A Method for Selecting a Representative Image of a Dataset Based on the Singular Value Decomposition

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.