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.

The relative efficiency of any particular image-coding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images from the natural environment (i.e., images with trees, rocks, bushes, etc). In this study, various coding schemes are compared in relation to how they represent the information in such natural images. The coefficients of such codes are represented by arrays of mechanisms that respond to local regions of space, spatial frequency, and orientation (Gabor-like transforms). For many classes of image, such codes will not be an efficient means of representing information. However, the results obtained with six natural images suggest that the orientation and the spatial-frequency tuning of mammalian simple cells are well suited for coding the information in such images if the goal of the code is to convert higher-order redundancy (e.g., correlation between the intensities of neighboring pixels) into first-order redundancy (i.e., the response distribution of the coefficients). Such coding produces a relatively high signal-to-noise ratio and permits information to be transmitted with only a subset of the total number of cells. These results support Barlow's theory that the goal of natural vision is to represent the information in the natural environment with minimal redundancy.

/pdf/relations-between-the-statistics-of-natural-images-and-the-12zwc2ox1f.pdf

Relations between the statistics of natural images and the response properties of cortical cells.

We present a system for recognizing human faces from single images out of a large database containing one image per person. Faces are represented by labeled graphs, based on a Gabor wavelet transform. Image graphs of new faces are extracted by an elastic graph matching process and can be compared by a simple similarity function. The system differs from the preceding one (Lades et al., 1993) in three respects. Phase information is used for accurate node positioning. Object-adapted graphs are used to handle large rotations in depth. Image graph extraction is based on a novel data structure, the bunch graph, which is constructed from a small get of sample image graphs.

/pdf/face-recognition-by-elastic-bunch-graph-matching-1ibe7ukghh.pdf

Face recognition by elastic bunch graph matching

We present a system for recognizing human faces from single images out of a large database with one image per person. The task is difficult because of image variation in terms of position, size, expression, and pose. The system collapses most of this variance by extracting concise face descriptions in the form of image graphs. In these, fiducial points on the face (eyes, mouth etc.) are described by sets of wavelet components (jets). Image graph extraction is based on a novel approach, the bunch graph, which is constructed from a small set of sample image graphs. Recognition is based on a straight-forward comparison of image graphs. We report recognition experiments on the FERET database and the Bochum database, including recognition across pose.

/pdf/face-recognition-by-elastic-bunch-graph-matching-21u1r888mk.pdf

Face Recognition by Elastic Bunch Graph Matching

A method for extracting information about facial expressions from images is presented. Facial expression images are coded using a multi-orientation multi-resolution set of Gabor filters which are topographically ordered and aligned approximately with the face. The similarity space derived from this representation is compared with one derived from semantic ratings of the images by human observers. The results show that it is possible to construct a facial expression classifier with Gabor coding of the facial images as the input stage. The Gabor representation shows a significant degree of psychological plausibility, a design feature which may be important for human-computer interfaces.

https://www.computer.org/csdl/pds/api/csdl/proceedings/download-article/12OmNB8kHXW/pdf

Coding facial expressions with Gabor wavelets

Adjacent simple cells recorded and "isolated" simultaneously from the same microelectrode placement were usually tuned to the same orientation and spatial frequency. The responses of the members of these "spatial frequency pairs" to drifting sine-wave gratings were cross-correlates. Within the middle range of the spatial frequency selectivity curves, the responses of the paired cells differed in phase by approximately 90 percent. This phase relationship suggests that adjacent simple cells tuned to the same spatial frequency and orientation represent paired sine and cosine filters in terms of their processing of afferent spatial inputs and truncated sine and cosine filters in terms of the output of simple cells.

Phase relationships between adjacent simple cells in the visual cortex

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Phase relationships between adjacent simple cells in the visual cortex