Image Analysis: Is the Fourier Transform Becoming Obsolete?

“…In other words, the main drawback of the FT is its lack of localisation: computing the FT is equivalent to analysing the signal with series of sine and cosine functions with a varying frequency. Since these analysing functions are not limited in space, there is no way to analyse the signal locally (Bonnet and Vautrot, 1997).…”

Section: Signal Processingmentioning

confidence: 99%

Some trends in microscope image processing

Bonnet

2004

Micron

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“…Conversely, extracting exhaustively the information contained in spectral images is also challenging, and requires the use of multivariate analysis strategies that allow for the segmentation and/or the reduction of the dimensionality of the data set. The earliest and most commonly used methods are principal component analysis (PCA) and k-means clustering [31,8,32,34,28,29,14,23]. Recently, the use of advanced statistical algorithms including Kullback-Leibler divergence [19] and t-distributed stochastic neighbourhood embedding (t-SNE) [15,25,23] have shown great promise to further discriminate and/or classify heterogeneities in spectral images.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Clustering of Spectral Images with Spatial Constraints for the Rapid Processing of Large and Heterogeneous Data Sets

et al. 2022

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When dealing with full spectrum images in which each pixel is characterized by a full spectrum, i.e. spectral images, standard segmentation methods, such as k-means or hierarchical clustering might be either inapplicable or inappropriate ; one aspect being the multi-GB size of such data set leading to very expensive computations. In the present contribution, we propose an approach to spectral image segmentation combining hierarchical clustering and spatial constraints. On the one hand spatial constraints allow to implement an algorithm with a reasonable computation time to obtain a segmentation and with a certain level of robustness with respect to the signal-to-noise ratio since the prior knowledge injected by the spatial constraint partially compensates for the increase in noise level. On the other hand hierarchical clustering provides a statistically sound and known framework that allows accurate reporting of the instrument noise model. In terms of applications, this segmentation problem is encountered particularly in the study of ancient materials that benefits from the wealth of information provided by the acquisition of spectral images.In the last few years, data collection has been considerably accelerated, enabling the characeterization of the sample with a high dynamic range in both the spatial dimensions and composition and leading to an average size of a single data set in the tens of GB range. Hence we also considered computational and memory complexity when developing the herein proposed algorithm. Taking on this application domain, we illustrate the proposed algorithm on a X-ray fluorescence spectral image collected on an ca. 100 Myr fossil fish, as well as on simulated data to assess the sensitivity of the results to the noise level. For such experiment, the lower sensitivity to noise simultaneously lead to an increase in the spatial definition of the collected spectral image, thanks to the faster acquisition time, and to a reduction in the potentially harmful radiation dose density to which the samples are subjected.

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Image Analysis: Is the Fourier Transform Becoming Obsolete?

Cited by 8 publications

References 20 publications

Enhanced feature analysis using wavelets for scanning probe microscopy images of surfaces

Enhanced feature analysis using wavelets for scanning probe microscopy images of surfaces

Some trends in microscope image processing

Hierarchical Clustering of Spectral Images with Spatial Constraints for the Rapid Processing of Large and Heterogeneous Data Sets

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