Showing papers by "David J. Heeger published in 1998"

Robust anisotropic diffusion

Abstract: Relations between anisotropic diffusion and robust statistics are described in this paper. Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The "edge-stopping" function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework. This connection leads to a new "edge-stopping" function based on Tukey's biweight robust estimator that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in an image that has been smoothed with anisotropic diffusion. Additionally, we derive a relationship between anisotropic diffusion and regularization with line processes. Adding constraints on the spatial organization of the line processes allows us to develop new anisotropic diffusion equations that result in a qualitative improvement in the continuity of edges.

Functional Magnetic Resonance Imaging of Early Visual Pathways in Dyslexia

Abstract: We measured brain activity, perceptual thresholds, and reading performance in a group of dyslexic and normal readers to test the hypothesis that dyslexia is associated with an abnormality in the magnocellular (M) pathway of the early visual system. Functional magnetic resonance imaging (fMRI) was used to measure brain activity in conditions designed to preferentially stimulate the M pathway. Speed discrimination thresholds, which measure the minimal increase in stimulus speed that is just noticeable, were acquired in a paradigm modeled after a previous study of M pathway-lesioned monkeys. Dyslexics showed reduced brain activity compared with controls both in primary visual cortex (V1) and in several extrastriate areas, including area MT and adjacent motion-sensitive areas (MT+) that are believed to receive a predominant M pathway input. There was a strong three-way correlation between brain activity, speed discrimination thresholds, and reading speed. Subjects with higher V1 and MT+ responses had lower perceptual thresholds (better performance) and were faster readers. These results support the hypothesis for an M pathway abnormality in dyslexia and imply strong relationships between the integrity of the M pathway, visual motion perception, and reading ability.

Theory and applications of steerable functions

Abstract: A function is called steerable if transformed versions of the function can be expressed using linear combinations of a fixed set of basis functions. Steerability is a very general and often desirable property. As a result, steerable functions have recently been applied to an assortment of problems in image processing, computer vision, and computer graphics. In this dissertation, we propose a framework, based on Lie group theory, for studying and constructing functions steerable under any smooth transformation group. We argue that Lie theory is the appropriate mathematical tool for analyzing the properties of these steerable functions. This position is supported by the fact that all existing analytical approaches to steerability can be consistently explained within the framework. The design of a suitable set of basis functions given any arbitrary steerable function is one of the main problems concerning steerable functions. To this end, we have developed two very different algorithms. The first algorithm is a symbolic method that can be implemented in any symbolic package. This algorithm derives the minimal set of basis functions automatically given an arbitrary steerable function. The second algorithm addresses two practical considerations: approximate steerability and local steerability. In practice, functions that need to be steered might not be steerable with a finite number of basis functions. Moreover, it is often the case that only a small subset of transformations within the group of transformations needs to be considered. In response to these two concerns, the second algorithm computes the optimal set of k basis functions to steer an arbitrary function under a subset of the group of transformations. Lastly, we demonstrate the usefulness of steerable functions in a variety of applications. In particular, we present five applications that use steerable functions: (1) continuum approximation in modeling human vision (a method of approximating an infinite number of interacting mechanisms in a model), (2) the design of optimal steerable filters for gradient-based motion estimation, (3) efficient linear re-rendering of synthetic scenes under changes in illumination, (4) the construction of invariants from steerable filters, and (5) the application of steerable functions to discrete sets of points and lines.

