A Method for Selecting a Representative Image of a Dataset Based on the Singular Value Decomposition
Pablo Soto-Quirós, Geovanni Figueroa-Mata, Nelson Zamora-Villalobos · 2023
In this paper, we present a novel approach for obtaining a representative image from a dataset$\mathcal{M}$based on the singular value decomposition (SVD). The proposed method consists of two phases: The first phase involves calculating a theoretical representative image$I_{T}$, which is obtained using some measure of central tendency. This image$I_{T}$may not necessarily represent an image from the dataset$\mathcal{M}$. Therefore, in the second phase, we calculate the practical representative image$I_P\in\mathcal{M}$by utilizing$I_{T}$and the image subspace generated by$\mathcal{M}$through an orthonormal basis, which spans the entire subspace$\mathcal{M}$. This basis is obtained using the SVD of the matrix formed by vectorizing the images in$\mathcal{M}$. Finally, we conduct simulations of the proposed method and compare it with existing methods in the literature. The advantages of our approach are analyzed and demonstrated through numerical experiments.