Location Dependent Dirichlet Processes

Sun, Shiliang; Paisley, John; Liu, Qiuyang

doi:10.1007/978-3-319-67777-4_6

Cited by 6 publications

(10 citation statements)

References 21 publications

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“…This relaxation smooths the ELBO and helps convergence. Finally, as noted by Sun, Paisley and Liu (2017) in a similar setting, the gamma normalization term presents computational difficulties, and we follow those authors in introducing an auxiliary variable ξ t to further lower bound this term (Sun, Paisley and Liu (2017)),…”

Section: 4mentioning

confidence: 94%

A Bayesian nonparametric approach to super-resolution single-molecule localization

et al. 2021

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We consider the problem of single-molecule identification in superresolution microscopy. Super-resolution microscopy overcomes the diffraction limit by localizing individual fluorescing molecules in a field of view. This is particularly difficult since each individual molecule appears and disappears randomly across time and because the total number of molecules in the field of view is unknown. Additionally, data sets acquired with superresolution microscopes can contain a large number of spurious fluorescent fluctuations caused by background noise.To address these problems, we present a Bayesian nonparametric framework capable of identifying individual emitting molecules in super-resolved time series. We tackle the localization problem in the case in which each individual molecule is already localized in space. First, we collapse observations in time and develop a fast algorithm that builds upon the Dirichlet process. Next, we augment the model to account for the temporal aspect of fluorophore photophysics. Finally, we assess the performance of our methods with ground-truth data sets having known biological structure. Introduction.Light microscopes are the workhorse of cellular biology, enabling the study of molecular processes within the cell. The resolution of light microscopes is limited by the interaction of light with the microscope's optical system, due to the physics of diffraction. Diffraction causes a blur on each light point source (lps). The response of the imaging system to a lps was first described by Airy (Airy (1835)) and is represented by the point spread function (psf) of the microscope. The image of an object under a microscope is the superposition of all the lps comprising the object convolved with the psf (Figure 1A). If two lps are close enough, the finite size of the psf prevents their separate recognition. Using this fact in 1873, Abbe (Abbe ( 1873)) formalized the definition of resolution as the smallest distance between two objects that prevent their individual identification. In particular, Abbe established that two light-emitting sources can be distinguished only if they are separated by a distance of at least d = λ 2NA , where λ is the wavelength of incoming light and NA is the numerical aperture of the microscope. The resolution of conventional light microscopy is typically limited to around 200 nm.Super-resolution microscopy (SRM) is an imaging methodology that allows researchers to overcome the diffraction limit imposed by conventional light microscopy (Betzig et al. (2006), Rust, Bates andZhuang (2006)). SRM resolves photoswitchable fluorophores in a field of view by sparsely and randomly activating individual light emitters and then localizing them with subdiffraction precision (Figure 1B). This technique has revolutionized the

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Section: 4mentioning

confidence: 94%

A Bayesian nonparametric approach to super-resolution single-molecule localization

et al. 2021

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“…This relaxation smooths the ELBO and helps convergence. Finally, as noted by [Sun, Paisley and Liu, 2017] in a similar setting, the gamma normalization term presents computational difficulties, and we follow those authors in introducing an auxiliary variable ξ t to further lower bound this term: [Sun, Paisley and Liu, 2017].…”

Section: 4mentioning

confidence: 96%

A Bayesian nonparametric approach to super-resolution single-molecule localization

Gabitto

Marie-Nelly

Pakman

et al. 2020

Preprint

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“…As indicated above, we use a prior P P (•; m, s) parametrized by location and scale (m, s). Previously proposed priors relied on a specific elaborations of the first term of Equation ( 5) which is required to guarantee that the prior probabilities sum to 1 [52,33] and often lead to solve a non-linear system of equations to update the prior probabilities. In contrast, Dirichlet and Logit-Normal distributions are defined on the simplex, therefore appropriate as prior distributions.…”

Section: Segmentation Inference By Expectation-maximizationmentioning

confidence: 99%

“…The Logit-Normal distribution [3] is directly parametrized by location and scale, however the update equations are also non-linear. The Dirichlet distribution was previously used to enforce spatial dependence directly [20] or in combination with a Gaussian process [52]. We propose instead a specific parametrization that has the considerable advantage of leading to a linear regularizing equation, that also satisfies a key requirement of well-calibrated probabilistic inference, i.e.…”

Section: Segmentation Inference By Expectation-maximizationmentioning

confidence: 99%

“…Relevant work in computer vision includes algorithms based on probabilistic mixture models extended to include Bayesian priors that favor grouping by proximity [33], e.g. via the distance dependent Chinese Restaurant Process [20], the spatially dependent Pitman-Yor process [51], and the Location Dependent Dirichlet Process (LDDP) [52], to restrain the search to partitions composed of contiguous components. Although promising, a main limitation of those approaches is their use of ad-hoc image descriptors and over-simplified assumptions about their statistics.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Model of Visual Segmentation

Vacher,

Mamassian,

Coen-Cagli

2018

Preprint

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Visual segmentation is a key perceptual function that partitions visual space and allows for detection, recognition and discrimination of objects in complex environments. The processes underlying human segmentation of natural images are still poorly understood. In part, this is because we lack segmentation models consistent with experimental and theoretical knowledge in visual neuroscience. Biological sensory systems have been shown to approximate probabilistic inference to interpret their inputs. This requires a generative model that captures both the statistics of the sensory inputs and expectations about the causes of those inputs. Following this hypothesis, we propose a probabilistic generative model of visual segmentation that combines knowledge about 1) the sensitivity of neurons in the visual cortex to statistical regularities in natural images; and 2) the preference of humans to form contiguous partitions of visual space. We develop an efficient algorithm for training and inference based on expectation-maximization and validate it on synthetic data. Importantly, with the appropriate choice of the prior, we derive an intuitive closed-form update rule for assigning pixels to segments: at each iteration, the pixel assignment probabilities to segments is the sum of the evidence (i.e. local pixel statistics) and prior (i.e. the assignments of neighboring pixels) weighted by their relative uncertainty. The model performs competitively on natural images from the Berkeley Segmentation Dataset (BSD), and we illustrate how the likelihood and prior components improve segmentation relative to traditional mixture models. Furthermore, our model explains some variability across human subjects as reflecting local uncertainty about the number of segments. Our model thus provides a viable approach to probe human visual segmentation.

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Location Dependent Dirichlet Processes

Cited by 6 publications

References 21 publications

A Bayesian nonparametric approach to super-resolution single-molecule localization

A Bayesian nonparametric approach to super-resolution single-molecule localization

A Bayesian nonparametric approach to super-resolution single-molecule localization

Probabilistic Model of Visual Segmentation

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