LUMINITA AURA VESE - Academia.edu (original) (raw)

Papers by LUMINITA AURA VESE

Springer eBooks, 2009

Page 1. Projected Gradient Based Color Image Decomposition Vincent Duval, Jean-François Aujol, an... more Page 1. Projected Gradient Based Color Image Decomposition Vincent Duval, Jean-François Aujol, and Luminita Vese 1 Institut TELECOM, TELECOM ParisTech, CNRS UMR 5141 vincent.duval@telecom-paristech.fr 2 CMLA ...

Proceedings of SPIE, Feb 23, 2012

Recent research in perinatal pathology argues that analyzing properties of the placenta may revea... more Recent research in perinatal pathology argues that analyzing properties of the placenta may reveal important information on how certain diseases progress. One important property is the structure of the placental fetal stems. Analysis of the fetal stems in a placenta could be useful in the study and diagnosis of some diseases like autism. To study the fetal stem structure effectively, we need to automatically and accurately track fetal stems through a sequence of digitized hematoxylin and eosin (H&E) stained histology slides. There are many problems in successfully achieving this goal. A few of the problems are: large size of images, misalignment of the consecutive H&E slides, unpredictable inaccuracies of manual tracing, very complicated texture patterns of various tissue types without clear characteristics, just to name a few. In this paper we propose a novel algorithm to achieve automatic tracing of the fetal stem in a sequence of H&E images, based on an inaccurate manual segmentation of a fetal stem in one of the images. This algorithm combines global affine registration, local non-affine registration and a novel 'dynamic' version of the active contours model without edges. We first use global affine image registration of all the images based on displacement, scaling and rotation. This gives us approximate location of the corresponding fetal stem in the image that needs to be traced. We then use the affine registration algorithm "locally" near this location. At this point, we use a fast non-affine registration based on L 2-similarity measure and diffusion regularization to get a better location of the fetal stem. Finally, we have to take into account inaccuracies in the initial tracing. This is achieved through a novel dynamic version of the active contours model without edges where the coefficients of the fitting terms are computed iteratively to ensure that we obtain a unique stem in the segmentation. The segmentation thus obtained can then be used as an initial guess to obtain segmentation in the rest of the images in the sequence. This constitutes an important step in the extraction and understanding of the fetal stem vasculature.

Proceedings of SPIE, Feb 10, 2011

In two dimensions, the Mumford and Shah functional for image segmentation and regularization15 ha... more In two dimensions, the Mumford and Shah functional for image segmentation and regularization15 has minimizers (u,K), where u is a piecewise-smooth approximation of the image data f, and K represents the set of discontinuities of u (a union of curves). Theoretically, the edge set K could include both closed and open curves. The current level set and piecewise-smooth Mumford-Shah based segmentation algorithms4, 23, 24 can only detect objects with closed edges, which are boundaries of open sets. We propose an efficient Mumford-Shah and level set based algorithm for segmenting images with edges which are made up of open curves or crack-tips. By adapting Smereka's open level set formulation21 to variational problems, we are able to extend the current piecewise-smooth and level-set based image segmentation methods, such as4, 23, 24 to the case of open curve segmentation. The algorithm retains many of the advantages of using level sets, such as well-defined boundaries and ability to change topology. We solve the resulting Euler-Lagrange equations by Sobolev H1 gradient descent, avoiding instability and the need for additional regularization of the level set functions, while also accelerating convergence to the reconstructed image. Finally, we present the numerical implementation and experimental results on various noisy images.

Proceedings of SPIE, Feb 15, 2007

This paper is devoted to a recent topic in image analysis: the decomposition of an image into a c... more This paper is devoted to a recent topic in image analysis: the decomposition of an image into a cartoon or geometric part, and an oscillatory or texture part. Here, we propose a practical solution to the (BV,G) model proposed by Y. Meyer 1. We impose that the cartoon is a function of bounded variation, while the texture is represented as the Laplacian of some function whose gradient belongs to L ∞. The problem thus becomes related with the absolutely minimizing Lipschitz extensions and the infinity Laplacian. Experimental results for image denoising and cartoon + texture separation, together with details of the algorithm, are also presented.