Modeling activity-dependent development in the retinogeniculate projection

Abstract: In higher mammals, the primary visual pathway starts with the ("retinogeniculate") projection from the retina to the dorsal lateral geniculate nucleus (dLGN) of the thalamus, which in turn projects to visual cortex. Although the retinal axons initially innervate the dLGN in a relatively disorganized manner, they are precisely arranged by maturity. Some dominant features of this organization emerge only under the influence of activity, yet these features are established before eye-opening or photoreceptor function. The crucial activity is supplied by spontaneous bursts of action potentials that propagate in waves across the immature retinal ganglion cell layer that projects to the dLGN. Under the influence of retinal activity, the retinal axons segregate into eye-specific layers, on/off sublayers, and precise retinotopic maps. This dissertation describes a formal computational framework for modeling and exploring the activity-dependent development of the retinogeniculate projection. The model is the first to support the development of layers, sublayers, and retinotopy in a unified framework. The model is constructed so as to be directly biologically interpretable and predictive. It refines based on realistic patterns of wave activity, retinal axon arbor change, and Hebbian synaptic weight change. In addition, the model is relatively tractable to formal analysis. This tractability makes the model relatively undemanding to simulate computationally and provides analytic insight into the dynamics of the model refinement. Several experimental predictions that follow directly from the model are described.

Rapid communication Psychophysical evidence for a magnocellular pathway deficit in dyslexia

Abstract: The relationship between reading ability and psychophysical performance was examined to test the hypothesis that dyslexia is associated with a deficit in the magnocellular (M) pathway. Speed discrimination thresholds and contrast detection thresholds were measured under conditions (low mean luminance, low spatial frequency, high temporal frequency) for which psychophysical performance presumably depends on M pathway integrity. Dyslexic subjects had higher psychophysical thresholds than controls in both the speed discrimination and contrast detection tasks, but only the differences in speed thresholds were statistically significant. In addition, there was a strong correlation between individual differences in speed thresholds and reading rates. These results support the hypothesis for an M pathway abnormality in dyslexia, and suggest that motion discrimination may be a more sensitive psychophysical predictor of dyslexia than contrast sensitivity. © 1998 Elsevier Science Ltd. All rights reserved.

A computational model of retinogeniculate development

Abstract: The retinal projection to the lateral geniculate nucleus (LGN) of the thalamus (the “retinogeniculate projection”) has become an ideal system for studying activity- dependent neural development. As the primary visual pathway to the cortex it is well studied, and it develops complex structures under the influence of spontaneous activity. Three models of development in the retinogeniculate system have been suggested.1,2,3 None of these models encompasses the full range of structural refinement in the system and none considers the physiological development of LGN neurons. This paper attempts to provided a cohesive, realistic, and biologically predictive framework in which to investigate the development of retinotopy, eye-specific layers and on/off sub-layers in the retinogeniculate projection. A brief introduction to the biological system will help situate the model.

Method for embedding signals in a color image

Abstract: A signal component (e.g., a period signal component such as a sinusoid) is added (210) to an original color image to form a modified color image, with the goal of embedding the signal in the image so that it is imperceptible to a human viewer. A comparing operation (240) uses a model of human perception to measure the perceptual difference between the original and modified images, identifying local areas of the modified image where the signal difference exceeds a threshold, indicating that the signal is perceptible to a human viewer. Using the perceptual difference measurement data; the signal is attenuated in the identified local areas that indicate a perceptually unacceptable difference, and this modified signal component is then added (210) to the original color image in a next iteration. Perceptual difference measurement and signal attenuation are iterated until the comparison operation determines that the signal difference is perceptually acceptable. The technique takes advantage of the fact that, although the spatial frequencies of the embedded signals are well within the range of spatial frequencies to which humans are normally quite sensitive in the luminance (black-white) vision channel, this sensitivity does not extend to the color vision bands. In an illustrated embodiment, a set of sinusoidal signals that form a grid are added to the color image; location (i.e., decoding) of the sinusoids, which does not require the original color image, allows computing a geometric mapping from an image with the embedded signals to the original image.

Machine operation method

Abstract: PROBLEM TO BE SOLVED: To provide a method of forming a corrected color image by adding an unperceivable signal to an original image without using the original image. SOLUTION: In this machine operation method, a color image I'(x, y) corrected by adding a signal S (x, y) to an original image I(x, y) is generated (210) and a human perception model is used to measure a perception difference ΔE(x, y) between the original color image I(x, y) and the corrected color image I'(x, y) (240), the perception difference ΔE(x, y) and a threshold value are compared to specify an area where the perception difference ΔE(x, y) is perceived by a human observer (270), a signal S (x, y) is attenuated in the area and an unperceivable difference is added to the original color image I(x, y).