Scale-dependent monotonicity and scale-dependent extrema

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:35863

Brooks, M

Scale-dependent monotonicity is a generalized notion of monotonicity that {open_quotes}ignores{close_quotes} numerical differences less than a given scale for real valued functions on a finite real domain, i.e. finite real functions. For each scale {delta} > 0 any finite real function`s domain can be partitioned into intervals upon which the function is {delta}-monotone. These intervals define the pieces for certain optimal piecewise monotone approximations. The intervals` endpoints define the function`s {delta}-extrema, i.e. the function`s extrema at scale {delta}. The extrema at a given scale are a subset of the extrema at any smaller scale. An extrema-preserving scale space for a finite real function F is a mapping from the scale parameter {delta} to a function having the same {delta}-extrema as F. Extrema preserving scale spaces can be constructed by piecewise filtering and approximation. Examples of such filters include certain types of linear, recursive, robust, and kernel filters. This talk will review the theory of scale-dependent monotonicity, scale-dependent extrema, and filters constructing extrema-preserving scale spaces.

• OSTI ID: 35863
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
COMPUTERIZED SIMULATION
CONVERGENCE
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
VARIATIONAL METHODS