SIAM Journal on Numerical Analysis, Oct 1, 1997

This paper is concerned with a classical denoising and deblurring problem in image recovery. Our ... more This paper is concerned with a classical denoising and deblurring problem in image recovery. Our approach is based on a variational method. By using the Legendre-Fenchel transform, we show how the nonquadratic criterion to be minimized can be split into a sequence of half-quadratic problems easier to solve numerically. First we prove an existence and uniqueness result, and then we describe the algorithm for computing the solution and we give a proof of convergence. Finally, we present some experimental results for synthetic and real images.

Journal of Mathematical Imaging and Vision, May 25, 2010

In this paper, we are interested in texture modeling with functional analysis spaces. We focus on... more In this paper, we are interested in texture modeling with functional analysis spaces. We focus on the case of color image processing, and in particular color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v. u should contain the geometric information of the original image, while v should be made of the oscillating patterns of f , such as textures. We propose here a scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. We provide a direct convergence proof of the scheme, and we give some analysis on color texture modeling.

Applied Mathematics and Optimization, Sep 6, 2001

In this paper we study, in the framework of functions of bounded variation, a general variational... more In this paper we study, in the framework of functions of bounded variation, a general variational problem arising in image recovery, introduced in [3]. We prove the existence and the uniqueness of a solution using lower semicontinuity results for convex functionals of measures. We also give a new and fine characterization of the subdifferential of the functional, together with optimality conditions on the solution, using duality techniques of Temam for the theory of time-dependent minimal surfaces. We study the associated evolution equation in the context of nonlinear semigroup theory and we give an approximation result in continuous variables, using-convergence. Finally, we discretize the problems by finite differences schemes and we present several numerical results for signal and image reconstruction.

Multiscale Modeling & Simulation, 2004

We propose a new multiscale image decomposition which offers a hierarchical, adaptive representat... more We propose a new multiscale image decomposition which offers a hierarchical, adaptive representation for the different features in general images. The starting point is a variational decomposition of an image, f = u 0 + v 0 , where [u 0 , v 0 ] is the minimizer of a J-functional, J(f, λ 0 ; X, Y) = inf u+v=f u X + λ 0 v p Y. Such minimizers are standard tools for image manipulations (e.g., denoising, deblurring, compression); see, for example, [M.

Lecture Notes in Computer Science, 2020

In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising ... more In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising and restoration, combining the advantages of fourth order models (without the staircase effect while preserving slopes) and nonlocal methods (preserving texture). For its numerical solution, we employ the L 2 gradient descent and finite difference methods to design explicit, semi-implicit, and implicit schemes. Numerical results for denoising and restoration are shown on synthetic images, real images, and texture images. Comparisons with local fourth order regularizer and the nonlocal total variation are made, which help illustrate the advantages of the proposed model.

Communications in Mathematical Sciences, 2008

We extend the ideas introduced in [33] for hierarchical multiscale decompositions of images. View... more We extend the ideas introduced in [33] for hierarchical multiscale decompositions of images. Viewed as a function f ∈ L 2 (Ω), a given image is hierarchically decomposed into the sum or product of simpler "atoms" u k , where u k extracts more refined information from the previous scale u k−1. To this end, the u k 's are obtained as dyadically scaled minimizers of standard functionals arising in image analysis. Thus, starting with v −1 := f and letting v k denote the residual at a given dyadic scale, λ k ∼ 2 k , the recursive step [u k ,v k ] = arginf Q T (v k−1 ,λ k) leads to the desired hierarchical decomposition, f ∼ P T u k ; here T is a blurring operator. We characterize such Q T-minimizers (by duality) and expand our previous energy estimates of the data f in terms of u k. Numerical results illustrate applications of the new hierarchical multiscale decomposition for blurry images, images with additive and multiplicative noise and image segmentation.

