Herbert Freeman

On the Encoding of Arbitrary Geometric Configurations

A method is described which permits the encoding of arbitrary geometric configurations so as to facilitate their analysis and manipulation by means of a digital computer. It is shown that one can determine through the use of relatively simple numerical techniques whether a given arbitrary plane curve is open or closed, whether it is singly or multiply connected, and what area it encloses. Further, one can cause a given figure to be expanded, contracted, elongated, or rotated by an arbitrary amount. It is shown that there are a number of ways of encoding arbitrary geometric curves to facilitate such manipulations, each having its own particular advantages and disadvantages. One method, the so-called rectangular-array type of encoding, is discussed in detail. In this method the slope function is quantized into a set of eight standard slopes. This particular representation is one of the simplest and one that is most readily utilized with present-day computing and display equipment.

Computer Processing of Line-Drawing Images

This paper describes various forms of line drawing representation, compares different schemes of quantization, and reviews the manner in which a line drawing can be extracted from a tracing or a photographic image. The subjective aspects of a line drawing are examined. Different encoding schemes are compared, with emphasis on the so-called chain code which is convenient for highly irregular line drawings. The properties of chain-coded line drawings are derived, and algorithms are developed for analyzing line drawings to determine various geometric features. Procedures are described for rotating, expanding, and smoothing line structures, and for establishing the degree of similarity between two contours by a correlation technique. Three applications are described in detail: automatic assembly of jigsaw puzzles, map matching, and optimum two-dimensional template layout

Determining the minimum-area encasing rectangle for an arbitrary closed curve

This paper describes a method for finding the rectangle of minimum area in which a given arbitrary plane curve can be contained. The method is of interest in certain packing and optimum layout problems. It consists of first determining the minimal-perimeter convex polygon that encloses the given curve and then selecting the rectangle of minimum area capable of containing this polygon. Three theorems are introduced to show that one side of the minimum-area rectangle must be collinear with an edge of the enclosed polygon and that the minimum-area encasing rectangle for the convex polygon is also the minimum-area rectangle for the curve.

A Multistage Solution of the Template-Layout Problem

The template-layout problem is to determine how to cut irregular-shaped two-dimensional pieces out of given stock sheets in an optimum manner without making an exhaustive search of all possible arrangements of the pieces. An algorithm is described for solving template-layout problems with a digital computer. The method of solution requires that the irregular shapes be enclosed, singly or in combination, in minimum area rectangles called modules. Individual modules will contain from one to perhaps eight optimally fitted irregular pieces. The modules are then packed into the given stock sheet(s) so as to optimize a specified objective function. The packing is carried out with a dynamic programming algorithm, which converts the multivariable problem into a multistage one. Successive iterations of the algorithm are used to determine whether higher order modules (containing more irregular-shaped pieces) improve the solution. A detailed description of the algorithm is given. An illustrative example is included and its computer solution is described. The paper concludes with an extension of the algorithm to an improved version which can be expected to yield solutions more closely approaching the true optimum.

On the Quantization of Line-Drawing Data

This paper describes the development of a criterion for the quantization of line-drawing data. The criterion provides a guide for selecting the quantization fineness required to assure that the significant features of given line-drawing data will be preserved in the quantization process. The criterion is based on viewing a line drawing as an elastic beam under flexure and selecting a quantization grid size that is fine enough to permit the line drawing to be represented by a beam of minimum strain energy. In this model, regions of sharp curvature of the line drawing correspond to regions of high strain-energy density of the elastic beam. The smoothest possible curve that can be reconstructed from a quantized representation is the minimum-energy curve that satisfies the constraints of the quantized data.

Informatik als Berufsbild

Der Titel meines Vortrages lautet „Informatik als Berufsbild“oder auf englisch „Informatics as a Profession“.