MINNESOTA UNIV MINNEAPOLIS DEPT OF MATHEMATICS
Most widely held works by MINNESOTA UNIV MINNEAPOLIS DEPT OF MATHEMATICS
Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach ( Book )
1 edition published in 1993 in English and held by 1 library worldwide
Computer vision deals with image understanding at various levels. At the low level, it addresses issues such us planar shape recognition and analysis. Some classical results on differential invariants associated to planar curves are relevant to planar object recognition under different views and partial occlusion, and recent results concerning the evolution of planar shapes under curvature controlled diffusion have found applications in geometric shape decomposition, smoothing, and analysis, as well as in other image processing applications. In this work we first give a modern approach to the theory of differential invariants, describing concepts like Lie theory, jets, and prolongations. Based on this and the theory of symmetry groups, we present a high level way of defining invariant geometric flows for a given Lie group. We then analyze in detail different subgroups of the projective group, which are of special interest for computer vision. We classify the corresponding invariant flows and show that the geometric heat flow is the simplest possible one. This uniqueness result, together with previously reported results which we review in this paper, confirms the importance of this class of flows.
Partial differential equations, calculus of variations, and fluid mechanics ( Book )
1 edition published in 1968 in English and held by 1 library worldwide
The principal investigator completed six research papers during the period September 1967 through June 1968. This work is described in detail in the attached report. The major effort was devoted to nonlinear partial differential equations, the goal being to determine the effect of severe nonlinearity on the soluability of boundary value problems. A classification scheme into regularly elliptic and singularly elliptic equations was obtained by which one can directly determine the degree of nonlinearity of elliptic equations, and corresponding necessary and sufficient conditions of solvability were discovered. In fluid mechanics, the exact asymptotic relationship between Prandtl's boundary layer theory and the full Navier-Stokes equations was established for the case of flows in a radially convergent plane channel. Finally, two papers treated the existence and geometrical behavior of similarity solutions of the boundary layer equations, for free convection near a heated wall and for compressible flows past a boundary surface. (Author).
Transmission problems for holomorphic fiber bundles ( Book )
1 edition published in 1964 in English and held by 1 library worldwide
Transmission problems for holomorphic fiber bundles in high-dimensional complex spaces are considered. Topological preparations pertaining to the notion of boundary values on a hypersurface by approach from various sides are first carried out. Certain analytic preparations are made, which are mainly concerned with holomorphic bundles of complex Lie groups acting on holomorphic fiber bundles. The transmission problems are then stated. To each holomorphically correct transmission function, a holomorphic fiber bundle is constructed such that the set of solutions of the transmission problem corresponds bijectively to the set of holomorphic section in the fiber bundle. Topologically correct transmission functions are discussed and related to homology theory. Holomorphically correct transmission functions are then considered.
Quasi-conformal functions tending to conformality at the boundary ( Book )
1 edition published in 1960 in English and held by 1 library worldwide
The purpose of this note is to show that the boundary correspondence induced by a quasi-conformal mapping is absolutely continuous and an analogue of Fatou's theorem is valid for quasi-conformal functions if one requires that the dilatation quotient in addition to being bounded tends to one sufficiently swiftly as the boundary is approached.
Cluster sets of pseudo-meromorphic functions ( Book )
1 edition published in 1961 in English and held by 1 library worldwide
PROCEEDINGS OF THE CONFERENCE ON COMPLEX ANALYSIS, MINNEAPOLIS 1964 ( Book )
1 edition published in 1965 in English and held by 1 library worldwide
Papers are given that were presented at the Minnesota Conference on Complex Analysis. Topics covered include Stein manifolds, polynomial convexity, quasi-conformal mappings, Kleinian groups, uniform algebras, complex Lie groups, analytic spaces, holomorphic fiber bundles, point modifications, pseudogroup structures, linear topological spaces, Riemann surfaces, complex manifolds, holomorphic mappings, projective geometry, several complex variables, Siegel space, and Teichmuller spaces. In all 26 papers are reported. (Author).