A locally adaptive zooming algorithm for digital images

Battiato, Sebastiano; Gallo, Giovanni; Stanco, Filippo

doi:10.1016/s0262-8856(02)00089-6

Cited by 160 publications

(114 citation statements)

References 11 publications

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“…Setting the derivative to 0, the optimal can be represented by (6) where is a matrix with similarity weights on the diagonal line.…”

Section: A One-dimensional Signalsmentioning

confidence: 99%

“…For the MLS estimator , we can derive (23) According to (6) and (12), we can derive the relationship between MLS estimator and KRR estimator as follows: (24) A good parameter should reduce the mean square error (MSE) of KRR estimator . Therefore, it is necessary to derive , where denotes the distance from KRR estimator to the ground true model weights .…”

Section: Regularization Parameters Settingmentioning

confidence: 99%

“…The algorithm in [5] is applied to a linearly expanded image as a post-process to enhance edges using a weighted average of neighboring pixels chosen explicitly by the Canny edge detector. In LAZA [6], Battiato et al use simple rules and configurable thresholds to explicitly detect edges and update the interpolation process accordingly. They further extend this work by using local gradient information based on a neural network to achieve better edge sharpness and computation efficiency [7], [8].…”

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confidence: 99%

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Image interpolation via regularized local linear regression

Liu

Zhao

Xiong

et al. 2010

28th Picture Coding Symposium

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Abstract-The linear regression model is a very attractive tool to design effective image interpolation schemes. Some regression-based image interpolation algorithms have been proposed in the literature, in which the objective functions are optimized by ordinary least squares (OLS). However, it is shown that interpolation with OLS may have some undesirable properties from a robustness point of view: even small amounts of outliers can dramatically affect the estimates. To address these issues, in this paper we propose a novel image interpolation algorithm based on regularized local linear regression (RLLR). Starting with the linear regression model where we replace the OLS error norm with the moving least squares (MLS) error norm leads to a robust estimator of local image structure. To keep the solution stable and avoid overfitting, we incorporate the 2 -norm as the estimator complexity penalty. Moreover, motivated by recent progress on manifold-based semi-supervised learning, we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points. Specifically, our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state-of-the-art interpolation algorithms, especially in image edge structure preservation.

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“…Setting the derivative to 0, the optimal can be represented by (6) where is a matrix with similarity weights on the diagonal line.…”

Section: A One-dimensional Signalsmentioning

confidence: 99%

Section: Regularization Parameters Settingmentioning

confidence: 99%

mentioning

confidence: 99%

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Image interpolation via regularized local linear regression

Liu

Zhao

Xiong

et al. 2010

28th Picture Coding Symposium

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show abstract

“…Thus, the VMF interpolation function f (·) produces the output which is restricted to the dynamic range of the input samples and thus, it never introduces new samples. The selective nature of the VMF operator and the use of the minimization concept ensure the outputting of the color vector which is the most similar, under the aggregated distance criterion (6), to other color vectors in W (p,q) .…”

Section: A a Vector Median Filtermentioning

confidence: 99%

“…Since a typical natural image exhibits significant spectral correlation among its RGB color planes, scalar techniques performed on the individual color channels are insufficient since the correlation between the channels is not considered producing thus various spectral artifacts and color shifts [1], [3]. Moreover, many conventional methods such as bilinear interpolation and spline based techniques listed in [4]- [6] often cause excessive blurring or geometric artifacts [3], [7]. Therefore, the development of the more sophisticated vector based, nonlinear approaches is of paramount importance.…”

Section: Introductionmentioning

confidence: 99%

Vector operators for color image zooming

Lukáč¹,

Plataniotis²,

Smołka³

et al. 2005

Proceedings of the IEEE International Symposium on Industrial Electronics, 2005. ISIE 2005.

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Abstract-This paper presents a vector filtering framework for color image zooming. Popular vector filters such as the vector median filter, the basic vector directional filter and the data-adaptive vector filter are used to enlarge the spatial resolution of the full-color, Red-Green-Blue images. Extensive experimentation reported int this paper indicates that the proposed color image zoomers preserve the spectral and spatial characteristics of the processed image and produce enlarged images without color shifts and artifacts.

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Two‐dimensional adaptive Whittaker–Shannon Sinc‐based zooming

Ciulla,

Shabani,

Yahaya

2024

Applied Research

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In this work, we introduce a novel image zooming methodology that transitions from a nonadaptive Sin‐based approach to an adaptive Sinc‐based zooming technique. The two techniques base their theoretical foundation on the Whittaker–Shannon interpolation formula and the Nyquist theorem. The evolution into adaptive Sinc‐based zoom is accomplished through the use of two novel concepts: (1) the pixel‐local scaled k‐space and (2) the k‐space filtering sigmoidal function. The pixel‐local scaled k‐space is the standardized and scaled k‐space magnitude of the image to zoom. The k‐space filtering sigmoidal function scales the pixel‐local scaled k‐space values into the numerical interval [0, 1]. Using these two novel concepts, the Whittaker–Shannon interpolation formula is elaborated and used to zoom images. Zooming is determined by the shape of the Sinc functions in the Whittaker–Shannon interpolation formula, which, in turn, depends on the combined effect of the pixel‐local scaled k‐space, the sampling rate, and the k‐space filtering sigmoidal function. The primary outcome of this research demonstrates that the Whittaker–Shannon interpolation formula can achieve successful zooms for values of the sampling rate significantly greater than the bandwidth. Conversely, when the sampling rate is much greater than the bandwidth, the nonadaptive technique fails to perform the zoom correctly. The conclusion is that the k‐space filtering sigmoidal function is identified as the crucial parameter in the adaptive Sinc‐based zoom technique. The implications of this research extend to Sinc‐based image zooming applications.

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A locally adaptive zooming algorithm for digital images

Cited by 160 publications

References 11 publications

Image interpolation via regularized local linear regression

Image interpolation via regularized local linear regression

Vector operators for color image zooming

Two‐dimensional adaptive Whittaker–Shannon Sinc‐based zooming

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