properties for digit group with the same word length, in word combinatorics. Correspondence and Incidence manifest themselves even into single digit fundamental property (i.e. ”evenness” and ”oddness”), till binary elementary symbols (”0”, ”1”). This new awareness can be exploited into the development of competitive optimized algorithm and application. Practical examples will be presented.