Holographic representations of images

We discuss a new type of holographic image representations that have advantages in a "distributed" world. We call these representations holographic. Arbitrary portions of a holographic representation enable reconstruction of the whole image, with distortions that decrease gradually with the increase in the size of the portions available. Holographic representations enable progressive refinement in image communication or retrieval tasks, with no restrictions on the order in which the data fragments (sections of the representation) are accessed or become available.

Phylogenetic analysis of tnpR genes in mercury resistant soil bacteria: the relationship between DNA sequencing and RFLP typing approaches

The diversity of resolvase (tnpR) genes carried by a number of mercury resistant soil bacteria has been investigated by DNA sequencing. The resulting DNA sequence information was compared to previously published tnpR DNA sequences and to previously published restriction fragment length polymorphism (RFLP) data, permitting the relationships between DNA sequencing and RFLP approaches to be studied by the use of phylogenetic trees. DNA maximum likelihood and DNA parsimony were used to construct a variety of phylogenetic trees. DNA sequencing confirmed the validity of RFLP analysis and highlighted the importance of restriction endonuclease choice upon the resulting RFLP patterns and dendrogram topology. The tnpR genes of two previously uncharacterised mercury resistant bacteria, T2-7 and T2-12 were also studied. DNA sequence data placed T2-7 in a previously described gene class, tnpR-D and T2-12 in a new gene class, tnpR-F. The significance of this data with respect to the recombination and evolution events occurring within bacterial populations are discussed.

Algebraic methods for image processing and computer vision

Many important problems in image processing and computer vision can be formulated as the solution of a system of simultaneous polynomial equations. Crucial issues include the uniqueness of solution and the number of solutions (if not unique), and how to find numerically all the solutions. The goal of this paper is to introduce to engineers and scientists some mathematical tools from algebraic geometry which are very useful in resolving these issues. Three-dimensional motion/structure estimation is used as the context. However, these tools should also be helpful in other areas including surface intersection in computer-aided design, and inverse position problems in kinematics/robotics. The tools to be described are Bezout numbers, Grobner bases, homotopy methods, and a powerful theorem which states that under rather general conditions one can draw general conclusions on the number of solutions of a polynomial system from a single numerical example.