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The representation of visual information in human striate cortex is of significance to machine vision. Invariance to certain geometrical transformations in the field-of-view may be provided by the computational anatomy of the visual cortex. For example, there is evidence that the retino-cortical mapping is closely approximated by a log-polar transform. When combined with the foveation response, log-polar mapping can provide a basis for translation, rotation, and scale-invariant perception. There is also evidence that the visual system is sensitive to the spatial frequency content of its input. Although a Fourier transform is physiologically implausible, some authors have suggested its use for invariant object recognition because the magnitude of the Fourier transform is shift invariant. The Fourier transform magnitude operation followed by log-polar mapping can also provide a basis for translation, rotation, and scale-invariant perception. Both of these image-transform (feature mapping) algorithms give mathematical invariance to translation, rotation, and dilation. For an automatic recognition system, however, the feature mapping module has to be robust to discretization error, noise, and possible obscuration. Robustness considerations led to the development of the bi- directional log-polar mapping (BPM) algorithm. The BPM algorithm overcomes the pixel- dropout problems associated with conventional approaches to log-polar mapping. The authors evaluate several feature mapping models, both biologically and mathematically inspired, for their effect on recognition performance when embedded in a neural-network-based, object- recognition system. The modular recognition system, consisting of image restoration, detection, segmentation, feature extraction, invariant mapping, and classification, is being developed to classify objects in laser radar range imagery. Synthetic laser radar range images of four vehicles rotated in the field-of-view, scaled to various ranges, and corrupted by increasing levels of sensor noise are used for this evaluation. This study indicates that feature mapping based on the bi-directional log-polar map provides translation, rotation, and scale- invariant recognition capabilities as well as robustness to noise and discretization.
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