The Nonlinear Geometry of Visual Neurons

Our current project is funded by a Google Faculty Research Award to David.

Recent Papers

Efficiency in visual systems

Sparse coding

The image to the right demonstrates the results of the sparse coding network with natural scenes described by Olshausen and Field (1996). Matlab software to run this algorithm is available from Bruno Olshausen's website. Such sparse components show a number of similarities to receptive fields of V1 simple cells. Several theoretical, computational, and experimental studies suggest that neurons encode sensory information using a small number of active neurons at any given point in time. This strategy, referred to as 'sparse coding', could possibly confer several advantages. First, it allows for increased storage capacity in associative memories; second, it makes the structure in natural signals explicit; third, it represents complex data in a way that is easier to read out at subsequent levels of processing; an d fourth, it saves energy. Recent physiological recordings from sensory neurons have indicated that sparse coding could be a ubiquitous strategy employed in several different modalities across different organisms.

For recent reviews, see:

• Graham and Field (2006): Sparse coding in the neocortex
• Olshausen and Field (2005): How close are we to understanding V1?
• Olshausen and Field (2004): What is the other 85% of V1 doing?

Related publications include:

• Graham, Chandler, and Field (2006): Can the theory of whitening explain the center-surround properties of retinal ganglion cell receptive fields?
• Olshausen and Field (2000): Vision and the Coding of Natural Images
• Field (1999): Wavelets, vision and the statistics of natural scenes
• Field (1999): Matched filters, wavelets and the statistics of natural scenes
• Field (1998): Visual Coding, Redundancy, and "Feature Detection"
• Olshausen and Field (1997): Sparse coding with an overcomplete basis set...
• Olshausen and Field (1996): Emergence of simple-cell receptive field properties by learning a sparse code for natural images
• Field (1994): What is the goal of sensory coding?
• Field (1994): Optimal coding of natural scenes
• Field (1993): Scale-invariance and self-similar 'wavelet' transforms...
• Field (1989): What the statistics of natural images tell us about visual coding
• Field (1987): Relations between the statistics of natural images and the response properties of cortical cells

Other publications related to theories of efficiency in visual systems:

• Webster, Werner, and Field (2005): Adaptation and the phenomenology of perception
• Brady and Field (2000): Local contrast in natural images: normalisation and coding efficiency

Modeling the self-similar structure in natural scenes

Natural scenes are approximately scale invariant with regards to both their power spectra and their phase spectra. Principally because of the phase spectra, wavelet-like transforms are capable of producing a sparse, informative representation of these images. Self-similar codes like the wavelet are effective for many natural phenomena because such phenomena show similar structures to those found in natural scenes. The processing of spatial patterns by the mammalian visual system shows a number of similarities to the 'wavelet transforms' which have attracted considerable interest outside of the study of sensory systems.

• The above image was created with algorithms based on Field 1993, 1994
• Explore a demonstration of multiscale self-similar structure with this AVI movie.

Contour integration by the human visual system

Above are examples of stimuli used in Field, Hayes, and Hess 1993. Move your mouse pointer over the images to see the path of elements that has been embedded in an array of randomly oriented elements (non-IE browsers only).

These stimuli were used in experiments to determine the rules that govern the perception of continuity. Using a forced-choice procedure, observers were found to be capable of identifying the path within a field of randomly-oriented elements eve n when the spacing between the elements was considerably larger than the size of any of the individual elements.

When the elements were oriented at angles up to +-60 deg relative to one another, the path was reliably identified. Alignment of the elements along the path was found to play a large role in the ability to detect the path. Small variations in the alignment or aligning the elements orthogonally significantly reduced the observer's ability to detect the presence of a path.

Related publications include:

• Field and Hayes (2004): Contour integration and the lateral connections of V1 neurons
• Hess, Hayes, and Field (2003): Contour integration and cortical processing
• Hess and Field (1999): Integration of contours: new insights
• Hess, McIlhagga, and Field (1997): Contour integration in strabismic amblyopia...
• Field, Hayes, and Hess (1997): The role of phase and contrast polarity in contour integration
• Hess and Field (1995): Contour integration across depth
• Field, Hayes, and Hess (1993): Contour integration by the human visual system...

Art and Natural Scenes

Related publications include:

• Graham and Field (2008): Variations in Intensity Statistics for Representational and Abstract Art, and for Art from the Eastern and Western Hemispheres
• Graham and Field (2007): Statistical regularities of art images and natural scenes: Spectra, sparseness and nonlinearities

Blur and Myopia

Related publications include:

• Hess, Schmidt, Dumoulin, and Field (2006): What regulates eye growth: image features or frequencies?
• Field and Brady (1997): Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes

Amblyopia

Related publications include:

• Hess, McIlhagga, and Field (1997): Contour integration in strabismic amblyopia...
• Hess and Field (1994): Are the spatial deficits in amblyopia due to uncalibrated disarray?
• Hess and Field (1993): Is the increased spatial uncertainty in the normal periphery due to spatial undersampling or uncalibrated disarray?

Psychophysics

Related publications include:

• Kingdom, Hayes, and Field (2001): Sensitivity to contrast histogram differences in synthetic wavelet-textures
• Field, Hayes, and Hess (2000): The roles of polarity and symmetry in the perceptual grouping of contour fragments
• Dakin, Hess, and Field (1998): Rapid communication...
• Brady and Field (1995): What's constant in contrast constancy...
• Knill, Field, and Kersten (1990): Human discrimination of fractal images
• Field and Nachmias (1984): Phase reversal discrimination

Physiology

Related publications include:

• Field and Tolhurst (1986): The structure and symmetry of simple cell receptive-field profiles in the cat's visual cortex

Top Cited

The following publications appear on Yury Petrov's list of Top 100 Vision Papers