Principal Component Analysis Using Structural Similarity Index for Images

TL;DR

This paper introduces a novel PCA variant called ISCA that uses SSIM instead of Euclidean distance, improving the analysis of image structures and distortions, bridging image quality assessment and manifold learning.

Contribution

It proposes a new PCA-based method utilizing SSIM for better structural feature capture in images, extending manifold learning techniques.

Findings

ISCA effectively discriminates different image distortions.

Kernel ISCA enhances analysis of complex image structures.

The method bridges image quality assessment with manifold learning.

Abstract

Despite the advances of deep learning in specific tasks using images, the principled assessment of image fidelity and similarity is still a critical ability to develop. As it has been shown that Mean Squared Error (MSE) is insufficient for this task, other measures have been developed with one of the most effective being Structural Similarity Index (SSIM). Such measures can be used for subspace learning but existing methods in machine learning, such as Principal Component Analysis (PCA), are based on Euclidean distance or MSE and thus cannot properly capture the structural features of images. In this paper, we define an image structure subspace which discriminates different types of image distortions. We propose Image Structural Component Analysis (ISCA) and also kernel ISCA by using SSIM, rather than Euclidean distance, in the formulation of PCA. This paper provides a bridge between image quality assessment and manifold learning opening a broad new area for future research.