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13
Denoising functional MR images: a comparison of wavelet denoising and Gaussian smoothing
 IEEE Transactions on Medical Imaging
, 2004
"... Abstract — We present a general waveletbased denoising scheme for functional magnetic resonance imaging (fMRI) data and compare it to Gaussian smoothing, the traditional denoising method used in fMRI analysis. Onedimensional WaveLab thresholding routines were adapted to twodimensional images, and ..."
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Cited by 20 (2 self)
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Abstract — We present a general waveletbased denoising scheme for functional magnetic resonance imaging (fMRI) data and compare it to Gaussian smoothing, the traditional denoising method used in fMRI analysis. Onedimensional WaveLab thresholding routines were adapted to twodimensional images, and applied to 2D wavelet coefficients. To test the effect of these methods on the signaltonoise ratio (SNR), we compared the SNR of 2D fMRI images before and after denoising, using both Gaussian smoothing and waveletbased methods. We simulated a fMRI series with a time signal in an active spot, and tested the methods on noisy copies of it. The denoising methods were evaluated in two ways: by the average temporal SNR inside the original activated spot, and by the shape of the spot detected by thresholding the temporal SNR maps. Denoising methods that introduce much smoothness are better suited for low SNRs, but for images of reasonable quality they are not preferable, because they introduce heavy deformations. Waveletbased denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions. We also performed statistical parametric mapping (SPM) on the denoised simulated time series, as well as on a real fMRI data set. False discovery rate control was used to correct for multiple comparisons. The results show that the methods that produce smooth images introduce more false positives. The less smoothing waveletbased methods, although generating more false negatives, produce a smaller total number of errors than Gaussian smoothing or waveletbased methods with a large smoothing effect. Index Terms — Functional neuroimaging, waveletbased denoising, Gaussian smoothing, statistical parametric mapping, false discovery rate control. I.
Highquality volume rendering with resampling in the frequency domain
 IN PROCEEDINGS OF EUROGRAPHICS / IEEE VGTC SYMPOSIUM ON VISUALIZATION
, 2005
"... This work introduces a volume rendering technique that is conceptually based on the shearwarp factorization. We propose to perform the shear transformation entirely in the frequency domain. Unlike the standard shearwarp algorithm, we allow for arbitrary sampling distances along the viewing rays, i ..."
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Cited by 11 (2 self)
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This work introduces a volume rendering technique that is conceptually based on the shearwarp factorization. We propose to perform the shear transformation entirely in the frequency domain. Unlike the standard shearwarp algorithm, we allow for arbitrary sampling distances along the viewing rays, independent of the view direction. The accurate scaling of the volume slices is achieved by using the zero padding interpolation property. Finally, a high quality gradient estimation scheme is presented which uses the derivative theorem of the Fourier transform. Experimental results have shown that the presented method outperforms established algorithms in the quality of the produced images. If the data is sampled above the Nyquist rate the presented method is capable of a perfect reconstruction of the original function.
Multiresolution Maximum Intensity Volume Rendering by Morphological Adjunction Pyramids
 In Data Visualization 2001. Proc. Joint Eurographics – IEEE TCVG Symposium on Visualization, May 2830, 2001
, 2001
"... We describe a multiresolution extension to maximum intensity projection (MIP) volume rendering, allowing progressive refinement and perfect reconstruction. The method makes use of morphological adjunction pyramids. The pyramidal analysis and synthesis operators are composed of morphological 3D e ..."
