Donald E. McClure

A nonlinear filter for film restoration and other problems in image processing

Abstract A filter is proposed for removing noise and other types of degradation. An application is explored to enhancement of frame sequences , motivated by the problem of film restoration for the movie industry. Experiments are performed on sequences from a degraded black and white copy of a recently released movie. Both temporal and spatial information are used in the restoration. Temporal information is obtained from the preceding unprocessed frame; spatial information enters by smoothing the current frame. The smoothing must be nonlinear in order to preserve boundaries.

Perfect spline solutions of L∞ extremal problems by control methods

Abstract Methods of analyzing linear time-optimal control problems are adapted to the analysis of the extremal problem ∥ L | 0 ∥ ∞ = inf | ϵU ∥ L |∥ ∞ ; L is a linear n th order differential operator and U is a flat in the Sobolev space W n ,∞ [ a , b ]. Existence and uniqueness of solutions are established for particular U determined by interpolation conditions at a and b . Solutions are characterized as perfect splines, enabling one to obtain solutions of perfect-spline interpolation problems. Further, existence of perfect-spline solutions is established for extremal and interpolation problems determined by more general flats U .

Image models in pattern theory

Abstract The pattern theory developed by U. Grenander provides a unified framework for the description of observed images in terms of algebraic and probabilistic processes that generate the images. The main elements of the general theory are outlined and specific image models are related to the general theory.

Image Models in Pattern Theory

The pattern theory developed by U. Grenander provides a unified framework for the description of observed images in terms of algebraic and probabilistic processes that generate the images. The main elements of the general theory are outlined and specific image models are related to the general theory.

PARTITIONING FOR HOMOGENEITY

SUMMARY Several statistical problems are introduced that are interrelated by the common goal of decomposing a population into homogeneous parts. This goal leads to an optimal partitioning problem. Its analysis yields precise characterizations of optimal partitions of univariate and bivariate populations. The characterizations can be used for computation of approximately optimal partitions.