Scale space view of curve estimation

Chaudhuri, Probal; Marron, J. S.

doi:10.1214/aos/1016218224

Cited by 203 publications

(161 citation statements)

References 32 publications

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“…This can be viewed as a Gaussian kernel Nadaraya-Watson type smoothing extended to manifolds [4]. Figure 3 shows a flattened thickness map illustrating how heat kernel smoothing can enhance the thickness pattern by increasing the signal-to-noise ratio.…”

Section: Theoremmentioning

confidence: 99%

Unified Statistical Approach to Cortical Thickness Analysis

Chung

Robbins

Evans

2005

Lecture Notes in Computer Science

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Abstract. This paper presents a unified image processing and analysis framework for cortical thickness in characterizing a clinical population. The emphasis is placed on the development of data smoothing and analysis framework. The human brain cortex is a highly convoluted surface. Due to the convoluted non-Euclidean surface geometry, data smoothing and analysis on the cortex are inherently difficult. When measurements lie on a curved surface, it is natural to assign kernel smoothing weights based on the geodesic distance along the surface rather than the Euclidean distance. We present a new data smoothing framework that address this problem implicitly without actually computing the geodesic distance and present its statistical properties. Afterwards, the statistical inference is based on the random field theory based multiple comparison correction. As an illustration, we have applied the method in detecting the regions of abnormal cortical thickness in 16 high functioning autistic children.

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Section: Theoremmentioning

confidence: 99%

Unified Statistical Approach to Cortical Thickness Analysis

Chung

Robbins

Evans

2005

Lecture Notes in Computer Science

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“…[20] Scale space analysis has been used the image processing and computer vision communities for over 20 years, but it first appears in the statistics literature with the SiZer (significant zero crossings of derivatives) method for detecting statistically significant scale-dependent features in a one-dimensional field [Chaudhuri and Marron, 2000]. This method was extended by Erästö and Holmström [2005], who incorporated Bayesian methods for identifying multiscale features.…”

Section: Previous Applications Of Scale Space To Climate Datamentioning

confidence: 99%

Scale space methods for climate model analysis

2013

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[1] In this paper, we introduce methods for evaluating climate model performance across spatial scales. These techniques are based on the "scale space" framework widely used in the image processing and computer vision communities. We discuss why the diffusion equation on the sphere provides a particularly attractive means of smoothing two-dimensional maps of global climate data. We establish that no structure is introduced into a map as an artifact of the smoothing procedure. This allows for the comparison of models and observations at multiple scales. As a test case for these methods, we compare the ability of high-and low-resolution versions of the Community Climate System Model (CCSM) to simulate the seasonal climatologies of surface air temperature (TAS), sea level pressure (PSL), and total precipitation rate (PR). For TAS, we find that the high-resolution model is better able to capture the boreal summer (JJA) climatological pattern at fine scales, although there is no such improvement in winter (DJF). We find the performances of the high-and low-resolution models to be similarly capable of capturing the summertime sea level pressure climatology at all scales. However, the high-resolution model PSL climatology is degraded for DJF, especially at larger scales. For both JJA and DJF precipitation climatologies, we find larger precipitation errors in the high-resolution model at the finest scales; however, performance at larger scales is improved.

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“…Structural adaptive segmentation (AS) combines ideas from scale space analysis (Chaudhuri and Marron, 2000), multiscale testing (Dümbgen and Spokoiny, 2001;Poline and Mazoyer, 1994a) and structural adaptive smoothing Tabelow et al, 2006). The approach described below directly provides an efficient solution to the problems of structure preserving denoising and signal detection in fMRI.…”

Section: Theoretical Backgroundmentioning

confidence: 99%