Herbert Freeman

Bio: Herbert Freeman is an academic researcher from New York University. The author has contributed to research in topics: Quantization (physics) & Multiplication. The author has an hindex of 6, co-authored 7 publications receiving 3579 citations.

On the Encoding of Arbitrary Geometric Configurations

Abstract: 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

Abstract: 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

Apictorial Jigsaw Puzzles: The Computer Solution of a Problem in Pattern Recognition

Abstract: This paper describes the development of a procedure that enables a digital computer to solve ``apictorial'' jigsaw puzzles, i.e., puzzles in which all pieces are uniformly gray and the only available information is the shape of the pieces. The problem was selected because it provided an excellent vehicle to develop computer techniques for manipulation of arbitrary geometric patterns, for pattern identification, and for game solving. The kinds of puzzles and their properties are discussed in detail. Methods are described for characterizing and classifying piece contours, for selecting and ordering pieces that are ``most likely'' to mate with a given piece, for determining likelihood of fit, for overcoming ambiguities, and for evaluation of the progressive puzzle assembly. An illustration of an actual computer solution of a puzzle is given.

A Multistage Solution of the Template-Layout Problem

Abstract: 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

Abstract: 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.

Algorithms for the reduction of the number of points required to represent a digitized line or its caricature

Abstract: All digitizing methods, as a general rule, record lines with far more data than is necessary for accurate graphic reproduction or for computer analysis. Two algorithms to reduce the number of points required to represent the line and, if desired, produce caricatures, are presented and compared with the most promising methods so far suggested. Line reduction will form a major part of automated generalization. Regle generale, les methodes numeriques enregistrent des lignes avec beaucoup plus de donnees qu'il n'est necessaire a la reproduction graphique precise ou a la recherche par ordinateur. L'auteur presente deux algorithmes pour reduire le nombre de points necessaires pour representer la ligne et produire des caricatures si desire, et les compare aux methodes les plus prometteuses suggerees jusqu'ici. La reduction de la ligne constituera une partie importante de la generalisation automatique.

The Algorithmic Beauty of Plants

Abstract: 1 Graphical modeling using L-systems.- 1.1 Rewriting systems.- 1.2 DOL-systems.- 1.3 Turtle interpretation of strings.- 1.4 Synthesis of DOL-systems.- 1.4.1 Edge rewriting.- 1.4.2 Node rewriting.- 1.4.3 Relationship between edge and node rewriting.- 1.5 Modeling in three dimensions.- 1.6 Branching structures.- 1.6.1 Axial trees.- 1.6.2 Tree OL-systems.- 1.6.3 Bracketed OL-systems.- 1.7 Stochastic L-systems.- 1.8 Context-sensitive L-systems.- 1.9 Growth functions.- 1.10 Parametric L-systems.- 1.10.1 Parametric OL-systems.- 1.10.2 Parametric 2L-systems.- 1.10.3 Turtle interpretation of parametric words.- 2 Modeling of trees.- 3 Developmental models of herbaceous plants.- 3.1 Levels of model specification.- 3.1.1 Partial L-systems.- 3.1.2 Control mechanisms in plants.- 3.1.3 Complete models.- 3.2 Branching patterns.- 3.3 Models of inflorescences.- 3.3.1 Monopodial inflorescences.- 3.3.2 Sympodial inflorescences.- 3.3.3 Polypodial inflorescences.- 3.3.4 Modified racemes.- 4 Phyllotaxis.- 4.1 The planar model.- 4.2 The cylindrical model.- 5 Models of plant organs.- 5.1 Predefined surfaces.- 5.2 Developmental surface models.- 5.3 Models of compound leaves.- 6 Animation of plant development.- 6.1 Timed DOL-systems.- 6.2 Selection of growth functions.- 6.2.1 Development of nonbranching filaments.- 6.2.2 Development of branching structures.- 7 Modeling of cellular layers.- 7.1 Map L-systems.- 7.2 Graphical interpretation of maps.- 7.3 Microsorium linguaeforme.- 7.4 Dryopteris thelypteris.- 7.5 Modeling spherical cell layers.- 7.6 Modeling 3D cellular structures.- 8 Fractal properties of plants.- 8.1 Symmetry and self-similarity.- 8.2 Plant models and iterated function systems.- Epilogue.- Appendix A Software environment for plant modeling.- A.1 A virtual laboratory in botany.- A.2 List of laboratory programs.- Appendix B About the figures.- Turtle interpretation of symbols.

The Quadtree and Related Hierarchical Data Structures

Abstract: Apercu sur les quadarbres et les structures de donnees hierarchiques. Elles sont basees sur le principe de decomposition recursive. L'accentuation est mise sur la representation de donnees dans les applications de traitement d'images, d'infographie, les systemes d'informations geographiques et la robotique. On examine en detail un certain nombre d'operations dans lesquelles de telles structures de donnees trouvent leur utilisation

Review of shape representation and description techniques

Abstract: More and more images have been generated in digital form around the world. There is a growing interest in 1nding images in large collections or from remote databases. In order to 1nd an image, the image has to be described or represented by certain features. Shape is an important visual feature of an image. Searching for images using shape features has attracted much attention. There are many shape representation anddescription techniques in the literature. In this paper, we classify and review these important techniques. We examine implementation procedures for each technique and discuss its advantages and disadvantages. Some recent research results are also included and discussed in this paper. Finally, we identify some promising techniques for image retrieval according to standard principles.