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Cited by 7 (4 self)
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We describe a multiresolution extension to maximum intensity projection (MIP) volume rendering, allowing progressive refinement and perfect reconstruction. The method makes use of morphological adjunction pyramids. The pyramidal analysis and synthesis operators are composed of morphological 3D erosion and dilation, combined with dyadic downsampling for analysis and dyadic upsampling for synthesis. In this case the MIP operator can be interchanged with the synthesis operator. This fact is the key to an efficient multiresolution MIP algorithm, because it allows the computation of the maxima along the line of sight on a coarse level, before applying a twodimensional synthesis operator to perform reconstruction of the projection image to a finer level. For interpolation and resampling of volume data, which is required to deal with arbitrary view directions, morphological sampling is used, an interpolation method well adapted to the nonlinear character of MIP. The structure of the resulting multiresolution algorithm is very similar to wavelet splatting, the main differences being that (i) linear summation of voxel values is replaced by maximum computation, and (ii) linear wavelet filters are replaced by (nonlinear) morphological filters.
Volumetric Attribute Filtering and Interactive Visualization using the MaxTree Representation
"... Abstract—The MaxTree, designed for morphological attribute filtering in image processing, is a data structure in which the nodes represent connected components for all threshold levels in a data set. Attribute filters compute some attribute describing the shape or size of each connected component, ..."
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Cited by 6 (2 self)
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Abstract—The MaxTree, designed for morphological attribute filtering in image processing, is a data structure in which the nodes represent connected components for all threshold levels in a data set. Attribute filters compute some attribute describing the shape or size of each connected component, and then decide which components to keep or to discard. In this paper, we augment the basic MaxTree data structure such that interactive volumetric filtering and visualization becomes possible. We introduce extensions that allow (i) direct, splattingbased, volume rendering, (ii) representation of the MaxTree on graphics hardware, and (iii) fast active cell selection for isosurface generation. In all three cases, we can use the MaxTree representation for visualization directly, without needing to reconstruct the volumetric data explicitly. We show that both filtering and visualization can be performed at interactive frame rates, ranging between 2.4 and 32 frames per seconds. In contrast, a standard texturebased volume visualization method manages only between 0.5 and 1.8 frames per second. For isovalue browsing, the experimental results show that the performance is comparable to the performance of an interval tree, where our method has the advantage that both filter threshold browsing and isolevel browsing are fast. It is shown that the methods using graphics hardware can be extended to other connected filters. Index Terms—MaxTree, nonlinear filtering, mathematical morphology, volume visualization, connected filters I.
Morphological Pyramids in Multiresolution MIP Rendering of Large Volume Data: Survey and New Results
 J. Math. Imag. Vision 2005
"... We recently proposed a multiresolution representation for maximum intensity projection (MIP) volume rendering based on morphological adjunction pyramids which allow progressive refinement and have the property of perfect reconstruction. In this algorithm the pyramidal analysis and synthesis operator ..."
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Cited by 4 (3 self)
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We recently proposed a multiresolution representation for maximum intensity projection (MIP) volume rendering based on morphological adjunction pyramids which allow progressive refinement and have the property of perfect reconstruction. In this algorithm the pyramidal analysis and synthesis operators are composed of morphological erosion and dilation, combined with dyadic downsampling for analysis and dyadic upsampling for synthesis. Here we introduce an alternative pyramid scheme in which a morphological opening instead of an erosion is used for pyramidal analysis. As a result, the approximation accuracy when rendering from higher levels of the pyramid is improved. Categories and Subject Descriptors (according to ACM CCS): I.3.6 [Computer Graphics]: Interaction techniques. I.4.10 [Image processing and Computer vision]: Image Representation, Hierarchical, Morphological.
Interactive transfer function control for monte carlo volume rendering
 In VV ’04: Proceedings of the 2004 IEEE Symposium on Volume Visualization and Graphics (VV’04
, 2004
"... Figure 1: Monte Carlo volume rendering with (b, d) and without (a, c) transfer function parameter tuning. Although Monte Carlo Volume Rendering (MCVR) is an efficient pointbased technique for generating simulated Xray images from large CT data, its practical application in medical imaging systems ..."
