Product-Normed Linear Spaces

Barnes, Belinda; Adjei, Isaac Akpor; Amponsah, S. K.; Harris, Eric

doi:10.29020/nybg.ejpam.v11i3.3284

Cited by 2 publications

(2 citation statements)

References 7 publications

(7 reference statements)

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“…Specifically, in many contexts, measuring the difference between two matrices is essential based on their effect on vectors. A norm on a vector space V is a function [21]: The norm of a vector can be thought of as the length or magnitude of the vector.…”

Section: Singular Value Decomposition (Svd)mentioning

confidence: 99%

Color to Grayscale Image Conversion Based on Singular Value Decomposition

Khudhair

Nidhal

Abbadi³

et al. 2023

IEEE Access

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Color information is useless for distinguishing significant edges and features in numerous applications. In image processing, a gray image discards much-unrequired data in a color image. The primary drawback of colour-to-grey conversion is eliminating the visually significant image pixels. A current proposal is a novel approach for transforming an RGB image into a grayscale image based on singular value decomposition (SVD). A specific factor magnifies one of the color channels (Red, Green, and Blue). A vector of three values (Red, Green, Blue) of each pixel in an image is decomposed using SVD into three matrices. The norm of the diagonal matrix was determined and then divided by a specific factor to obtain the grey value of the corresponding pixel. The contribution of the proposed method gives the user high flexibility to produce many versions of gray images with varying contrasts, which is very helpful in many applications. Furthermore, SVD allows for image reconstruction by combining the weighting of each channel with the singular value matrix. This results in a grayscale image that more accurately captures the actual intensity values of the image and preserves more color information than traditional grayscale conversion methods, resulting in loss of color information. The proposed method was compared with a similar method (converting the color image into grayscale) and was found to be the most efficient.INDEX TERMS Decolorization, grey image, image conversion, SVD, technological development. I. INTRODUCTIONCurrently, most of the captured images are color images. However, it is frequently necessary to convert a color image to grayscale images for printing, aesthetic intents, object detection, and publishing as less expensive, helping colorblind people preserve visual cues [1]. Color-to-grayscale conversion is the process of reducing the image dimensions by transforming the RGB tristimulus values (Red, Green, Blue) ∈ R 3 to the intensity value (I) R [2]. The lightness valuesThe associate editor coordinating the review of this manuscript and approving it for publication was Mingbo Zhao . ranged from zero (black) to 255 (white), as shown in Fig. 1. Generally, the conversion process produces an image with lower contrast than the original color image. The goal of each conversion algorithm is to preserve the local luminance consistency, global consistency, image contrast information, and hue order as much as possible [3]. Different processing methods are required for each pixel in various image-processing applications. Processing RGB pixels is not feasible due to high storage requirements and computation costs. The best solution to these issues is to convert an RGB image into a grayscale image [4]. Grayscale images are mainly used for shape characteristics, edge detection, circular objects, and

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Section: Singular Value Decomposition (Svd)mentioning

confidence: 99%

Color to Grayscale Image Conversion Based on Singular Value Decomposition

Khudhair

Nidhal

Abbadi³

et al. 2023

IEEE Access

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“…Beberapa peneliti mengkonstruksi ruang bernorma baru yaitu dengan memodifikasi norma seperti apa yang dilakukan oleh Barnes, et al (2018). Jika sebuah norma dalam ruang vektor E atas lapangan bilangan real ℝ adalah sebuah pemetaan ‖ ‖ 𝑬 ∶ 𝑬 ⟶ ℝ yang memenuhi sifat berikut: (N1).…”

Section: Pendahuluanunclassified

Keberadaan Hasil Kali Langsung dari Ruang Bernorma

Agustito

Kuncoro

Irfan

2022

UJM

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Keberadaan hasil kali langsung tidak selalu ada dalam sebuah kategori. Pada kategori dari ruang vektor bersama dengan transfomarsi linear (operator linear) memiliki hasil kali langsung berhingga maupun tak-hingga; artinya kategori tersebut tertutup di bawah hasil kali langsung berhingga maupun tak-berhingga, tetapi dalam kategori ruang bernorma bersama dengan operator linear terbatasnya tidak memiliki hasil kali langsung tak-berhingga namun hanya memiliki hasil kali langsung berhingga saja; artinya kategori tersebut tertutup di bawah hasil kali langsung berhingga saja dan tidak untuk hasil kali langsung tak-hingga. Sebagai akibat keberadaan hasil kali langsung berhingga dari ruang bernorma adalah adalah ruang banach jika dan hanya jika E1, ..., En juga merupakan ruang banach.

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Product-Normed Linear Spaces

Cited by 2 publications

References 7 publications

Color to Grayscale Image Conversion Based on Singular Value Decomposition

Color to Grayscale Image Conversion Based on Singular Value Decomposition

Keberadaan Hasil Kali Langsung dari Ruang Bernorma

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