Edge blur, a prevalent feature of natural images, is believed to facilitate multiple visual processes including segmentation and depth perception. Furthermore, image descriptions that explicitly combine blur and shape information provide complete representations of naturalistic scenes. Here we report the first demonstration of blur encoding in primate visual cortex: neurons in macaque V4 exhibit tuning for both object shape and boundary blur, with observed blur tuning not explained by potential confounds including stimulus size, intensity, or curvature. A descriptive model wherein blur selectivity is cast as a distinct neural process that modulates the gain of shape-selective V4 neurons explains observed data, supporting the hypothesis that shape and blur are fundamental features of a sufficient neural code for natural image representation in V4.
The midlevel visual cortical area V4 in the primate is thought to be critical for the neural representation of visual shape. Several studies agree that V4 neurons respond to contour features, e.g., convexities and concavities along a shape boundary, that are more complex than the oriented segments encoded by neurons in the primary visual cortex. Here we compare two distinct approaches to modeling V4 shape selectivity: one based on a spectral receptive field (SRF) map in the orientation and spatial frequency domain and the other based on a map in an object-centered angular position and contour curvature space. We test the ability of these two characterizations to account for the responses of V4 neurons to a set of parametrically designed two-dimensional shapes recorded previously in the awake macaque. We report two lines of evidence suggesting that the SRF model does not capture the contour sensitivity of V4 neurons. First, the SRF model discards spatial phase information, which is inconsistent with the neuronal data. Second, the amount of variance explained by the SRF model was significantly less than that explained by the contour curvature model. Notably, cells best fit by the curvature model were poorly fit by the SRF model, the latter being appropriate for a subset of V4 neurons that appear to be orientation tuned. These limitations of the SRF model suggest that a full understanding of midlevel shape representation requires more complicated models that preserve phase information and perhaps deal with object segmentation.
This paper presents a sparse representation of 2D planar shape through the composition of warping functions, termed formlets, localized in scale and space. Each formlet subjects the 2D space in which the shape is embedded to a localized isotropic radial deformation. By constraining these localized warping transformations to be diffeomorphisms, the topology of shape is preserved, and the set of simple closed curves is closed under any sequence of these warpings. A generative model based on a composition of formlets applied to an embryonic shape, e.g., an ellipse, has the advantage of synthesizing only those shapes that could correspond to the boundaries of physical objects. To compute the set of formlets that represent a given boundary, we demonstrate a greedy coarse-to-fine formlet pursuit algorithm that serves as a non-commutative generalization of matching pursuit for sparse approximations. We evaluate our method by pursuing partially occluded shapes, comparing performance against a contour-based sparse shape coding framework.
Perceptual grouping of the bounding contours of objects is a crucial step in visual scene understanding and object recognition. The standard perceptual model for this task, supported by a convergence of physiological and psychophysical evidence, is based upon an association field that governs local grouping, and a Markov or transitivity assumption that allows global contours to be inferred solely from these local cues. However, computational studies suggest that these local cues may not be sufficient for reliable identification of object boundaries in natural scenes. Here we employ a novel psychophysical method to assess the potential role of more global factors in the perceptual grouping of natural object contours. Observers were asked to detect briefly presented fragmented target contours in oriented element noise. We employed natural animal shape stimuli, which in addition to local grouping cues possess global regularities that could potentially be exploited to guide grouping and thereby improve target detection performance. To isolate the role of these global regularities we contrasted performance with open and closed control target stimuli we call local metamers, as they afford the same local grouping cues as animal shapes. We found that performance for closed metamers exceeded performance for open metamers, while performance for animal targets exceeded both, indicating that global grouping cues represented in higher visual areas codetermine the association between orientation signals coded in early visual cortex. These results demand a revision to the standard model for perceptual grouping of contours to accommodate feedback from higher visual areas coding global shape properties.
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