Cubic splines for image interpolation and digital filtering

Hou, H. S.; Andrews, Harry C.

doi:10.1109/tassp.1978.1163154

Cited by 1,008 publications

(106 citation statements)

References 21 publications

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“…The method uses a cubic interpolation through the kernel that convolves with the original measurements 20 . The last method are the B-splines interpolation that is implemented as the nominal resampling method for the S2 L1C products 17,21 . Both cubic convolution and B-splines require a 4×4 kernel grid that produces a smoother image at the expense of a more demanding computational requirement 20,21 .…”

Section: Orthorectification Uncertainty Propagationmentioning

confidence: 99%

“…The last method are the B-splines interpolation that is implemented as the nominal resampling method for the S2 L1C products 17,21 . Both cubic convolution and B-splines require a 4×4 kernel grid that produces a smoother image at the expense of a more demanding computational requirement 20,21 . Figure 9 shows the results for the three different interpolation schemes presented above.…”

Section: Orthorectification Uncertainty Propagationmentioning

confidence: 99%

“…L1C uncertainty at different positions of the pixel and introducing a fully correlated absolute calibration coefficient uncertainty A(b) for the L1B measurements using the bi-linear interpolation (d), cubic convolution (e) and B-splines (f). Non-uniform radiance kernel (values from left to right and up to down in a 4x4 kernel) [ [21,20,10,14], [15,30,24,50], [10,12,30,60], [12,45,36,15]…”

Section: Parameter Uniform and Full Random Uniform And A(b) Correlatedmentioning

confidence: 99%

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Novel techniques for the analysis of the TOA radiometric uncertainty

et al. 2016

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In the framework of the European Copernicus programme, the European Space Agency (ESA) has launched the Sentinel-2 (S2) Earth Observation (EO) mission which provides optical high spatial -resolution imagery over land and coastal areas. As part of this mission, a tool (named S2-RUT, from Sentinel-2 Radiometric Uncertainty Tool) estimates the radiometric uncertainties associated to each pixel using as input the top-of-atmosphere (TOA) reflectance factor images provided by ESA. The initial version of the tool has been implemented -code and user guide available 1 -and integrated as part of the Sentinel Toolbox. The tool required the study of several radiometric uncertainty sources as well as the calculation and validation of the combined standard uncertainty in order to estimate the TOA reflectance factor uncertainty per pixel. Here we describe the recent research in order to accommodate novel uncertainty contributions to the TOA reflectance uncertainty estimates in future versions of the tool. The two contributions that we explore are the radiometric impact of the spectral knowledge and the uncertainty propagation of the resampling associated to the orthorectification process. The former is produced by the uncertainty associated to the spectral calibration as well as the spectral variations across the instrument focal plane and the instrument degradation. The latter results of the focal plane image propagation into the provided orthoimage. The uncertainty propagation depends on the radiance levels on the pixel neighbourhood and the pixel correlation in the temporal and spatial dimensions. Special effort has been made studying non-stable scenarios and the comparison with different interpolation methods.

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Section: Orthorectification Uncertainty Propagationmentioning

confidence: 99%

Section: Orthorectification Uncertainty Propagationmentioning

confidence: 99%

Section: Parameter Uniform and Full Random Uniform And A(b) Correlatedmentioning

confidence: 99%

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Novel techniques for the analysis of the TOA radiometric uncertainty

et al. 2016

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“…Due to insufficient number of observations, image SR is a severely ill-conditioned problem that needs to be regularized via employing various image models and prior knowledge [1][2][3][4][5][6][7][8][9][10][11][12][13]. Among these models, image SR based on sparse representation over learned adaptive dictionaries has received an increased interest [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Coupled dictionary learning for multimodal image super-resolution

Song

Mota

Deligiannis

et al. 2016

2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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Real-world data processing problems often involve multiple data modalities, e.g., panchromatic and multispectral images, positron emission tomography (PET) and magnetic resonance imaging (MRI) images. As these modalities capture information associated with the same phenomenon, they must necessarily be correlated, although the precise relation is rarely known. In this paper, we propose a coupled dictionary learning (CDL) framework to automatically learn these relations. In particular, we propose a new data model to characterize both similarities and discrepancies between multimodal signals in terms of common and unique sparse representations with respect to a group of coupled dictionaries. However, learning these coupled dictionaries involves solving a highly non-convex structural dictionary learning problem. To address this problem, we design a coupled dictionary learning algorithm, referred to sequential recursive optimization (SRO) algorithm, to sequentially learn these dictionaries in a recursive manner. By capitalizing on our model and algorithm, we conceive a CDL based multimodal image super-resolution (SR) approach. Practical multispectral image SR experiments demonstrate that our SR approach outperforms the bicubic interpolation and the state-of-the-art dictionary learning based image SR approach, with Peak-SNR (PSNR) gains of up to 8.2 dB and 5.1 dB, respectively.

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“…The interpolation-restoration SR methods tend to be the simplest, both conceptually and in terms of the computational complexity [1]. A wide variety of such methods have been proposed in the literature [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A collaborative adaptive Wiener filter for multi-frame super-resolution

Mohamed

Hardie

2015

Front. Phys.

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Factors that can limit the effective resolution of an imaging system may include aliasing from under-sampling, blur from the optics and external factors, and sensor noise. Image restoration and super-resolution (SR) techniques can be used to improve image resolution. One SR method, developed recently, is the adaptive Wiener filter (AWF) SR algorithm. This is a multi-frame SR method that combines registered temporal frames through a joint nonuniform interpolation and restoration process to provide a high-resolution image estimate. Variations of this method have been demonstrated to be effective for multi-frame SR, as well demosaicing RGB and polarimetric imagery. While the AWF SR method effectively exploits subpixel shifts between temporal frames, it does not exploit self similarity within the observed imagery. However, very recently, the current authors have developed a multi-patch extension of the AWF method. This new method is referred to as a collaborative AWF (CAWF). The CAWF method employs a finite size moving window. At each position, we identify the most similar patches in the image within a given search window about the reference patch. A single-stage weighted sum of all of the pixels in all of the similar patches is used to estimate the center pixel in the reference patch. Like the AWF, the CAWF can perform nonuniform interpolation, deblurring, and denoising jointly. The big advantage of the CAWF, vs. the AWF, is the CAWF can also exploit self-similarity. This is particularly beneficial for treating low signal-to-noise ratio (SNR) imagery. To date, the CAWF has only been developed for Nyquist-sampled single-frame image restoration. In this paper, we extend the CAWF method for multi-frame SR. We provide a quantitative performance comparison between the CAWF SR and the AWF SR techniques using real and simulated data. We demonstrate that CAWF SR outperforms AWF SR, especially in low SNR applications.

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Cubic splines for image interpolation and digital filtering

Cited by 1,008 publications

References 21 publications

Novel techniques for the analysis of the TOA radiometric uncertainty

Novel techniques for the analysis of the TOA radiometric uncertainty

Coupled dictionary learning for multimodal image super-resolution

A collaborative adaptive Wiener filter for multi-frame super-resolution

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