A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Representation of local geometry in the visual system
Biological Cybernetics
The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generic Neighborhood Operators
IEEE Transactions on Pattern Analysis and Machine Intelligence
Edge Detection and Ridge Detection with Automatic Scale Selection
International Journal of Computer Vision
Deformable Kernels for Early Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Slow feature analysis: unsupervised learning of invariances
Neural Computation
Biophysiologically plausible implementations of the maximum operation
Neural Computation
Image Representation by Complex Cell Responses
Neural Computation
IEEE Transactions on Signal Processing
Shiftable multiscale transforms
IEEE Transactions on Information Theory - Part 2
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The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modeled by Gabor functions or gaussian derivatives. Gabor functions can also be combined in an energy model of the complex cell response. This letter proposes an alternative model of the complex cell, based on gaussian derivatives. It is most important to account for the insensitivity of the complex response to small shifts of the image. The new model uses a linear combination of the first few derivative filters, at a single position, to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model, unlike previous approaches, is based on the scale space theory of visual processing. In particular, the complex cell is built from filters that respond to the 2D differential structure of the image. The computational aspects of the new model are studied in one and two dimensions, using the steerability of the gaussian derivatives. The response of the model to basic images, such as edges and gratings, is derived formally. The response to natural images is also evaluated, using statistical measures of shift insensitivity. The neural implementation and predictions of the model are discussed.