Multi-modal 3D Shape Reconstruction Under Calibration Uncertainty using Parametric Level Set Methods

Eliasof, Moshe; Sharf, Andrei; Treister, Eran

doi:10.48550/arxiv.1904.10379

Cited by 2 publications

(11 citation statements)

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“…. N. The ψ j (r) are often taken to be RBFs [21,26,36,47,49,50,56,64]. We will refer to use of such basis functions as "traditional PaLS," and it is against such representations that we compare our new PaLEnTIR representation.…”

Section: Parametric Level Set Methodsmentioning

confidence: 99%

“…One of the issues is that it can only produce circular cross-sections. For certain classes of shapes, such as one that are highly anisotropic, the use of circular cross sections is inefficient [26]. It is also stated in [26] that in 3D models that adopt RBF representation, such as in [45], that is restricted spherical cross sections, results in limited expressiveness and spherical effects in the reconstructed objects.…”

Section: Parametric Level-sets Enhancedmentioning

confidence: 99%

“…Moreover, it was shown in [2] that the low order representation of the inverse problem makes it possible to use Newton and quasi-Newton methods for determining the PaLS parameters. In recent work, the PaLS model in [2] and variants have been used across a range of application areas and imaging modalities including geophysics [52,53] and reservoir monitoring [34,35], image segmentation [54], acoustic scattering [21], dynamic tomography [56], dual-energy computed tomography [64], electrical impedance tomography [49,50], electromagnetic imaging [36], electrical capacitance tomography [47], and multi-modal imaging [26].…”

mentioning

confidence: 99%

“…A second area of limitation for PaLS concerns the family of basis functions used to model the level set function. In a traditional PaLS setting, the level set function is obtained using a weighted superposition of a set of predetermined collection of basis functions, most often radial basis functions (RBFs) [21,36,47,49,50,56,64] but also polynomials [40], multiquadrics [54], ellipsoidal [26], and polytopes [54]. We focus here on RBFs due to their prevalence as well as a some nice properties specifically of compactly supported RBFs [2].…”

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confidence: 99%

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Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

Ozsar¹,

Kilmer²,

Miller³

et al. 2022

Preprint

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For inverse problems where one is concerned with recovering the shape and contrast of an unknown number of objects embedded in a medium, parametric level set (PaLS) methods provide much of the flexibility of traditional level set methods while avoiding many of the difficulties such as regularization, re-initialization. In this paper, we consider the restoration and reconstruction of piecewise constant objects in two and three dimensions using PaLEnTIR , a significantly enhanced PaLS model relative to the current state-of-the-art. The primary contribution of this paper is a new PaLS formulation which requires only a single level set function to recover a scene with piecewise constant objects possessing multiple unknown contrasts. Our model offers distinct advantages over current approaches to the multi-contrast, multi-object problem, all of which require multiple level sets and explicit estimation of the contrast magnitudes. Given upper and lower bounds on the contrast, our approach is able to recover objects with any distribution of contrasts and eliminates the need to know either the number of contrasts in a given scene or their values. We provide an iterative process for finding these space-varying contrast limits. Relative to most PaLS methods which employ radial basis functions (RBFs), our model makes use of non-isotropic basis functions, thereby expanding the class of shapes that a PaLS model of a given complexity can approximate. Finally, PaLEnTIR improves the conditioning of the Jacobian matrix required as part of the parameter identification process and consequently accelerates the optimization methods by controlling the magnitude of the PaLS expansion coefficients, fixing the centers of the basis functions, and the uniqueness of parametric to image mappings provided by the new parameterization. We demonstrate the performance of the new approach using both 2D and 3D variants of X-ray computed tomography, diffuse optical tomography (DOT), denoising, deconvolution problems. Application to experimental sparse CT data and simulated data with different types of noise are performed to further validate the proposed method.

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Section: Parametric Level Set Methodsmentioning

confidence: 99%

Section: Parametric Level-sets Enhancedmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

Ozsar¹,

Kilmer²,

Miller³

et al. 2022

Preprint

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show abstract

“…This includes [13,14,15] that are based on the Mumford-Shah model [16] where boundaries are represented using level-sets [17]. Recently, the parametric levelset method [18] has been used for tomographic segmentation in [19,20] where level-sets are represented as an aggregation of radial basis functions. Although the parametric level-set method has fewer unknown variables, its forward projection still depends on a regular grid.…”

Section: Related Workmentioning

confidence: 99%

Shape from Projections via Differentiable Forward Projector for Computed Tomography

Koo,

Dahl,

Bærentzen

et al. 2020

Preprint

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In tomography, forward projection of 3D meshes has been mostly studied to simulate data acquisition. However, such works did not consider an inverse process of estimating shapes from projections. In this paper, we propose a differentiable forward projector for 3D meshes, to bridge the gap between the forward model for 3D surfaces and optimization. We view the forward projection as a rendering process, and make it differentiable by extending a recent work in differentiable rasterization. We use the proposed forward projector to reconstruct 3D shapes directly from projections. Experimental results for single-object problems show that our method outperforms the traditional voxel-based methods on noisy simulated data. We also apply our method on real data from electron tomography to estimate the shapes of some nanoparticles.

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Multi-modal 3D Shape Reconstruction Under Calibration Uncertainty using Parametric Level Set Methods

Cited by 2 publications

References 0 publications

Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

Shape from Projections via Differentiable Forward Projector for Computed Tomography

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