Waveform Segmentation Through Functional Approximation

Waveform segmentation is treated as a problem of piecewise linear uniform (minmax) approximation. Various algorithms are reviewed and a new one is proposed based on discrete optimization. Examples of its applications are shown on terrain profiles, scanning electron microscope data, and electrocardiograms. The processing is sufficiently fast to allow its use on-line. The results of the segmentation can be used for pattern recognition, data compression, and nonlinear filtering not only for waveforms but also for pictures and maps. In the latter case some additional preprocessing is required and it is described in [19].

[1]  R. Bellman.  On the approximation of curves by line segments using dynamic programming , 1961, CACM.

[2]  Brian Gluss,et al.  Further remarks on line segment curve-fitting using dynamic programming , 1962, Commun. ACM.

[3]  C. Lawson.  Characteristic properties of the segmented rational minmax approximation problem , 1964 .

[4]  R. Narasimhan,et al.  Labeling Schemata and Synctactic Descriptions of Pictures , 1964, Inf. Control..

[5]  J. Rice.  The approximation of functions , 1964 .

[6]  R S LEDLEY,et al.  HIGH-SPEED AUTOMATIC ANALYSIS OF BIOMEDICAL PICTURES. , 1964, Science.

[7]  M. Newman,et al.  Interpolation and approximation , 1965 .

[8]  H. Keller,et al.  Analysis of Numerical Methods , 1969 .

[9]  George Nagy,et al.  State of the art in pattern recognition , 1968 .

[10]  L. Schumaker.  Uniform Approximation by Chebyshev Spline Functions. II: Free Knots , 1968 .

[11]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.

[12]  Martin D. Levine,et al.  Feature extraction: A survey , 1969 .

[13]  Alan C. Shaw,et al.  A Formal Picture Description Scheme as a Basis for Picture Processing Systems , 1969, Inf. Control..

[14]  Azriel Rosenfeld,et al.  Picture Processing by Computer , 1969, CSUR.

[15]  Ulf Grenander,et al.  Foundations of pattern analysis , 1969 .

[16]  R. Esch,et al.  Computational methods for best spline function approximation , 1969 .

[17]  King-Sun Fu,et al.  Feature Selection in Pattern Recognition , 1970, IEEE Trans. Syst. Sci. Cybern..

[18]  K. Fu.  2 Statistical Pattern Recognition , 1970 .

[19]  Ugo Montanari,et al.  A note on minimal length polygonal approximation to a digitized contour , 1970, CACM.

[20]  T. Pavlidis.  Piecewise Approximation of Functions of Two Variables and Its Application in Topographical Data Reduction. , 1970 .

[21]  SATOSI WATANABE,et al.  Ungrammatical grammar in pattern recognition , 1971, Pattern Recognit..

[22]  H. Bremermann.  A method of unconstrained global optimization , 1970 .

[23]  Claude L. Fennema,et al.  Scene Analysis Using Regions , 1970, Artif. Intell..

[24]  R A Kirsch,et al.  Computer determination of the constituent structure of biological images. , 1971, Computers and biomedical research, an international journal.

[25]  Anthony N. Mucciardi,et al.  A Comparison of Seven Techniques for Choosing Subsets of Pattern Recognition Properties , 1971, IEEE Transactions on Computers.

[26]  P. H. Swain,et al.  On Syntactic Pattern Recognition , 1971 .

[27]  T. Pavlidis.  Linguistic Analysis of Waveforms , 1971 .

[28]  D. Braess.  Chebyshev approximation by spline functions with free knots , 1971 .

[29]  Theodosios Pavlidis,et al.  A Segmentation Technique for Waveform Classification , 1972, IEEE Transactions on Computers.

[30]  Theodosios Pavlidis,et al.  STRUCTURAL PATTERN RECOGNITION: PRIMITIVES AND JUXTAPOSITION RELATIONS* , 1972 .

[31]  Kenneth Steiglitz,et al.  Randomized Pattern Search , 1972, IEEE Transactions on Computers.

[32]  Theodosios Pavlidis,et al.  Segmentation of pictures and maps through functional approximation , 1972, Comput. Graph. Image Process..

[33]  Laveen N. Kanal,et al.  ON LINGUISTIC, STATISTICAL AND MIXED MODELS FOR PATTERN RECOGNITION , 1972 .

[34]  Urs Ramer,et al.  An iterative procedure for the polygonal approximation of plane curves , 1972, Comput. Graph. Image Process..

[35]  T. Pavlidis,et al.  Uniform piecewise polynomial approximation with variable joints , 1974 .