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Martin D. Fox

Bio: Martin D. Fox is an academic researcher from University of Connecticut. The author has contributed to research in topics: Doppler effect & Image resolution. The author has an hindex of 17, co-authored 67 publications receiving 5631 citations.


Papers
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Proceedings ArticleDOI
20 Jun 2005
TL;DR: A new variational formulation for geometric active contours that forces the level set function to be close to a signed distance function, and therefore completely eliminates the need of the costly re-initialization procedure.
Abstract: In this paper, we present a new variational formulation for geometric active contours that forces the level set function to be close to a signed distance function, and therefore completely eliminates the need of the costly re-initialization procedure. Our variational formulation consists of an internal energy term that penalizes the deviation of the level set function from a signed distance function, and an external energy term that drives the motion of the zero level set toward the desired image features, such as object boundaries. The resulting evolution of the level set function is the gradient flow that minimizes the overall energy functional. The proposed variational level set formulation has three main advantages over the traditional level set formulations. First, a significantly larger time step can be used for numerically solving the evolution partial differential equation, and therefore speeds up the curve evolution. Second, the level set function can be initialized with general functions that are more efficient to construct and easier to use in practice than the widely used signed distance function. Third, the level set evolution in our formulation can be easily implemented by simple finite difference scheme and is computationally more efficient. The proposed algorithm has been applied to both simulated and real images with promising results.

2,005 citations

Journal ArticleDOI
TL;DR: A new variational level set formulation in which the regularity of the level set function is intrinsically maintained during thelevel set evolution called distance regularized level set evolution (DRLSE), which eliminates the need for reinitialization and thereby avoids its induced numerical errors.
Abstract: Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.

1,947 citations

Patent
01 Jun 1987
TL;DR: In this article, a bandage assembly for percutaneous administration of a medicament generates sonic vibrations to produce sonophoresis, and a second piezoelectric polymer element may surround the cavity to generate vibrations parallel to the skin to stretch the pores.
Abstract: A bandage assembly for percutaneous administration of a medicament generates sonic vibrations to produce sonophoresis. The assembly has a bandage member with a cavity containing a medicament and having a piezoelectric polymer element extending thereacross. An sonic generator is coupled to the piezoelectric polymer element to supply it with energy to produce sonic vibrations perpendicular to the skin to drive the medicament into the pores. A second piezoelectric polymer element may surround the cavity to generate vibrations parallel to the skin to stretch the pores.

491 citations

Journal ArticleDOI
TL;DR: The development and testing of a noninvasive true phase optical polarimetry sensing system to monitor in vivo glucose concentrations is described and the applicability of this optical sensor for glucose movement is demonstrated.
Abstract: The development and testing of a noninvasive true phase optical polarimetry sensing system to monitor in vivo glucose concentrations is described. To demonstrate the applicability of this optical sensor for glucose movement, the authors calibrate the system and then test it in vitro using both a glass test cell filled with glucose solution in the physiologic range, with a path length of 0.9 cm to approximate the 1-cm path length present in the anterior chamber of the eye, and then on an excised human eye. The technique used helium neon laser light which was coupled through a rotating linear polarizer along with two stationary linear polarizers and two detectors to produce reference and signal outputs whose amplitudes varied sinusoidally with a frequency of twice the angular velocity of the rotating polarizer, and whose phase was proportional to the rotation of the linear polarization vector passing through the glucose solution. >

190 citations

Patent
25 Aug 2006
TL;DR: A system for providing enhanced digital images as mentioned in this paper includes an image receiving device for accepting at least one digital image and obtaining digital information therefrom; a computer program product comprising machine readable instructions stored on machine readable media.
Abstract: A system for providing enhanced digital images includes an image receiving device for accepting at least one digital image and obtaining digital information therefrom; a computer program product comprising machine readable instructions stored on machine readable media, the instructions for providing enhanced digital images by performing upon the at least one digital image at least one of: a minimum directional derivative search, a multi-channel median boosted anisotropic diffusion, an non-homogeneous anisotropic diffusion technique and a pixel compounding technique.

