Kernel Regression for Image Processing and Reconstruction

Takeda, Hiroyuki; Farsiu, Sina; Milanfar, Peyman

doi:10.1109/tip.2006.888330

Cited by 1,247 publications

(1,061 citation statements)

References 37 publications

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“…Furthermore, it is desirable to have kernels that adapt themselves to the local structure of the measured signal, providing, for instance, strong filtering along an edge rather than across it. This last point is indeed the motivation behind the steering KR framework [22] which we will review in Section 2.2.…”

Section: Kernel Regression In 2-dmentioning

confidence: 97%

“…We fix λ ′ = 0.1, λ ′′ = 0.1, and α = 0.2 in this work. More details about the effectiveness and the choice of the parameters can be found in [22]. With the above choice of the smoothing matrix and a Gaussian kernel, we now have the steering kernel function as…”

Section: Steering Kernel Functionmentioning

confidence: 99%

“…In a related work [24], we presented a space-time video upscaling method, called 3-D iterative steering kernel regression (3-D ISKR), in which explicit subpixel motion estimation is again avoided. 3-D ISKR is an extension of 2-D steering kernel regression (SKR) proposed in [22,21]. SKR is closely related to bilateral filtering [25,3] and normalized convolution [17].…”

Section: Introductionmentioning

confidence: 99%

“…In this chapter, we build upon the 2-D steering kernel regression framework proposed in [22], and develop a spatiotemporal (3-D) framework for processing video. Specifically, we propose an approach we call motion-assisted steering kernel (MASK) regression.…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, local kernel regression is applied to compute weighted least-squares optimal pixel estimates. Although 2-D kernel regression has been applied to achieve super-resolution reconstruction through fusion of multiple pre-registered frames on to a 2-D plane [22,17], the proposed method is different in that it does not require explicit motion compensation of the video frames. Instead, we use 3-D weighting kernels that are "warped" according to estimated motion vectors, such that the regression process acts directly upon the video data.…”

Section: Introductionmentioning

confidence: 99%

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Spatiotemporal Video Upscaling Using Motion-Assisted Steering Kernel (MASK) Regression

Takeda

Beek²,

Milanfar

2010

Signals and Communication Technology

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In this chapter, we present Motion Assisted Steering Kernel (MASK) regression, a novel multi-frame approach for interpolating video data spatially, temporally, or spatiotemporally, and for video noise reduction, including compression artifact removal. The MASK method takes both local spatial orientations and local motion vectors into account and adaptively constructs a suitable filter at every position of interest. Moreover, we present a practical algorithm based on MASK that is both robust and computationally efficient. In order to reduce the computational and memory requirements, we process each frame in a block-by-block manner, utilizing a block-based motion model. Instead of estimating the local dominant orientation by singular value decomposition, we estimate the orientations based on a technique similar to vector quantization. We develop a technique to locally adapt the regression order, which allows enhancing the denoising effect in flat areas, while effectively preserving major edges and detail in texture areas. Comparisons between MASK and other state-of-the-art video upscaling methods demonstrate the effectiveness of our approach.

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Section: Kernel Regression In 2-dmentioning

confidence: 97%

Section: Steering Kernel Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spatiotemporal Video Upscaling Using Motion-Assisted Steering Kernel (MASK) Regression

Takeda

Beek²,

Milanfar

2010

Signals and Communication Technology

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Abnormal Foveal Morphology in Ocular Albinism Imaged With Spectral-Domain Optical Coherence Tomography

Chong¹

2009

Arch Ophthalmol

123

101

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To evaluate the spectrum of foveal architecture in pediatric albinism and to assess the utility of spectral-domain optical coherence tomography (OCT) in ocular imaging of children with nystagmus. Methods: Spectral-domain OCT imaging was performed on study subjects in 3 groups: subjects with ocular albinism (OA) or suspected OA with foveal hypoplasia, with nystagmus, and with or without iris transillumination; a subject with oculocutaneous albinism and Hermansky-Pudlak syndrome; and control subjects. Dense volumetric scans of each fovea were captured using standard and handheld spectral-domain OCT devices. Images were postprocessed and scored for the presence and configuration of each retinal layer across the fovea. Results: High-quality spectral-domain OCT images obtained from each subject revealed a range of abnormalities in subjects with OA or suspected OA and the subject with oculocutaneous albinism and Hermansky-Pudlak syndrome: persistence of an abnormal, highly reflective band across the fovea, multiple inner retinal layers normally absent at the center of the fovea, and loss of the normally thickened photoreceptor nuclear layer at the fovea when compared with that in control subjects. The optic nerve was elevated in multiple eyes of subjects with OA or suspected OA and the subject with oculocutaneous albinism and Hermansky-Pudlak syndrome. Conclusions: A spectrum of foveal morphological abnormalities is seen in subjects with OA or suspected OA, which in some cases contrasted with previous studies using time-domain OCT. These OCT findings clarify the morphology of foveal hypoplasia seen clinically. This imaging modality may be useful in evaluating children.

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A KDE‐Based Random Walk Method for Modeling Reactive Transport With Complex Kinetics in Porous Media

Sole‐Mari

Fernàndez-García

Rodríguez‐Escales

et al. 2017

Water Resources Research

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In recent years, a large body of the literature has been devoted to study reactive transport of solutes in porous media based on pure Lagrangian formulations. Such approaches have also been extended to accommodate second‐order bimolecular reactions, in which the reaction rate is proportional to the concentrations of the reactants. Rather, in some cases, chemical reactions involving two reactants follow more complicated rate laws. Some examples are (1) reaction rate laws written in terms of powers of concentrations, (2) redox reactions incorporating a limiting term (e.g., Michaelis‐Menten), or (3) any reaction where the activity coefficients vary with the concentration of the reactants, just to name a few. We provide a methodology to account for complex kinetic bimolecular reactions in a fully Lagrangian framework where each particle represents a fraction of the total mass of a specific solute. The method, built as an extension to the second‐order case, is based on the concept of optimal Kernel Density Estimator, which allows the concentrations to be written in terms of particle locations, hence transferring the concept of reaction rate to that of particle location distribution. By doing so, we can update the probability of particles reacting without the need to fully reconstruct the concentration maps. The performance and convergence of the method is tested for several illustrative examples that simulate the Advection‐Dispersion‐Reaction Equation in a 1‐D homogeneous column. Finally, a 2‐D application example is presented evaluating the need of fully describing non‐bilinear chemical kinetics in a randomly heterogeneous porous medium.

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Kernel Regression for Image Processing and Reconstruction

Cited by 1,247 publications

References 37 publications

Spatiotemporal Video Upscaling Using Motion-Assisted Steering Kernel (MASK) Regression

Spatiotemporal Video Upscaling Using Motion-Assisted Steering Kernel (MASK) Regression

Abnormal Foveal Morphology in Ocular Albinism Imaged With Spectral-Domain Optical Coherence Tomography

A KDE‐Based Random Walk Method for Modeling Reactive Transport With Complex Kinetics in Porous Media

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