Two-dimensional spatial linear filters are constrained by general uncertainty relations that limit their attainable information resolution for orientation, spatial frequency, and two-dimensional (2D) spatial position. The theoretical lower limit for the joint entropy, or uncertainty, of these variables is achieved by an optimal 2D filter family whose spatial weighting functions are generated by exponentiated bivariate second-order polynomials with complex coefficients, the elliptic generalization of the one-dimensional elementary functions proposed in Gabor’s famous theory of communication [ J. Inst. Electr. Eng.93, 429 ( 1946)]. The set includes filters with various orientation bandwidths, spatial-frequency bandwidths, and spatial dimensions, favoring the extraction of various kinds of information from an image. Each such filter occupies an irreducible quantal volume (corresponding to an independent datum) in a four-dimensional information hyperspace whose axes are interpretable as 2D visual space, orientation, and spatial frequency, and thus such a filter set could subserve an optimally efficient sampling of these variables. Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial–2D-spectral information resolution. The variety of their receptive-field dimensions and orientation and spatial-frequency bandwidths, and the correlations among these, reveal several underlying constraints, particularly in width/length aspect ratio and principal axis organization, suggesting a polar division of labor in occupying the quantal volumes of information hyperspace. Such an ensemble of 2D neural receptive fields in visual cortex could locally embed coarse polar mappings of the orientation–frequency plane piecewise within the global retinotopic mapping of visual space, thus efficiently representing 2D spatial visual information by localized 2D spectral signatures.

Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters.

Neuronal Synchrony: A Versatile Code for the Definition of Relations?

We introduce a new general framework for the recognition of complex visual scenes, which is motivated by biology: We describe a hierarchical system that closely follows the organization of visual cortex and builds an increasingly complex and invariant feature representation by alternating between a template matching and a maximum pooling operation. We demonstrate the strength of the approach on a range of recognition tasks: From invariant single object recognition in clutter to multiclass categorization problems and complex scene understanding tasks that rely on the recognition of both shape-based as well as texture-based objects. Given the biological constraints that the system had to satisfy, the approach performs surprisingly well: It has the capability of learning from only a few training examples and competes with state-of-the-art systems. We also discuss the existence of a universal, redundant dictionary of features that could handle the recognition of most object categories. In addition to its relevance for computer vision, the success of this approach suggests a plausibility proof for a class of feedforward models of object recognition in cortex

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Robust Object Recognition with Cortex-Like Mechanisms

Properties of the receptive fields of simple cells in macaque cortex were compared with properties of independent component filters generated by independent component analysis (ICA) on a large set of natural images. Histograms of spatial frequency bandwidth, orientation tuning bandwidth, aspect ratio and length of the receptive fields match well. This indicates that simple cells are well tuned to the expected statistics of natural stimuli. There is no match, however, in calculated and measured distributions for the peak of the spatial frequency response: the filters produced by ICA do not vary their spatial scale as much as simple cells do, but are fixed to scales close to the finest ones allowed by the sampling lattice. Possible ways to resolve this discrepancy are discussed.

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Independent component filters of natural images compared with simple cells in primary visual cortex.

We recorded from single neurons in the middle temporal visual area (MT) of the macaque monkey and studied their direction and orientation selectivity. We also recorded from single striate cortex (V1) neurons in order to make direct comparisons with our observations in area MT. All animals were immobilized and anesthetized with nitrous oxide. Direction selectivity of 110 MT neurons was studied with three types of moving stimuli: slits, single spots, and random-dot fields. All of the MT neurons were found to be directionally selective using one or more of these stimuli. MT neurons exhibited a broad range of direction-tuning bandwidths to all stimuli (minimum = 32 degrees, maximum = 186 degrees, mean = 95 degrees). On average, responses were strongly unidirectional and of similar magnitude for all three stimulus types. Orientation selectivity of 89 MT neurons was studied with stationary flashed slits. Eighty-three percent were found to be orientation selective. Overall, orientation-tuning bandwidths were significantly narrower (mean = 64 degrees) than direction-tuning bandwidths for moving stimuli. Moreover, responses to stationary-oriented stimuli were generally smaller than those to moving stimuli. Direction selectivity of 55 V1 neurons was studied with moving slits; orientation selectivity of 52 V1 neurons was studied with stationary flashed slits. In V1, compared with MT, direction-tuning bandwidths were narrower (mean = 68 degrees). Moreover, V1 responses to moving stimuli were weaker, and bidirectional tuning was more common. The mean orientation-tuning bandwidth in V1 was also significantly narrower than that in MT (mean = 52 degrees), but the responses to stationary-oriented stimuli were of similar magnitude in the two areas. We examined the relationship between optimal direction and optimal orientation for MT neurons and found that 61% had an orientation preference nearly perpendicular to the preferred direction of motion, as is the case for all V1 neurons. However, another 29% of MT neurons had an orientation preference roughly parallel to the preferred direction. These observations, when considered together with recent reports claiming sensitivity of some MT neurons to moving visual patterns (39), suggest specific neural mechanisms underlying pattern-motion sensitivity in area MT. These results support the notion that area MT represents a further specialization over area V1 for stimulus motion processing. Furthermore, the marked similarities between direction and orientation tuning in area MT in macaque and owl monkey support the suggestion that these areas are homologues.

Norva Hepler

Papers

The orientation and direction selectivity of cells in macaque visual cortex