182 citations


Cited by
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Journal ArticleDOI
TL;DR: A new variational level set formulation in which the regularity of the level set function is intrinsically maintained during thelevel set evolution called distance regularized level set evolution (DRLSE), which eliminates the need for reinitialization and thereby avoids its induced numerical errors.
Abstract: Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.

1,947 citations

Journal ArticleDOI
TL;DR: This work proposes a region-based active contour model that draws upon intensity information in local regions at a controllable scale to cope with intensity inhomogeneity and shows desirable performances of this model.
Abstract: Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions at a controllable scale. A data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation with a level set regularization term, from which a curve evolution equation is derived for energy minimization. Due to a kernel function in the data fitting term, intensity information in local regions is extracted to guide the motion of the contour, which thereby enables our model to cope with intensity inhomogeneity. In addition, the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function. Experimental results for synthetic and real images show desirable performances of our method.

1,630 citations

Journal ArticleDOI
TL;DR: A novel region-based method for image segmentation, which is able to simultaneously segment the image and estimate the bias field, and the estimated bias field can be used for intensity inhomogeneity correction (or bias correction).
Abstract: Intensity inhomogeneity often occurs in real-world images, which presents a considerable challenge in image segmentation. The most widely used image segmentation algorithms are region-based and typically rely on the homogeneity of the image intensities in the regions of interest, which often fail to provide accurate segmentation results due to the intensity inhomogeneity. This paper proposes a novel region-based method for image segmentation, which is able to deal with intensity inhomogeneities in the segmentation. First, based on the model of images with intensity inhomogeneities, we derive a local intensity clustering property of the image intensities, and define a local clustering criterion function for the image intensities in a neighborhood of each point. This local clustering criterion function is then integrated with respect to the neighborhood center to give a global criterion of image segmentation. In a level set formulation, this criterion defines an energy in terms of the level set functions that represent a partition of the image domain and a bias field that accounts for the intensity inhomogeneity of the image. Therefore, by minimizing this energy, our method is able to simultaneously segment the image and estimate the bias field, and the estimated bias field can be used for intensity inhomogeneity correction (or bias correction). Our method has been validated on synthetic images and real images of various modalities, with desirable performance in the presence of intensity inhomogeneities. Experiments show that our method is more robust to initialization, faster and more accurate than the well-known piecewise smooth model. As an application, our method has been used for segmentation and bias correction of magnetic resonance (MR) images with promising results.

1,201 citations

Patent
24 Oct 2006
TL;DR: In this article, a support structure for positioning sensors on a physiologic tunnel for measuring physical, chemical and biological parameters of the body and to produce an action according to the measured value of the parameters.
Abstract: Support structures for positioning sensors on a physiologic tunnel for measuring physical, chemical and biological parameters of the body and to produce an action according to the measured value of the parameters. The support structure includes a sensor fitted on the support structures using a special geometry for acquiring continuous and undisturbed data on the physiology of the body. Signals are transmitted to a remote station by wireless transmission such as by electromagnetic waves, radio waves, infrared, sound and the like or by being reported locally by audio or visual transmission. The physical and chemical parameters include brain function, metabolic function, hydrodynamic function, hydration status, levels of chemical compounds in the blood, and the like. The support structure includes patches, clips, eyeglasses, head mounted gear and the like, containing passive or active sensors positioned at the end of the tunnel with sensing systems positioned on and accessing a physiologic tunnel.

1,147 citations

Proceedings ArticleDOI
04 Oct 2008
TL;DR: An image super-resolution approach using a novel generic image prior - gradient profile prior, which is a parametric prior describing the shape and the sharpness of the image gradients is proposed.
Abstract: In this paper, we propose an image super-resolution approach using a novel generic image prior - gradient profile prior, which is a parametric prior describing the shape and the sharpness of the image gradients. Using the gradient profile prior learned from a large number of natural images, we can provide a constraint on image gradients when we estimate a hi-resolution image from a low-resolution image. With this simple but very effective prior, we are able to produce state-of-the-art results. The reconstructed hi-resolution image is sharp while has rare ringing or jaggy artifacts.

928 citations