On reconstructing curved object boundaries from sparse sets of X-ray images

Sullivan, Steve; Noble, J. Alison; Ponce, Jean

doi:10.1007/bfb0034974

Cited by 4 publications

(5 citation statements)

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“…(16), and deformation f int after the internal (curve-driven) update from Eq. (18). Note that in our implementation f ext = τ |δ i |.…”

Section: Resultsmentioning

confidence: 99%

“…Unlike methods that fit the curve to local features as e.g. sharp edges [17,18], our curve is deformed so that the resulting segmentation of the reconstruction domain fits the data according to the global energy from Eq. (8).…”

Section: Resultsmentioning

confidence: 99%

“…There are a few examples [17] and [18] of using a parametric deformable curve for tomographic reconstruction. These methods attempt to locate the boundaries of the object by exploiting the discontinuities in the sinogram, while [19] handles both 2D and 3D segmentation of a single closed object with a forward model based on ray tracing.…”

Section: Related Workmentioning

confidence: 99%

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Computing segmentations directly from x-ray projection data via parametric deformable curves

Dahl¹,

Dahl²,

Hansen³

2017

Meas. Sci. Technol.

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We describe an efficient algorithm that computes a segmented reconstruction directly from x-ray projection data. Our algorithm uses a parametric curve to define the segmentation. Unlike similar approaches which are based on level-sets, our method avoids a pixel or voxel grid; hence the number of unknowns is reduced to the set of points that define the curve, and attenuation coefficients of the segments. Our current implementation uses a simple closed curve and is capable of separating one object from the background. However, our basic algorithm can be applied to an arbitrary topology and multiple objects corresponding to different attenuation coefficients in the reconstruction. Through systematic tests we demonstrate a high robustness to the noise, and an excellent performance under a small number of projections.

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“…(16), and deformation f int after the internal (curve-driven) update from Eq. (18). Note that in our implementation f ext = τ |δ i |.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Computing segmentations directly from x-ray projection data via parametric deformable curves

Dahl¹,

Dahl²,

Hansen³

2017

Meas. Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…al. [82]. The latter method was devised as an alternative to the level set method of Osher and Sethian [64] which is needed to evolve wavefronts according to geometric optics.…”

Section: Motion Of Curves In Three Spatial Dimensionsmentioning

confidence: 99%

“…Other tomographics reconstruction techniques have been proposed, for example those that utilize discrete tomagraphy strategies [80,73,81,82], and deformable models [83,84,85,86,87]. The literature also describes many xli examples of level sets as curve and surface models for image segmentation [7,6,41,88].…”

Section: Related Workmentioning

confidence: 99%

Level set and PDE methods for computer graphics

Breen

Fedkiw

Museth

et al. 2004

ACM SIGGRAPH 2004 Course Notes

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Course AbstractLevel set methods, an important class of partial differential equation (PDE) methods, define dynamic surfaces implicitly as the level set (isosurface) of a sampled, evolving nD function. The course begins with preparatory material that introduces the concept of using partial differential equations to solve problems in computer graphics, geometric modeling and computer vision. This will include the structure and behavior of several different types of differential equations, e.g. the level set equation and the heat equation, as well as a general approach to developing PDE-based applications. The second stage of the course will describe the numerical methods and algorithms needed to actually implement the mathematics and methods presented in the first stage. The course closes with detailed presentations on several level set/PDE applications, including image/video inpainting, pattern formation, image/volume processing, 3D shape reconstruction, image/volume segmentation, image/shape morphing, geometric modeling, anisotropic diffusion, and natural phenomena simulation. PrerequisitesKnowledge of calculus, linear algebra, computer graphics, geometric modeling, image processing and computer vision. Some familiarity with differential geometry, differential equations, numerical computing and image processing is strongly recommended, but not required. participates in the reviewing process for a number of journals and funding agencies. He has published over 45 research papers in computational physics, computer graphics and vision, as well as a new book on level set methods. Additionally, he has been a consultant for Industrial Light + Magic for the last three years.

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Level Set Segmentation of Biological Volume Datasets

Breen

Whitaker

Museth³

et al.

Handbook of Biomedical Image Analysis

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This chapter describes level set techniques for extracting surface models from a broad variety of biological volume datasets. These techniques have been incorporated into a more general framework that includes other volume processing algorithms. The volume datasets are produced from standard 3D imaging devices, and are all noisy samplings of complex biological structures with boundaries that have low and often varying contrasts. The level set segmentation method, which is well documented in the literature, creates a new volume from the input data by solving an initial value partial differential equation (PDE) with user-defined feature-extracting terms. Given the local/global nature of these terms, proper initialization of the level set algorithm is extremely important. Thus, level set deformations alone are not sufficient, they must be combined with powerful pre-processing and data analysis techniques in order to produce successful segmentations. This chapter describes the pre-processing and data analysis techniques that have been developed for a number of segmentation applications, as well as the general structure of our framework. Several standard volume processing algorithms have been incorporated into the framework in order to segment datasets generated from MRI, CT and TEM scans.A technique based on moving least-squares has been developed for segmenting multiple non-uniform scans of a single object. New scalar measures have been defined for extracting structures from diffusion tensor MRI scans. Finally, a direct approach to the segmentation of incomplete tomographic data using density parameter estimation is described. These techniques, combined with level set surface deformations, allow us to segment many different types of biological volume datasets.

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On reconstructing curved object boundaries from sparse sets of X-ray images

Cited by 4 publications

References 0 publications

Computing segmentations directly from x-ray projection data via parametric deformable curves

Computing segmentations directly from x-ray projection data via parametric deformable curves

Level set and PDE methods for computer graphics

Level Set Segmentation of Biological Volume Datasets

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