Ocean Sensing and Monitoring XV

The MIDAS Journal

We propose a new nonlinear image registration model which is based on nonlinear elastic regulariz... more We propose a new nonlinear image registration model which is based on nonlinear elastic regularization and unbiased registration. The nonlinear elastic and the unbiased regularization terms are simplified using the change of variables by introducing an unknown that approximates the Jacobian matrix of the displacement field. This reduces the minimization to involve linear differential equations. In contrast to recently proposed unbiased fluid registration method, the new model is written in a unified variational form and is minimized using gradient descent. As a result, the new unbiased nonlinear elasticity model is computationally more efficient and easier to implement than the unbiased fluid registration. The unbiased large-deformation nonlinear elasticity method was tested using volumetric serial magnetic resonance images and shown to have some advantages for medical imaging applications.

IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium, 2018

Multi-angle Imaging Spectro-Radiometer (MISR) instrument provides the multi-angle images of aeros... more Multi-angle Imaging Spectro-Radiometer (MISR) instrument provides the multi-angle images of aerosols and clouds. There are a multitude of challenges for accurate stereo imaging of clouds and aerosols including the high variation of radiative properties of aerosols and clouds within an image. In this work, we adapt an image model to separate two specific types of clouds frequently appearing in MISR images. Specifically, we separate cirrus and cumulus clouds in the two-dimensional MISR single-channel images. We characterize these two cloud types according to their spatial variations and optical brightness. Cirrus clouds appear smooth and optically thin, while cumulus clouds present high optical oscillations and appear brighter. We adapt the additive piecewise-smooth (APS) model for this cloud separation task. We describe the differences between our results and the results of the previous joint work of the second author on cloud separation.

In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising ... more In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising and restoration, combining the advantages of fourth order models (without the staircase effect while preserving slopes) and nonlocal methods (preserving texture). For its numerical solution, we employ the L gradient descent and finite difference methods to design explicit, semi-implicit, and implicit schemes. Numerical results for denoising and restoration are shown on synthetic images, real images, and texture images. Comparisons with local fourth order regularizer and the nonlocal total variation are made, which help illustrate the advantages of the proposed model.

Earth Observing Systems XXVI, 2021

We use large datasets from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Im... more We use large datasets from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to derive AIRS spatial response functions and study their potential variations over the mission. The new reconstructed spatial response functions can be used to reduce errors in the radiances in non-uniform scenes and improve products generated using both AIRS and MODIS data. AIRS spatial response functions are distinct for each of its 2378 channels and each of its 90 scan angles. We develop the mathematical model and the optimization framework for deriving spatial response functions for two AIRS channels with low water vapor absorption and various scan angles. We quantify uncertainties in the derived reconstructions and study how they differ from pre-flight spatial response functions. We show that our approach generates reconstructions that agree with the data more accurately compared to pre-flight spatial responses. We derive spatial response functions using data collected during successive dates in order to ascertain the repeatability of the reconstructed spatial response functions. We also compare the derived spatial response functions based on data collected in the beginning, the middle, and at the current state of the mission in order to study changes in reconstructions over time.

2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, 2021

The purpose of this work is to use data from the Atmospheric Infrared Sounder (AIRS) and the Mode... more The purpose of this work is to use data from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to refine our knowledge of post-launch AIRS point spread functions (PSFs), including suspected changes over the mission. We develop methodology, by deriving mathematical optimization formulation based on variational principles and Sobolev gradient descent, for reconstruction of AIRS spatial response functions. We use the data over the ocean, collected for the duration of a day, to reconstruct a single PSF. We examine the repeatability of our reconstructions by computing PSFs based on data collected during two consecutive days, and also investigating the change in the reconstructions by comparing the reconstructed PSF based on data collected in the beginning and the middle of the mission. We also quantify uncertainties in our reconstruction results.

