Weighted Fourier Series Representation and Its Application to Quantifying the Amount of Gray Matter

Chung, Moo K.; Dalton, Kim M.; Shen, Li; Evans, Alan C.; Davidson, Richard J.

doi:10.1109/tmi.2007.892519

Cited by 173 publications

(208 citation statements)

References 51 publications

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“…The signal µ is estimated using heat kernel smoothing [5] and plotted as the red line. Now we increase y from −∞ to ∞.…”

Section: #R(hmentioning

confidence: 99%

“…The cortical thickness is mapped onto a unit sphere and goes through heat kernel smoothing [5] Among various cortical measures, in this paper we consider cortical thickness, which has been used in characterizing various clinical populations [6] [38]. High resolution magnetic resonance images of age-matched right-handed males (6 high functioning autistic and 11 normal controls) were obtained using a 3-Tesla GE SIGNA scanner.…”

Section: Figmentioning

confidence: 99%

“…where µ is the unknown mean signal, to be estimated, and is noise [5] [15] [19] [20] [26] [37]. The unknown signal is usually estimated by various spatial image smoothing techniques over M. The most widely used smoothing technique is kernel smoothing and its variants because of their simplicity, and because they provide the theoretical context for scale spaces and Gaussian random field theory [33] [37].…”

Section: Introductionmentioning

confidence: 99%

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Persistence Diagrams of Cortical Surface Data

Chung

Bubenik

Kim

2009

Lecture Notes in Computer Science

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Abstract. We present a novel framework for characterizing signals in images using techniques from computational algebraic topology. This technique is general enough for dealing with noisy multivariate data including geometric noise. The main tool is persistent homology which can be encoded in persistence diagrams. These are scatter plots of paired local critical values of the signal. One of these diagrams visually shows how the number of connected components of the sublevel sets of the signal changes. The use of local critical values of a function differs from the usual statistical parametric mapping framework, which mainly uses the mean signal in quantifying imaging data. Our proposed method uses all the local critical values in characterizing the signal and by doing so offers a completely new data reduction and analysis framework for quantifying the signal. As an illustration, we apply this method to a 1D simulated signal and 2D cortical thickness data.

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“…The signal µ is estimated using heat kernel smoothing [5] and plotted as the red line. Now we increase y from −∞ to ∞.…”

Section: #R(hmentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Persistence Diagrams of Cortical Surface Data

Chung

Bubenik

Kim

2009

Lecture Notes in Computer Science

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“…An outer cortical surface M is assumed to be a smooth 2D Riemannian manifold topologically equivalent to a unit sphere [8] [5]. The outer cortical surface is obtained from a T 1 -weighted magnetic resonance image using a deformable surface algorithm [12] and represented as a triangle mesh consisting of 40,962 vertices and 81,920 triangles ( Figure 1).…”

Section: Methodsmentioning

confidence: 99%

Encoding Neuroanatomical Information using Weighted Spherical Harmonic Representation

Chung

Dalton

Davidson

2007

2007 IEEE/SP 14th Workshop on Statistical Signal Processing

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Cortical surfaces can be modeled using the recently developed weighed spherical harmonic (SPHARM) representation. The weighted-SPHARM representation incorporates data smoothing, parametrization and surface registration in a unified mathematical framework. The weighted-SPHARM represents the surface coordinates as a weighted linear combination of spherical harmonics in such a way that it solves a heat equation. The representation can decomposes an arbitrary surface into symmetric and asymmetric parts with respect to mirror reflection. By analyzing this unique decomposition, surface asymmetry can be quantified. We have applied our technique in quantifying abnormal brain asymmetry in autistic subjects.

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“…f may be represented by 4D spherical harmonics as a series expansion [7], , and I is the vector of image intensities. We approximate the solution to this large dense linear least squares system using iterative residual fitting [8]. The NLK D ± s completely define a 3D intensity volume, and may be used to approximate the original image within series truncation limits.…”

Section: D Spherical Harmonics (4dsh)mentioning

confidence: 99%

Detection of Deformable Objects in 3D Images Using Markov-Chain Monte Carlo and Spherical Harmonics

Khairy¹,

Reynaud²,

Stelzer³

2008

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2008

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Abstract. We address the problem of segmenting 3D microscopic volumetric intensity images of a collection of spatially correlated objects (such as fluorescently labeled nuclei in a tissue). This problem arises in the study of tissue morphogenesis where cells and cellular components are organized in accord with biological role and fate. We formulate the image model as stochastically generated based on biological priors and physics of image formation. We express the segmentation problem in terms of Bayesian inference and use datadriven Markov Chain Monte Carlo to fit the image model to data. We perform an initial step in which the intensity volume is approximated as an expansion in 4D spherical harmonics, the coefficients of which capture the general organization of objects. Since cell nuclei are membrane-bound their shapes are subject to membrane lipid bilayer bending energy, which we use to constrain individual contours. Moreover, we parameterize the nuclear contours using spherical harmonic functions, which provide a shape description with no restriction to particular symmetries. We demonstrate the utility of our approach using synthetic and real fluorescence microscopy data.

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Weighted Fourier Series Representation and Its Application to Quantifying the Amount of Gray Matter

Abstract: As an illustration, the WFS is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects. Within the WFS framework, cortical thickness and gray matter density are computed and compared.

Cited by 173 publications

References 51 publications

Persistence Diagrams of Cortical Surface Data

Persistence Diagrams of Cortical Surface Data

Encoding Neuroanatomical Information using Weighted Spherical Harmonic Representation

Detection of Deformable Objects in 3D Images Using Markov-Chain Monte Carlo and Spherical Harmonics

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