Optimal Mass Transport: Signal processing and machine-learning applications

Kolouri, Soheil; Park, Se Rim; Thorpe, Matthew; Slepčev, Dejan; Rohde, Gustavo K.

doi:10.1109/msp.2017.2695801

Cited by 309 publications

(235 citation statements)

References 39 publications

Supporting

Mentioning

228

Contrasting

Order By: Relevance

“…We hypothesize that transforming MRI data using the new TBM approach can facilitate both discovery as well as visualization of discriminating differences in a manner similar to 1D and 2D signal analysis previously reported [13, 14, 15, 16, 17, 18, 19]. Ultimately, the goals of discovering objective clinical markers and understanding structure-function relationships would be facilitated by a technique that could assess structural changes underlying clinical phenotype in a fully automated manner without information loss and visualize the shifts in tissue distribution as a series of radiology images as part of a unified framework.…”

Section: Introductionmentioning

confidence: 88%

“…Optimal mass transport theory developed two major formulations: one in the continuous domain utilizing a transport map called the Monge formulation, and one able to work with discrete masses such as dirac delta called the Kantorovich formulation. These are further described in [19]. In this paper, we consider digital signals as being sampled from a continuous domain and employ the Monge formulation of the problem.…”

Section: Optimal Mass Transport For Signal Transformationmentioning

confidence: 99%

“…This linear embedding is generative, thus, any arbitrary point in the LOT space can be directly inverted and visualized in the image domain [13, 17, 18, 19] as a new image according to the synthesis equation [13, 17]

I false(x false) = italicdet false(D f^{- 1} false(x false) false) I_{0} false(f^{- 1} false(x false) false) where f^{- 1} false(x false) is the inverse mapping of f false(x false)

…”

Section: Optimal Mass Transport For Signal Transformationmentioning

confidence: 99%

“…Prior work demonstrates that when we transform 1D and 2D signals in other applications using TBM [13, 14, 15, 16, 17, 18, 19], complex and nonlinear morphology in the image domain can be described by linear classification and regression models in the transform domain. Furthermore, the key advance of TBM is that it is generative and enables direct visualization of the interface between signal classes through inverse TBM transformation [19]. The TBM technique computes the distance needed to morph one image with respect to a common template using the mathematics of optimal mass transport (OMT).…”

Section: Introductionmentioning

confidence: 99%

“…The TBM technique computes the distance needed to morph one image with respect to a common template using the mathematics of optimal mass transport (OMT). Optimal mass transport has a long mathematical history, starting in the 1700s with Monge and most recently due to its myriad applications in signal and data analysis [19]. As Figure 2 illustrates, unlike deformation-based approaches, OMT can match both shape and texture variations simultaneously; thus, information is not missed.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Discovery and visualization of structural biomarkers from MRI using transport-based morphometry

et al. 2018

Self Cite

View full text Add to dashboard Cite

Disease in the brain is often associated with subtle, spatially diffuse, or complex tissue changes that may lie beneath the level of gross visual inspection, even on magnetic resonance imaging (MRI). Unfortunately, current computer-assisted approaches that examine pre-specified features, whether anatomically-defined (i.e. thalamic volume, cortical thickness) or based on pixelwise comparison (i.e. deformation-based methods), are prone to missing a vast array of physical changes that are not well-encapsulated by these metrics. In this paper, we have developed a technique for automated pattern analysis that can fully determine the relationship between brain structure and observable phenotype without requiring any a priori features. Our technique, called transport-based morphometry (TBM), is an image transformation that maps brain images loss-lessly to a domain where they become much more separable. The new approach is validated on structural brain images of healthy older adult subjects where even linear models for discrimination, regression, and blind source separation enable TBM to independently discover the characteristic changes of aging and highlight potential mechanisms by which aerobic fitness may mediate brain health later in life. TBM is a generative approach that can provide visualization of physically meaningful shifts in tissue distribution through inverse transformation. The proposed framework is a powerful technique that can potentially elucidate genotype-structural-behavioral associations in myriad diseases.

show abstract

Section: Introductionmentioning

confidence: 88%

Section: Optimal Mass Transport For Signal Transformationmentioning

confidence: 99%

I false(x false) = italicdet false(D f^{- 1} false(x false) false) I_{0} false(f^{- 1} false(x false) false) where f^{- 1} false(x false) is the inverse mapping of f false(x false)

…”

Section: Optimal Mass Transport For Signal Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Discovery and visualization of structural biomarkers from MRI using transport-based morphometry

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

Imaging Biomarkers for Alzheimer's Disease Using Magnetic Resonance Microscopy

Badea¹,

Stout²,

Cofer³

et al. 2022

Magnetic Resonance Microscopy

View full text Add to dashboard Cite

Cell Image Classification: A Comparative Overview

et al. 2020

Self Cite

View full text Add to dashboard Cite

Cell image classification methods are currently being used in numerous applications in cell biology and medicine. Applications include understanding the effects of genes and drugs in screening experiments, understanding the role and subcellular localization of different proteins, as well as diagnosis and prognosis of cancer from images acquired using cytological and histological techniques. The article also reviews three main approaches for cell image classification most often used: numerical feature extraction, end-to-end classification with neural networks (NNs), and transport-based morphometry (TBM). In addition, we provide comparisons on four different cell imaging datasets to highlight the relative strength of each method. The results computed using four publicly available datasets show that numerical features tend to carry the best discriminative information for most of the classification tasks. Results also show that NN-based methods produce state-of-the-art results in the dataset that contains a relatively large number of training samples. Data augmentation or the choice of a more recently reported architecture does not necessarily improve the classification performance of NNs in the datasets with limited number of training samples. If understanding and visualization are desired aspects, TBM methods can offer the ability to invert classification functions, and thus can aid in the interpretation of results. These and other comparison outcomes are discussed with the aim of clarifying the advantages and disadvantages of each method. © 2020 International Society for Advancement of Cytometry Key terms image informatics; computational biology; cell biology; digital pathology Interpretation of images of cells has always played important roles in science and medicine. From their discovery in 1665, observation of the spatiotemporal characteristics of cells through microscopic technology has enabled us to better understand the structure of living cells, as well as how they perform certain functions (1,2). In addition, scientists have long used microscopes to evaluate the efficacy of different compounds for drug development (3-9). In medicine, as another example, the observation of cell morphology has long been used to discern malignancy in cancer cells (10-13).Cells are known to exhibit complex phenotypes such as differences in shape, gene expression, subcellular protein localization, and other qualities. In addition, cell cultures, tissues, and organs are known to exhibit complex heterogeneity of phenotypes. The combination of intricate phenotype differences together with their heterogeneous responses to different conditions (e.g., diseases) has made decoding biological processes an increasingly complex task. Thus computational approaches for analyzing images of cells have been used increasingly to aid in the task of decoding the complexity of biological processes. A common task useful in many practical situations is determining the category of a given cell or set of cells: a task known as cell classification.Auto...

show abstract

Optimal Mass Transport: Signal processing and machine-learning applications

Cited by 309 publications

References 39 publications

Discovery and visualization of structural biomarkers from MRI using transport-based morphometry

Discovery and visualization of structural biomarkers from MRI using transport-based morphometry

Imaging Biomarkers for Alzheimer's Disease Using Magnetic Resonance Microscopy

Cell Image Classification: A Comparative Overview

Contact Info

Product

Resources

About