Journal of Mathematical Imaging and Vision, 2016

Shape Analysis" is an interesting research area which contains many thought-provoking problems an... more Shape Analysis" is an interesting research area which contains many thought-provoking problems and mathematical challenges, especially at the representation level. Shape of an object is considered as the enclosing surface (the boundary) or the enclosed interior. One of the major challenges is to define representations of "shapes" that can be manipulated by image processing methods. This is an important need in practice because more often than not shapes need to be extracted or recovered from raw images; moreover, the process of recovering shapes from raw images highly benefits from prior knowledge of candidate shapes. One of the key means of shape representation is the Euclidean Distance Transform (EDT), which is governed by the Eikonal Equation. The values of the EDT at each interior point give the distance to the nearest boundary point. This distance notion is used in almost any problem that requires integrating shape and image information; e.g., a rich variety of shape-guided image processing or shape extraction tasks. Especially in the 1990s, the idea of embedding shapes as zeros of the signed EDT is highly popularized by the level-set B Sibel Tari

SPIE Proceedings, 2007

This paper is devoted to a recent topic in image analysis: the decomposition of an image into a c... more This paper is devoted to a recent topic in image analysis: the decomposition of an image into a cartoon or geometric part, and an oscillatory or texture part. Here, we propose a practical solution to the (BV,G) model proposed by Y. Meyer 1. We impose that the cartoon is a function of bounded variation, while the texture is represented as the Laplacian of some function whose gradient belongs to L ∞. The problem thus becomes related with the absolutely minimizing Lipschitz extensions and the infinity Laplacian. Experimental results for image denoising and cartoon + texture separation, together with details of the algorithm, are also presented.

2009 16th IEEE International Conference on Image Processing (ICIP), 2009

This paper presents a new image segmentation framework which employs a shape prior in the form of... more This paper presents a new image segmentation framework which employs a shape prior in the form of an edge strength function to introduce a higher-level influence on the segmentation process. We formulate segmentation as the minimization of three coupled functionals, respectively, defining three processes: prior-guided segmentation, shape feature extraction and local deformation estimation. Particularly, the shape feature extraction process is in charge of estimating an edge strength function from the evolving object region. The local deformation estimation process uses this function to determine a meaningful correspondence between a given prior and the evolving object region, and the deformation map estimated in return supervises the segmentation by enforcing the evolving object boundary towards the prior shape.

Springer eBooks, 2009

Page 1. Projected Gradient Based Color Image Decomposition Vincent Duval, Jean-François Aujol, an... more Page 1. Projected Gradient Based Color Image Decomposition Vincent Duval, Jean-François Aujol, and Luminita Vese 1 Institut TELECOM, TELECOM ParisTech, CNRS UMR 5141 vincent.duval@telecom-paristech.fr 2 CMLA ...

Proceedings of SPIE, Feb 23, 2012

Recent research in perinatal pathology argues that analyzing properties of the placenta may revea... more Recent research in perinatal pathology argues that analyzing properties of the placenta may reveal important information on how certain diseases progress. One important property is the structure of the placental fetal stems. Analysis of the fetal stems in a placenta could be useful in the study and diagnosis of some diseases like autism. To study the fetal stem structure effectively, we need to automatically and accurately track fetal stems through a sequence of digitized hematoxylin and eosin (H&E) stained histology slides. There are many problems in successfully achieving this goal. A few of the problems are: large size of images, misalignment of the consecutive H&E slides, unpredictable inaccuracies of manual tracing, very complicated texture patterns of various tissue types without clear characteristics, just to name a few. In this paper we propose a novel algorithm to achieve automatic tracing of the fetal stem in a sequence of H&E images, based on an inaccurate manual segmentation of a fetal stem in one of the images. This algorithm combines global affine registration, local non-affine registration and a novel 'dynamic' version of the active contours model without edges. We first use global affine image registration of all the images based on displacement, scaling and rotation. This gives us approximate location of the corresponding fetal stem in the image that needs to be traced. We then use the affine registration algorithm "locally" near this location. At this point, we use a fast non-affine registration based on L 2-similarity measure and diffusion regularization to get a better location of the fetal stem. Finally, we have to take into account inaccuracies in the initial tracing. This is achieved through a novel dynamic version of the active contours model without edges where the coefficients of the fitting terms are computed iteratively to ensure that we obtain a unique stem in the segmentation. The segmentation thus obtained can then be used as an initial guess to obtain segmentation in the rest of the images in the sequence. This constitutes an important step in the extraction and understanding of the fetal stem vasculature.

