A general framework for low level vision

Sochen, Nir; Kimmel, Ron; Malladi, R.

doi:10.1109/83.661181

Cited by 553 publications

(447 citation statements)

References 42 publications

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“…To increase the detection sensitivity to changes in surface-based data, it is possible to run a time-dependent PDE, such as a LaplaceBeltrami flow, in the parameter space of the surface. This produces a scale space of diffused data I(x, t) (Chung et al, 2001a,b;Nielsen et al, 1994;Sochen et al, 1998;Worsley, 1996) on the cortex. This acts as a prefilter to enhance detection of effects at different scales (Huiskamp, 1991): I(x, t n + 1 ) = I(x, t n ) + Dt.j 2 LB I(x, t n + 1 ).…”

Section: Parameterization Of the Time Axismentioning

confidence: 99%

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

et al. 2004

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This paper describes algorithms that can identify patterns of brain structure and function associated with Alzheimer's disease, schizophrenia, normal aging, and abnormal brain development based on imaging data collected in large human populations. Extraordinary information can be discovered with these techniques: dynamic brain maps reveal how the brain grows in childhood, how it changes in disease, and how it responds to medication. Genetic brain maps can reveal genetic influences on brain structure, shedding light on the nature-nurture debate, and the mechanisms underlying inherited neurobehavioral disorders. Recently, we created time-lapse movies of brain structure for a variety of diseases. These identify complex, shifting patterns of brain structural deficits, revealing where, and at what rate, the path of brain deterioration in illness deviates from normal. Statistical criteria can then identify situations in which these changes are abnormally accelerated, or when medication or other interventions slow them. In this paper, we focus on describing our approaches to map structural changes in the cortex. These methods have already been used to reveal the profile of brain anomalies in studies of dementia, epilepsy, depression, childhoodand adult-onset schizophrenia, bipolar disorder, attention-deficit/ hyperactivity disorder, fetal alcohol syndrome, Tourette syndrome, Williams syndrome, and in methamphetamine abusers. Specifically, we describe an image analysis pipeline known as cortical pattern matching that helps compare and pool cortical data over time and across subjects. Statistics are then defined to identify brain structural differences between groups, including localized alterations in cortical thickness, gray matter density (GMD), and asymmetries in cortical organization. Subtle features, not seen in individual brain scans, often emerge when population-based brain data are averaged in this way. Illustrative examples are presented to show the profound effects of development and various diseases on the human cortex. Dynamically spreading waves of gray matter loss are tracked in dementia and schizophrenia, and these sequences are related to normally occurring changes in healthy subjects of various ages. D 2004 Published by Elsevier Inc.

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Section: Parameterization Of the Time Axismentioning

confidence: 99%

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

et al. 2004

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“…The second step, the enhancement stage, involves an anisotropic inverse diffusion flow in color space, which is an extension of Gabor's geometric filter [6], and is based on the geometric framework for color introduced in [8] and [11]. It is also related to Weickert's texture enhancement method [12], and to the recent results of Sapiro and Ringach [10], and Cottet and El Ayyadi [2].…”

Section: Introductionmentioning

confidence: 99%

Demosaicing: Image reconstruction from color CCD samples

Kimmel

1998

Computer Vision — ECCV'98

163

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Abstract-A simplified color image formation model is used to construct an algorithm for image reconstruction from CCD sensors samples. The proposed method involves two successive steps. The first is motivated by Cok's template matching technique, while the second step uses steerable inverse diffusion in color. Classical linear signal processing techniques tend to oversmooth the image and result in noticeable color artifacts along edges and sharp features. The question is how should the different color channels support each other to form the best possible reconstruction. Our answer is to let the edges support the color information, and the color channels support the edges, and thereby achieve better perceptual results than those that are bounded by the sampling theoretical limit.Index Terms-Color enhancement, image reconstruction, multichannel nonlinear image processing, steerable inverse diffusion.

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“…Geometric flows have become an established approach to image analysis, data processing and surface generation in the past two decades. Particularly, the application of mean curvature flows has been a popular subject in applied mathematics for image analysis, material design [40, 49, 50] and surface processing [71]. The first use of partial differential equations (PDEs) for image analysis dates back to 1983 [64].…”

Section: Introductionmentioning

confidence: 99%

High-order fractional partial differential equation transform for molecular surface construction

Chen

Wei

2012

Computational and Mathematical Biophysics

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Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

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A general framework for low level vision

Cited by 553 publications

References 42 publications

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

Demosaicing: Image reconstruction from color CCD samples

High-order fractional partial differential equation transform for molecular surface construction

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