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Cited by 4 (0 self)
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Figure 1: Monte Carlo volume rendering with (b, d) and without (a, c) transfer function parameter tuning. Although Monte Carlo Volume Rendering (MCVR) is an efficient pointbased technique for generating simulated Xray images from large CT data, its practical application in medical imaging systems is limited by the relatively expensive preprocessing. The quality of images is strongly influenced by the transfer function, which maps a data value onto a sampling probability. An appropriate transfer function concentrates the point samples onto the region of interest. Since it is data dependent, a fine parameter tuning is necessary. However, the costly preprocessing has to be repeated whenever the transfer function parameters are modified. In this paper a new preprocessing algorithm is proposed for MCVR, which allows for an interactive transfer function control in the rendering phase, providing a visual feedback in a couple of seconds. In order to rapidly recompute point samples according to the modified transfer function, an efficient hybrid sampling strategy is applied, which combines the advantages of the probabilistic Monte Carlo sampling and the deterministic quasiMonte Carlo sampling.
Monte carlo volume rendering
 In Proc. of IEEE Visualization
, 2003
"... Figure 1: Perspective quasiMonte Carlo volume rendering of an engine block using progressive refinement. In this paper a novel volumerendering technique based on Monte Carlo integration is presented. As a result of a preprocessing, a point cloud of random samples is generated using a normalized co ..."
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Cited by 1 (0 self)
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Figure 1: Perspective quasiMonte Carlo volume rendering of an engine block using progressive refinement. In this paper a novel volumerendering technique based on Monte Carlo integration is presented. As a result of a preprocessing, a point cloud of random samples is generated using a normalized continuous reconstruction of the volume as a probability density function. This point cloud is projected onto the image plane, and to each pixel an intensity value is assigned which is proportional to the number of samples projected onto the corresponding pixel area. In such a way a simulated Xray image of the volume can be obtained. Theoretically, for a fixed image resolution, there exists an M number of samples such that the average standard deviation of the estimated pixel intensities is under the level of quantization error regardless of the number of voxels. Therefore Monte Carlo Volume Rendering (MCVR) is mainly proposed to efficiently visualize large volume data sets. Furthermore, network applications are also supported, since the tradeoff between image quality and interactivity can be adapted to the bandwidth of the client/server connection by using progressive refinement.
und
"... To my parents Frequency domain volume rendering (FDVR), also known as Fourier volume rendering (FVR), is currently the asymptotically fastest volume rendering method known. In accordance to the Fourier projection slice theorem this method needs the 3D spatial data to be transformed to the frequency ..."
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To my parents Frequency domain volume rendering (FDVR), also known as Fourier volume rendering (FVR), is currently the asymptotically fastest volume rendering method known. In accordance to the Fourier projection slice theorem this method needs the 3D spatial data to be transformed to the frequency domain in a preprocessing step by use of the fast Fourier transform (FFT). The perframe rendering includes the user interaction part (the user chooses a viewing direction) and the computational part (resampling of a slice plane perpendicular to the viewing direction and an inverse 2D FFT) to generate an Xray like image. My idea was to adapt the regular algorithm to the bodycentered cubic (BCC) lattice (i. e., one additional sample is placed right into the center of eight neighboring samples making up a cube) as this special sampling geometry has the great advantage of needing 29.3 % fewer samples but maintaining
The Effect of Image Enhancement on the Statistical Analysis of Functional Neuroimages: WaveletBased Denoising and Gaussian Smoothing
"... We present a general waveletbased denoising scheme for functional neuroimages and compare it to Gausssian smoothing, using the quality of the subsequent statistical analysis as a measure. Statistical analysis is done with the SPM method, and FDR control is used to correct for multiple hypothesis te ..."
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We present a general waveletbased denoising scheme for functional neuroimages and compare it to Gausssian smoothing, using the quality of the subsequent statistical analysis as a measure. Statistical analysis is done with the SPM method, and FDR control is used to correct for multiple hypothesis testing. Tests are done on simulated data as well as on a real fMRI data set.
Polyphase decompositions and shiftinvariant discrete wavelet transforms
"... in the frequency domain ..."