Proceedings of SPIE, Feb 10, 2011

In two dimensions, the Mumford and Shah functional for image segmentation and regularization15 ha... more In two dimensions, the Mumford and Shah functional for image segmentation and regularization15 has minimizers (u,K), where u is a piecewise-smooth approximation of the image data f, and K represents the set of discontinuities of u (a union of curves). Theoretically, the edge set K could include both closed and open curves. The current level set and piecewise-smooth Mumford-Shah based segmentation algorithms4, 23, 24 can only detect objects with closed edges, which are boundaries of open sets. We propose an efficient Mumford-Shah and level set based algorithm for segmenting images with edges which are made up of open curves or crack-tips. By adapting Smereka's open level set formulation21 to variational problems, we are able to extend the current piecewise-smooth and level-set based image segmentation methods, such as4, 23, 24 to the case of open curve segmentation. The algorithm retains many of the advantages of using level sets, such as well-defined boundaries and ability to change topology. We solve the resulting Euler-Lagrange equations by Sobolev H1 gradient descent, avoiding instability and the need for additional regularization of the level set functions, while also accelerating convergence to the reconstructed image. Finally, we present the numerical implementation and experimental results on various noisy images.

Proceedings of SPIE, Feb 15, 2007

This paper is devoted to a recent topic in image analysis: the decomposition of an image into a c... more This paper is devoted to a recent topic in image analysis: the decomposition of an image into a cartoon or geometric part, and an oscillatory or texture part. Here, we propose a practical solution to the (BV,G) model proposed by Y. Meyer 1. We impose that the cartoon is a function of bounded variation, while the texture is represented as the Laplacian of some function whose gradient belongs to L ∞. The problem thus becomes related with the absolutely minimizing Lipschitz extensions and the infinity Laplacian. Experimental results for image denoising and cartoon + texture separation, together with details of the algorithm, are also presented.

SIAM Journal on Numerical Analysis, Oct 1, 1997

This paper is concerned with a classical denoising and deblurring problem in image recovery. Our ... more This paper is concerned with a classical denoising and deblurring problem in image recovery. Our approach is based on a variational method. By using the Legendre-Fenchel transform, we show how the nonquadratic criterion to be minimized can be split into a sequence of half-quadratic problems easier to solve numerically. First we prove an existence and uniqueness result, and then we describe the algorithm for computing the solution and we give a proof of convergence. Finally, we present some experimental results for synthetic and real images.

Journal of Mathematical Imaging and Vision, May 25, 2010

In this paper, we are interested in texture modeling with functional analysis spaces. We focus on... more In this paper, we are interested in texture modeling with functional analysis spaces. We focus on the case of color image processing, and in particular color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v. u should contain the geometric information of the original image, while v should be made of the oscillating patterns of f , such as textures. We propose here a scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. We provide a direct convergence proof of the scheme, and we give some analysis on color texture modeling.

Applied Mathematics and Optimization, Sep 6, 2001

In this paper we study, in the framework of functions of bounded variation, a general variational... more In this paper we study, in the framework of functions of bounded variation, a general variational problem arising in image recovery, introduced in [3]. We prove the existence and the uniqueness of a solution using lower semicontinuity results for convex functionals of measures. We also give a new and fine characterization of the subdifferential of the functional, together with optimality conditions on the solution, using duality techniques of Temam for the theory of time-dependent minimal surfaces. We study the associated evolution equation in the context of nonlinear semigroup theory and we give an approximation result in continuous variables, using-convergence. Finally, we discretize the problems by finite differences schemes and we present several numerical results for signal and image reconstruction.

