This paper describes a general purpose algorithm to segment any kind of lesions in CT images. The... more This paper describes a general purpose algorithm to segment any kind of lesions in CT images. The algorithm expects a click or a stroke inside the lesion from the user and learns gray level properties on the fly. It then uses the random walker algorithm and combines multiple 2D segmentation results to produce the final 3D segmentation of the lesion. Quantitative evaluation on 293 lesions demonstrates that the method is ready for clinical use.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006
Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an a... more Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.
In this work, we present a common framework for seeded image segmentation algorithms that yields ... more In this work, we present a common framework for seeded image segmentation algorithms that yields two of the leading methods as special cases -The Graph Cuts and the Random Walker algorithms. The formulation of this common framework naturally suggests a new, third, algorithm that we develop here. Specifically, the former algorithms may be shown to minimize a certain energy with respect to either an ℓ 1 or an ℓ 2 norm. Here, we explore the segmentation algorithm defined by an ℓ ∞ norm, provide a method for the optimization and show that the resulting algorithm produces an accurate segmentation that demonstrates greater stability with respect to the number of seeds employed than either the Graph Cuts or Random Walker methods.
Interactive segmentation is often performed on images that have been stored on disk (e.g., a medi... more Interactive segmentation is often performed on images that have been stored on disk (e.g., a medical image server) for some time prior to user interaction. We propose to use this time to perform an offline precomputation of the segmentation prior to user interaction that significantly decreases the amount of user time necessary to produce a segmentation. Knowing how to effectively precompute the segmentation prior to user interaction is difficult, since a user may choose to guide the segmentation algorithm to segment any object (or multiple objects) in the image. Consequently, precomputation performed prior to user interaction must be performed without any knowledge of the user interaction. Specifically, we show that one may precompute several eigenvectors of the weighted Laplacian matrix of a graph and use this information to produce a linear-time approximation of the Random Walker segmentation algorithm, even without knowing where the foreground/background seeds will be placed. Finally, we also show that this procedure may be interpreted as a seeded (interactive) Normalized Cuts algorithm.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006
A novel method is proposed for performing multilabel, interactive image segmentation. Given a sma... more A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or pre-defined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the pre-labeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs.
In the short time since publication of Boykov and Jolly's seminal paper , graph cuts have become ... more In the short time since publication of Boykov and Jolly's seminal paper , graph cuts have become well established as a leading method in 2D and 3D semi-automated image segmentation. Although this approach is computationally feasible for many tasks, the memory overhead and supralinear time complexity of leading algorithms results in an excessive computational burden for high-resolution data. In this paper, we introduce a multilevel banded heuristic for computation of graph cuts that is motivated by the wellknown narrow band algorithm in level set computation. We perform a number of numerical experiments to show that this heuristic drastically reduces both the running time and the memory consumption of graph cuts while producing nearly the same segmentation result as the conventional graph cuts. Additionally, we are able to characterize the type of segmentation target for which our multilevel banded heuristic will yield different results from the conventional graph cuts. The proposed method has been applied to both 2D and 3D images with promising results.
The recently introduced random walker segmentation algorithm of has been shown to have desirable ... more The recently introduced random walker segmentation algorithm of has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires user-specified labels and produces a segmentation where each segment is connected to a labeled pixel. We show that incorporation of a nonparametric probability density model allows for an extended random walkers algorithm that can locate disconnected objects and does not require user-specified labels. Finally, we show that this formulation leads to a deep connection with the popular graph cuts method of .
This paper describes a general purpose algorithm to segment any kind of lesions in CT images. The... more This paper describes a general purpose algorithm to segment any kind of lesions in CT images. The algorithm expects a click or a stroke inside the lesion from the user and learns gray level properties on the fly. It then uses the random walker algorithm and combines multiple 2D segmentation results to produce the final 3D segmentation of the lesion. Quantitative evaluation on 293 lesions demonstrates that the method is ready for clinical use.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006
Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an a... more Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.
In this work, we present a common framework for seeded image segmentation algorithms that yields ... more In this work, we present a common framework for seeded image segmentation algorithms that yields two of the leading methods as special cases -The Graph Cuts and the Random Walker algorithms. The formulation of this common framework naturally suggests a new, third, algorithm that we develop here. Specifically, the former algorithms may be shown to minimize a certain energy with respect to either an ℓ 1 or an ℓ 2 norm. Here, we explore the segmentation algorithm defined by an ℓ ∞ norm, provide a method for the optimization and show that the resulting algorithm produces an accurate segmentation that demonstrates greater stability with respect to the number of seeds employed than either the Graph Cuts or Random Walker methods.
Interactive segmentation is often performed on images that have been stored on disk (e.g., a medi... more Interactive segmentation is often performed on images that have been stored on disk (e.g., a medical image server) for some time prior to user interaction. We propose to use this time to perform an offline precomputation of the segmentation prior to user interaction that significantly decreases the amount of user time necessary to produce a segmentation. Knowing how to effectively precompute the segmentation prior to user interaction is difficult, since a user may choose to guide the segmentation algorithm to segment any object (or multiple objects) in the image. Consequently, precomputation performed prior to user interaction must be performed without any knowledge of the user interaction. Specifically, we show that one may precompute several eigenvectors of the weighted Laplacian matrix of a graph and use this information to produce a linear-time approximation of the Random Walker segmentation algorithm, even without knowing where the foreground/background seeds will be placed. Finally, we also show that this procedure may be interpreted as a seeded (interactive) Normalized Cuts algorithm.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006
A novel method is proposed for performing multilabel, interactive image segmentation. Given a sma... more A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or pre-defined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the pre-labeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs.
In the short time since publication of Boykov and Jolly's seminal paper , graph cuts have become ... more In the short time since publication of Boykov and Jolly's seminal paper , graph cuts have become well established as a leading method in 2D and 3D semi-automated image segmentation. Although this approach is computationally feasible for many tasks, the memory overhead and supralinear time complexity of leading algorithms results in an excessive computational burden for high-resolution data. In this paper, we introduce a multilevel banded heuristic for computation of graph cuts that is motivated by the wellknown narrow band algorithm in level set computation. We perform a number of numerical experiments to show that this heuristic drastically reduces both the running time and the memory consumption of graph cuts while producing nearly the same segmentation result as the conventional graph cuts. Additionally, we are able to characterize the type of segmentation target for which our multilevel banded heuristic will yield different results from the conventional graph cuts. The proposed method has been applied to both 2D and 3D images with promising results.
The recently introduced random walker segmentation algorithm of has been shown to have desirable ... more The recently introduced random walker segmentation algorithm of has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires user-specified labels and produces a segmentation where each segment is connected to a labeled pixel. We show that incorporation of a nonparametric probability density model allows for an extended random walkers algorithm that can locate disconnected objects and does not require user-specified labels. Finally, we show that this formulation leads to a deep connection with the popular graph cuts method of .
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Papers by Leo Grady