Visual Image Analysis by Square Wavelets: Empirical Evidence Supporting a Theoretical Agreement between Wavelet Analysis and Receptive Field Organization of Visual Cortical Neurons

Abstract

It was proposed that the human visual system analyzes images into square wavelets. To test this view, comparisons were made between the perceived similarity-dissimilarity of alphabet letters and the wavelet analyses of those same letters. For the proposal to be considered tenable, the coefficients of the wavelet analysis of similar letters must be similar, and the coefficients of the wavelet analysis of dissimilar letters must be dissimilar. From a selection of 12 letters, four pairs of letters had been reported by Van der Heijden, Malhas, and Van den Roovaart as very similar, and four other pairs of letters dissimilar. Each of the 12 letters was separately depicted in 8×8 matrices, and the signal represented by each of the matrices was analyzed into square wavelets using a new and original procedure which yielded a single set of coefficients for each matrix. Correlations between sets of coefficients were high ( r ranged from .88 to 58) for those letter pairs judged high in similarity; correlations were low ( r ranged from −02 to .29) for those letter pairs judged low in similarity. When the correlations between the coefficients of wavelets of all eight-letter pairs were compared with the judged similarity-dissimilarity of all eight-letter pairs, the linear agreement was statistically significant. Agreement was found between the neurophysiological mapping of receptive fields of visual cortical neurons and the vectors or the pattern of pluses and minuses which characterized the wavelet analysis. Furthermore, regeneration of the visual image, or the pattern of neural activity representing the image, could be described by a tree-like flow of information among visual cortical neurons which received response data from visual receptive fields, the response data being wavelet coefficients. Results indicate the analysis accurately produces reliable transformations of visual patterns and may be a process used by the visual system.