Multiscale Modeling & Simulation, 2004

We propose a new multiscale image decomposition which offers a hierarchical, adaptive representat... more We propose a new multiscale image decomposition which offers a hierarchical, adaptive representation for the different features in general images. The starting point is a variational decomposition of an image, f = u 0 + v 0 , where [u 0 , v 0 ] is the minimizer of a J-functional, J(f, λ 0 ; X, Y) = inf u+v=f u X + λ 0 v p Y. Such minimizers are standard tools for image manipulations (e.g., denoising, deblurring, compression); see, for example, [M.

Lecture Notes in Computer Science, 2020

In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising ... more In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising and restoration, combining the advantages of fourth order models (without the staircase effect while preserving slopes) and nonlocal methods (preserving texture). For its numerical solution, we employ the L 2 gradient descent and finite difference methods to design explicit, semi-implicit, and implicit schemes. Numerical results for denoising and restoration are shown on synthetic images, real images, and texture images. Comparisons with local fourth order regularizer and the nonlocal total variation are made, which help illustrate the advantages of the proposed model.

Communications in Mathematical Sciences, 2008

We extend the ideas introduced in [33] for hierarchical multiscale decompositions of images. View... more We extend the ideas introduced in [33] for hierarchical multiscale decompositions of images. Viewed as a function f ∈ L 2 (Ω), a given image is hierarchically decomposed into the sum or product of simpler "atoms" u k , where u k extracts more refined information from the previous scale u k−1. To this end, the u k 's are obtained as dyadically scaled minimizers of standard functionals arising in image analysis. Thus, starting with v −1 := f and letting v k denote the residual at a given dyadic scale, λ k ∼ 2 k , the recursive step [u k ,v k ] = arginf Q T (v k−1 ,λ k) leads to the desired hierarchical decomposition, f ∼ P T u k ; here T is a blurring operator. We characterize such Q T-minimizers (by duality) and expand our previous energy estimates of the data f in terms of u k. Numerical results illustrate applications of the new hierarchical multiscale decomposition for blurry images, images with additive and multiplicative noise and image segmentation.

Ocean Sensing and Monitoring XV

The MIDAS Journal

We propose a new nonlinear image registration model which is based on nonlinear elastic regulariz... more We propose a new nonlinear image registration model which is based on nonlinear elastic regularization and unbiased registration. The nonlinear elastic and the unbiased regularization terms are simplified using the change of variables by introducing an unknown that approximates the Jacobian matrix of the displacement field. This reduces the minimization to involve linear differential equations. In contrast to recently proposed unbiased fluid registration method, the new model is written in a unified variational form and is minimized using gradient descent. As a result, the new unbiased nonlinear elasticity model is computationally more efficient and easier to implement than the unbiased fluid registration. The unbiased large-deformation nonlinear elasticity method was tested using volumetric serial magnetic resonance images and shown to have some advantages for medical imaging applications.

IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium, 2018

Multi-angle Imaging Spectro-Radiometer (MISR) instrument provides the multi-angle images of aeros... more Multi-angle Imaging Spectro-Radiometer (MISR) instrument provides the multi-angle images of aerosols and clouds. There are a multitude of challenges for accurate stereo imaging of clouds and aerosols including the high variation of radiative properties of aerosols and clouds within an image. In this work, we adapt an image model to separate two specific types of clouds frequently appearing in MISR images. Specifically, we separate cirrus and cumulus clouds in the two-dimensional MISR single-channel images. We characterize these two cloud types according to their spatial variations and optical brightness. Cirrus clouds appear smooth and optically thin, while cumulus clouds present high optical oscillations and appear brighter. We adapt the additive piecewise-smooth (APS) model for this cloud separation task. We describe the differences between our results and the results of the previous joint work of the second author on cloud separation.

In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising ... more In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising and restoration, combining the advantages of fourth order models (without the staircase effect while preserving slopes) and nonlocal methods (preserving texture). For its numerical solution, we employ the L gradient descent and finite difference methods to design explicit, semi-implicit, and implicit schemes. Numerical results for denoising and restoration are shown on synthetic images, real images, and texture images. Comparisons with local fourth order regularizer and the nonlocal total variation are made, which help illustrate the advantages of the proposed model.

