An Evaluation of Prefiltered Reconstruction Schemes for Volume Rendering

Csébfalvi, Balázs

doi:10.1109/tvcg.2007.70414

Cited by 23 publications

(28 citation statements)

References 18 publications

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“…Proof: Writing down (9) explicitly in terms of integrals yields (13) We start from the left-hand side of (13) and use the fact that is scale-invariant (12) to obtain (14) Then, comparing the right-hand side of (13) and (14), we infer that must necessarily satisfy (15) where . Differentiating (15) with respect to and setting , we get (16) where we have used the fact that (there is no scaling for in (12)) and is a real number.…”

Section: ) Data-fidelity Termmentioning

confidence: 99%

“…Fitting 3-D data on geometric shapes is also best done by taking the interpolation model into consideration [11]. Other applications where it plays a vital role include volume rendering for visualization of scalar fields [12]- [14], evaluation of image gradients [15], [16], and texture mapping where a 2-D image is painted on a 3-D surface [17], [18]. Recently, it has also been used for modeling diffusion tensors in magnetic resonance imaging (MRI) [19].…”

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confidence: 99%

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Regularized Interpolation for Noisy Images

Ramani

Thévenaz

Unser

2010

IEEE Trans. Med. Imaging

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Abstract-Interpolation is the means by which a continuously defined model is fit to discrete data samples. When the data samples are exempt of noise, it seems desirable to build the model by fitting them exactly. In medical imaging, where quality is of paramount importance, this ideal situation unfortunately does not occur. In this paper, we propose a scheme that improves on the quality by specifying a tradeoff between fidelity to the data and robustness to the noise. We resort to variational principles, which allow us to impose smoothness constraints on the model for tackling noisy data. Based on shift-, rotation-, and scale-invariant requirements on the model, we show that the -norm of an appropriate vector derivative is the most suitable choice of regularization for this purpose. In addition to Tikhonov-like quadratic regularization, this includes edge-preserving total-variation-like (TV) regularization. We give algorithms to recover the continuously defined model from noisy samples and also provide a data-driven scheme to determine the optimal amount of regularization. We validate our method with numerical examples where we demonstrate its superiority over an exact fit as well as the benefit of TV-like nonquadratic regularization over Tikhonov-like quadratic regularization.

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Section: ) Data-fidelity Termmentioning

confidence: 99%

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confidence: 99%

Regularized Interpolation for Noisy Images

Ramani

Thévenaz

Unser

2010

IEEE Trans. Med. Imaging

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“…Such a prefiltering is not unique. Different prefilters lead to different resultant frequency responses [Csébfalvi 2008]. Although optimal prefilters have been proposed for the trilinear kernel as well [Blu et al 2004;Condat et al 2005], according to our experience, they do not change the frequencydomain behavior as much as for the tricubic B-spline filtering.…”

Section: Introductionmentioning

confidence: 99%

Interactively controlling the smoothing and postaliasing effects in volume visualization

Csébfalvi

Domonkos

2009

Proceedings of the 25th Spring Conference on Computer Graphics

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In volume-rendering applications an appropriate resampling filter is usually chosen by making a compromise between quality and efficiency. Generally, the fine details can be reconstructed by filters of wider support that can better approximate the ideal low-pass filter. On the other hand, if the data is noisy, a filter of a good pass-band behavior might even emphasize the noise. Therefore, to visualize noisy data, a filter of a higher smoothing effect is more favorable. Thus, the choice of the reconstruction filter depends on the quality of the data and the purpose of the visualization as well.In this paper, we propose a scalable volume-rendering technique for interactively controlling the frequency-domain behavior of the reconstruction. Applying our method, the trade-off between the smoothing and postaliasing effects can be set on the fly by using a single slider.

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“…To fully exploit the approximation power of a given reconstruction space, it is required to prefilter the data [35]. The interest of prefiltering for the visualization community has been recognized [9,18], but has not been transposed to derivative reconstruction so far. A notable exception is the recent work of Csébfalvi et al [10] in which they propose FIR derivative prefilters designed to fully exploit the approximation power of the reconstruction space.…”

Section: Introductionmentioning

confidence: 99%

“…A notable exception is the recent work of Csébfalvi et al [10] in which they propose FIR derivative prefilters designed to fully exploit the approximation power of the reconstruction space. Our motivation is the same as in [10]. However, we depart from existing approaches to design IIR prefilters with specific properties, either within the OP framework or by designing combinations of interpolation prefilters and finite differences.…”

Section: Introductionmentioning

confidence: 99%

Gradient Estimation Revitalized

Alim

Möller

Condat

2010

IEEE Trans. Visual. Comput. Graphics

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Fig. 1. DVR images of the carp dataset. Left: Original Cartesian (256 3 ) dataset reconstructed using prefiltered tricubic B-splines and shaded using the analytic gradient. Middle: Downsampled Cartesian (128 3 ) dataset reconstructed using prefiltered tricubic B-splines and shaded by interpolating the gradient obtained through a fourth-order central differencing scheme (pFIR). Right: The middle dataset shaded using our proposed fourth-order shifted gradient estimation scheme (pFIR-s). Notice how the details in the bones and skull are much better preserved as compared to the central-differencing scheme even though the underlying scalar interpolation is the same. This gain in quality comes at no additional cost.Abstract-We investigate the use of a Fourier-domain derivative error kernel to quantify the error incurred while estimating the gradient of a function from scalar point samples on a regular lattice. We use the error kernel to show that gradient reconstruction quality is significantly enhanced merely by shifting the reconstruction kernel to the centers of the principal lattice directions. Additionally, we exploit the algebraic similarities between the scalar and derivative error kernels to design asymptotically optimal gradient estimation filters that can be factored into an infinite impulse response interpolation prefilter and a finite impulse response directional derivative filter. This leads to a significant performance gain both in terms of accuracy and computational efficiency. The interpolation prefilter provides an accurate scalar approximation and can be re-used to cheaply compute directional derivatives on-the-fly without the need to store gradients. We demonstrate the impact of our filters in the context of volume rendering of scalar data sampled on the Cartesian and Body-Centered Cubic lattices. Our results rival those obtained from other competitive gradient estimation methods while incurring no additional computational or storage overhead.

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An Evaluation of Prefiltered Reconstruction Schemes for Volume Rendering

Cited by 23 publications

References 18 publications

Regularized Interpolation for Noisy Images

Regularized Interpolation for Noisy Images

Interactively controlling the smoothing and postaliasing effects in volume visualization

Gradient Estimation Revitalized

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