Rational Spline Image Upscaling with Constraint Parameters

Xunxiang, Yao; Zhang, Yunfeng; Bao, Fangxun; Zhang, Caiming

doi:10.3390/mca21040048

Cited by 5 publications

(3 citation statements)

References 28 publications

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“…In our capacity as Rothko fans, we wondered if we might be able to reveal in Rothko's paintings something he did not know about his own paintings or something he considered important but which the average image viewer did not observe (or simply a digitization error). The topic of revealing details in images has already been discussed in [5,6], where different image analysis approaches are provided to reveal invisible or hardly discernible details in art and manuscripts based on blind source separation or linear discriminant analysis.…”

Section: Introductionmentioning

confidence: 99%

Applying Quaternions to Recognize Hidden Details in Images: Rothko as a Case Study

Aharony,

Hindi,

Valdman

et al. 2023

MCA

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Images or paintings with homogeneous colors may appear dull to the naked eye; however, there may be numerous details in the image that are expressed through subtle changes in color. This manuscript introduces a novel approach that can uncover these concealed details via a transformation that increases the distance between adjacent pixels, ultimately leading to a newly modified version of the input image. We chose the artworks of Mark Rothko—famous for their simplicity and limited color palette—as a case study. Our approach offers a different perspective, leading to the discovery of either accidental or deliberate clusters of colors. Our method is based on the quaternion ring, wherein a suitable multiplication can be used to boost the color difference between neighboring pixels, thereby unveiling new details in the image. The quality of the transformation between the original image and the resultant versions can be measured by the ratio between the number of connected components in the original image (m) and the number of connected components in the output versions (n), which usually satisfies nm≫1. Although this procedure has been employed as a case study for artworks, it can be applied to any type of image with a similar simplicity and limited color palette.

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Section: Introductionmentioning

confidence: 99%

Applying Quaternions to Recognize Hidden Details in Images: Rothko as a Case Study

Aharony,

Hindi,

Valdman

et al. 2023

MCA

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show abstract

“…Gao et al [6,7] have discussed various types of image interpolation using rational cubic spline (cubic/linear). Meanwhile, Yao et al [21] and Zhang et al [22][23] also have constructed various types of rational cubic spline interpolation for image interpolation. However, their schemes also have no free parameters.…”

Section: Introductionmentioning

confidence: 99%

“…[24] and Karim and Saaban [11]. (c) There are no free parameters to control the final image interpolation in the works of Gao et al [6,7], Saaban et al [17], Wang and Tan [18], Zhang et al [21][22][23]. (d) The optimal parameters are obtained via numerical simulations and local control properties.…”

Section: Introductionmentioning

confidence: 99%

Rational Bi-Quartic Spline With Six Parameters for Surface Interpolation With Application in Image Enlargement

Karim

2020

IEEE Access

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A new rational bi-quartic spline interpolation scheme is constructed in this study. This rational bi-quartic spline has six free parameters that can be used to refine the final interpolating surface. The degree of smoothness attained is C 1 continuity. Image interpolation is one of the methods in image processing that is used to rescale the images, either downscaling or upscaling. The proposed rational bi-quartic spline will be used to interpolate the missing pixel in image interpolation. We employ an algorithm that will speed up the process as well as be able to produce the quality upscaling images. We measure the quality of the proposed method by calculating peak-signal-to-noise-ratio (PSNR). Based on numerical comparison, the proposed scheme gives higher PSNR (consequently smaller RMSE) unlike some existing schemes. Thus, the new rational bi-quartic spline with six parameters is better than the existing scheme via an efficient algorithm. All numerical simulations and graphical results are presented using MATLAB. INDEX TERMS Image interpolation; parameters; algorithm; bi-quartic spline; image quality.

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Rational bicubic Ball for image interpolation

Zulkifli

Karim

Shafie

et al. 2019

J. Phys.: Conf. Ser.

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In this study, a new rational bicubic Ball with six free parameters is proposed for image interpolation. These free parameters can be used to refine the shape of the surface. This rational bicubic Ball function is constructed by using tensor product approach. The proposed scheme is tested to grayscale image upscale. An efficient algorithm is employed to upscales the original image with factor 2 and 4. The effectiveness of proposed scheme is measured in terms of Peak Signal-to-Noise Ratio (PSNR), Root Mean Square Error (RMSE) and Feature SIMilarity (FSIM) index including comparison with some existing schemes. Numerical and graphical results for image interpolation are presented by using MATLAB. We found out the proposed scheme resulting with higher PSNR and FSIM and smaller in RMSE. Thus, the new rational bicubic Ball with six parameters is better than the existing schemes.

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Rational Spline Image Upscaling with Constraint Parameters

Cited by 5 publications

References 28 publications

Applying Quaternions to Recognize Hidden Details in Images: Rothko as a Case Study

Applying Quaternions to Recognize Hidden Details in Images: Rothko as a Case Study

Rational Bi-Quartic Spline With Six Parameters for Surface Interpolation With Application in Image Enlargement

Rational bicubic Ball for image interpolation

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