Earth Observing Systems XXVI, 2021

We use large datasets from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Im... more We use large datasets from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to derive AIRS spatial response functions and study their potential variations over the mission. The new reconstructed spatial response functions can be used to reduce errors in the radiances in non-uniform scenes and improve products generated using both AIRS and MODIS data. AIRS spatial response functions are distinct for each of its 2378 channels and each of its 90 scan angles. We develop the mathematical model and the optimization framework for deriving spatial response functions for two AIRS channels with low water vapor absorption and various scan angles. We quantify uncertainties in the derived reconstructions and study how they differ from pre-flight spatial response functions. We show that our approach generates reconstructions that agree with the data more accurately compared to pre-flight spatial responses. We derive spatial response functions using data collected during successive dates in order to ascertain the repeatability of the reconstructed spatial response functions. We also compare the derived spatial response functions based on data collected in the beginning, the middle, and at the current state of the mission in order to study changes in reconstructions over time.

2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, 2021

The purpose of this work is to use data from the Atmospheric Infrared Sounder (AIRS) and the Mode... more The purpose of this work is to use data from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to refine our knowledge of post-launch AIRS point spread functions (PSFs), including suspected changes over the mission. We develop methodology, by deriving mathematical optimization formulation based on variational principles and Sobolev gradient descent, for reconstruction of AIRS spatial response functions. We use the data over the ocean, collected for the duration of a day, to reconstruct a single PSF. We examine the repeatability of our reconstructions by computing PSFs based on data collected during two consecutive days, and also investigating the change in the reconstructions by comparing the reconstructed PSF based on data collected in the beginning and the middle of the mission. We also quantify uncertainties in our reconstruction results.

Journal of Mathematical Imaging and Vision, 2016

Shape Analysis" is an interesting research area which contains many thought-provoking problems an... more Shape Analysis" is an interesting research area which contains many thought-provoking problems and mathematical challenges, especially at the representation level. Shape of an object is considered as the enclosing surface (the boundary) or the enclosed interior. One of the major challenges is to define representations of "shapes" that can be manipulated by image processing methods. This is an important need in practice because more often than not shapes need to be extracted or recovered from raw images; moreover, the process of recovering shapes from raw images highly benefits from prior knowledge of candidate shapes. One of the key means of shape representation is the Euclidean Distance Transform (EDT), which is governed by the Eikonal Equation. The values of the EDT at each interior point give the distance to the nearest boundary point. This distance notion is used in almost any problem that requires integrating shape and image information; e.g., a rich variety of shape-guided image processing or shape extraction tasks. Especially in the 1990s, the idea of embedding shapes as zeros of the signed EDT is highly popularized by the level-set B Sibel Tari

SPIE Proceedings, 2007

This paper is devoted to a recent topic in image analysis: the decomposition of an image into a c... more This paper is devoted to a recent topic in image analysis: the decomposition of an image into a cartoon or geometric part, and an oscillatory or texture part. Here, we propose a practical solution to the (BV,G) model proposed by Y. Meyer 1. We impose that the cartoon is a function of bounded variation, while the texture is represented as the Laplacian of some function whose gradient belongs to L ∞. The problem thus becomes related with the absolutely minimizing Lipschitz extensions and the infinity Laplacian. Experimental results for image denoising and cartoon + texture separation, together with details of the algorithm, are also presented.

2009 16th IEEE International Conference on Image Processing (ICIP), 2009

This paper presents a new image segmentation framework which employs a shape prior in the form of... more This paper presents a new image segmentation framework which employs a shape prior in the form of an edge strength function to introduce a higher-level influence on the segmentation process. We formulate segmentation as the minimization of three coupled functionals, respectively, defining three processes: prior-guided segmentation, shape feature extraction and local deformation estimation. Particularly, the shape feature extraction process is in charge of estimating an edge strength function from the evolving object region. The local deformation estimation process uses this function to determine a meaningful correspondence between a given prior and the evolving object region, and the deformation map estimated in return supervises the segmentation by enforcing the evolving object boundary towards the prior shape.