The perceptual organization of texture flow: a contextual inference approach

Ben-Shahar, Ohad; Zucker, Steven W.

doi:10.1109/tpami.2003.1190568

Cited by 69 publications

(84 citation statements)

References 65 publications

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“…For non-planar curves in E 3 , a notion of transport is provided by an osculating helix, as used in [21] for 3D curve inference in diffusion MRI. The more general case of 2D streamline (or texture) flow has been addressed in [5], where a right helicoid model has been used as an osculating object. Extending these ideas to the case of 3D streamline flow is non-trivial and a key contribution of this paper is the use of minimal surface theory to resolve this question.…”

Section: Transportmentioning

confidence: 99%

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On the Differential Geometry of 3D Flow Patterns: Generalized Helicoids and Diffusion MRI Analysis

Savadjiev

Zucker

Siddiqi

2007

2007 IEEE 11th International Conference on Computer Vision

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Configurations of dense locally parallel 3D curves occur in medical imaging, computer vision and graphics. Examples include white matter fibre tracts, textures, fur and hair. We develop a differential geometric characterization of such structures by considering the local behaviour of the associated 3D frame field, leading to the associated tangential, normal and bi-normal curvature functions. Using results from the theory of generalized minimal surfaces we adopt a generalized helicoid model as an osculating object and develop the connection between its parameters and these curvature functions. These developments allow for the construction of parametrized 3D vector fields (sampled osculating objects) to locally approximate these patterns. We apply these results to the analysis of diffusion MRI data via a type of 3D streamline flow. Experimental results on data from a human brain demonstrate the advantages of incorporating the full differential geometry.

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Section: Transportmentioning

confidence: 99%

“…represents a right helicoidal surface over the xy plane in 3D Euclidean space [5], which is known by the classical theorem of Catalan to be a minimal surface in E 3 (see e.g. [1]).…”

Section: Sketch Of Proof Of Propositionmentioning

confidence: 99%

On the Differential Geometry of 3D Flow Patterns: Generalized Helicoids and Diffusion MRI Analysis

Savadjiev

Zucker

Siddiqi

2007

2007 IEEE 11th International Conference on Computer Vision

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“…These two scalars, defined at each point of the ODT, are called its tangential curvature ( T ) and normal curvature ( N ), respectively (16), and they represent the initial rate of change of the ODT orientation in its tangential and normal directions, respectively (Fig. 2).…”

Section: From Geometry To Saliency In Odtsmentioning

confidence: 99%

Visual saliency and texture segregation without feature gradient

Ben-Shahar

2006

Proc. Natl. Acad. Sci. U.S.A.

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A central notion in the study of texture segregation is that of feature gradient (or feature contrast). In orientation-based texture segregation, orientation gradients have indeed played a fundamental role in explaining behavioral results. Here, however, we show that general, smoothly varying, orientation-defined textures (ODTs) exhibit striking perceptual singularities that are completely unpredictable from orientation gradients. These singularities defy not only popular texture segregation theories but also virtually all computational segmentation methods, and they confound previous behavioral studies with smoothly varying ODTs. We provide psychophysical evidence that perceptual singularities in smooth ODTs are salient visual features consistent across observers and with significant effect on the perception and segregation of oriented textures. We further show that, although orientation gradients cannot predict them, perceptual singularities in smooth ODTs emerge directly from, and can be spatially localized by, two ODT curvatures. Given the traditional role of feature gradients in early vision, the significance of these findings extends well beyond orientation-based texture segregation to issues ranging from curve integration and fragment grouping, through the perception of 3D shape, to the functional organization of the primary visual cortex.curvature ͉ perceptual organization ͉ perceptual singularity measure

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“…2(b), as an intensity function of angle (θ) versus position x 1 . It is evident that this output aggregates along a a continuous curve (or submanifold), dubbled a texture flow in the work of [6]. When the exact location of the submanifold of maximum intensity in Fig.…”

Section: Introductionmentioning

confidence: 96%

“…Inspired by the work of [6] we achieve a globally optimal assignment of curvatures to the cortical surface by using a dictionary of smooth flow fields on the surface. Each smooth flow field provides a hypothesis for the slope of the texture A texture manifold depicts change in orientation of the neighboring curves in space flow on the cerebral cortex.…”

Section: Introductionmentioning

confidence: 99%

A Texture Manifold for Curve-Based Morphometry of the Cerebral Cortex

Boucher

Evans

Siddiqi

2011

Medical Computer Vision. Recognition Techniques and Applications in Medical Imaging

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Abstract. The cortical surface of the human brain is composed of folds that are juxtaposed alongside one another. Several methods have been proposed to study the shape of these folds, e.g., by first segmenting them on the cortical surface or by analysis via a continuous deformation of a common template. A major disadvantage of these methods is that, while they can localize shape differences, they cannot easily identify the directions in which they occur. The type of deformation that causes a fold to change in length is quite different from that which causes it to change in width. Furthermore, these two deformations may have a completely different biological interpretation. In this article we propose a method to analyze such deformations using directional filters locally adapted to the geometry of the folding pattern. Motivated by the texture flow literature in computer vision we recover flow fields that maintain a fixed angle with the orientation of folds, over a significant spatial extent. We then trace the flow fields to determine which correspond to the shape changes that are the most salient. Using the OASIS database, we demonstrate that in addition to known regions of atrophy, our method can find subtle but statistically significant shape deformations.

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The perceptual organization of texture flow: a contextual inference approach

Cited by 69 publications

References 65 publications

On the Differential Geometry of 3D Flow Patterns: Generalized Helicoids and Diffusion MRI Analysis

On the Differential Geometry of 3D Flow Patterns: Generalized Helicoids and Diffusion MRI Analysis

Visual saliency and texture segregation without feature gradient

A Texture Manifold for Curve-Based Morphometry of the Cerebral Cortex

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