Walsh-Hadamard Transformations in Image Processing

摘要

A technique is presented for obtaining the Walsh-Hadamard (W-H) transform of a picture in real-time by operating separately on each picture line. Overlap of scanning and computations, results in savings of the total time required to transform a picture. For digital computer processing core storage requirements are reduced. The technique leads to the hardware implementation of a machine capable of performing real-time parallel W-H transformation. The 'axis-symmetry' parameter of the Walsh functions is defined and the axis-symmetry number and the period of a Walsh function are derived from its sequency number. Analysis of Walsh spectra establishes the relations between image samples and Walsh spectrum coefficients. Walsh functions are used in designing a feature extractor. The axis-symmetry histogram is obtained from the Walsh spectrum of a pattern by adding the squares of the spectrum coefficients that correspond to a given axis-symmetry number tau and plotting these against tau. Axis-symmetry histograms result in great dimensionality in the feature space. (Author)