The Converging Squares Algorithm: An Efficient Method for Locating Peaks in Multidimensions

The converging squares algorithm is a method for locating peaks in sampled data of two dimensions or higher. There are two primary advantages of this algorithm over conventional methods. First, it is robust with respect to noise and data type. There are no empirical parameters to permit adjustment of the process, so results are completely objective. Second, the method is computationally efficient. The inherent structure of the algorithm is that of a resolution pyramid. This enhances computational efficiency as well as contributing to the quality of noise immunity of the method. The algorithm is detailed for two-dimensional data, and is described for three-dimensional data. Quantitative comparisons of computation are made with two conventional peak picking methods. Applications to biomedical image analysis, and for industrial inspection tasks are discussed.

[1]  Marvin Minsky,et al.  Steps toward Artificial Intelligence , 1995, Proceedings of the IRE.

[2]  Azriel Rosenfeld,et al.  Algorithms and Hardware Technology for Image Recognition , 1976 .

[3]  R. Cabot.  A note on the application of the Hilbert transform to time delay estimation , 1981 .

[4]  J. R. Jordan,et al.  Correlation-function peak detector , 1981 .

[5]  S. Levialdi,et al.  Basics of cellular logic with some applications in medical image processing , 1979, Proceedings of the IEEE.

[6]  J. A. Cox.  Evaluation Of Peak Location Algorithms With Subpixel Accuracy For Mosaic Focal Planes , 1981, Optics & Photonics.

[7]  Allen Newell,et al.  Report on a general problem-solving program , 1959, IFIP Congress.

[8]  Azriel Rosenfeld,et al.  Peak Detection Using Difference Operators , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Steven L. Horowitz,et al.  A syntactic algorithm for peak detection in waveforms with applications to cardiography , 1975, Commun. ACM.

[10]  E. Hall,et al.  Hierarchical search for image matching , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[11]  Azriel Rosenfeld,et al.  Hierarchical Representation of Waveforms , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.