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.
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used as the similarity criterion between the original and the reconstructed images. The proposed criterion called Convex SIMilarity (CSIM) index is a modified version of the Structural SIMilarity (SSIM) index, which despite its predecessor, is convex and uni-modal. We derive mathematical properties for the proposed index and show how to optimally choose the param…
Universität Bremen（不来梅大学）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希·赫兹研究所）；Technische Universität Berlin（柏林工业大学）；Berlin Institute of Technology（柏林工业大学）
In most practical situations, the compression or transmission of images and videos creates distortions that will eventually be perceived by a human observer. Vice versa, image and video restoration techniques, such as inpainting or denoising, aim to enhance the quality of experience of human viewers. Correctly assessing the similarity between an image and an undistorted reference image as subjectively experienced by a human viewer can thus lead to significant improvements in any transmission, compression, or restoration system. This paper introduces the Haar wavelet-based perceptual similarity…
In 2018, at the World Economic Forum in Davos it was presented a new countries' economic performance metric named the Inclusive Development Index (IDI) composed of 12 indicators. The new metric implies that countries might need to realize structural reforms for improving both economic expansion and social inclusion performance. That is why, it is vital for the IDI calculation method to have strong statistical and mathematical basis, so that results are accurate and transparent for public purposes. In the current work, we propose a novel approach for the IDI estimation - the Ranking Relative Pr…
Functional Principal Component Analysis for Manifold-Indexed Data
The Institute for Data Innovation in Science, Seoul National University（首尔大学数据创新科学研究所）；Department of Statistics and School of Transdisciplinary Innovations, Seoul National University（首尔大学统计学院与跨学科创新学院）
Sharif University of Technology（谢里夫理工大学）；Qom University of Technology（库姆理工大学）
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image processing and for this purpose, we suggest an iterative sparse recovery algorithm based on constrained $l_1$-norm minimization with a new fidelity metric. The proposed metric called Convex SIMilarity (CSIM) index, is a simplified version of the Structural SIMilarity (SSIM) index…
École de technologie supérieure（高等技术学院）；McGill University（麦吉尔大学）
Applications of perceptual image quality assessment (IQA) in image and video processing, such as image acquisition, image compression, image restoration and multimedia communication, have led to the development of many IQA metrics. In this paper, a reliable full reference IQA model is proposed that utilize gradient similarity (GS), chromaticity similarity (CS), and deviation pooling (DP). By considering the shortcomings of the commonly used GS to model human visual system (HVS), a new GS is proposed through a fusion technique that is more likely to follow HVS. We propose an efficient and effec…
In this paper, we consider the problem of forming machine cell in cellular manufacturing (CM). The major problem in the design of a CM system is to identify the part families and machine groups and consequently to form manufacturing cells. The aim of this article is to formulate a multivariate approach based on a correlation analysis for solving cell formation problem. The proposed approach is carried out in two phases. In the first phase, the correlation matrix is used as an original similarity coefficient matrix. In the second phase, Principal Component Analysis (PCA) is applied to find the …
National Center for Atmospheric Research（美国国家大气研究中心）；Colorado School of Mines（科罗拉多矿业学院）
Data visualization is a critical component in terms of interacting with floating-point output data from large model simulation codes. Indeed, postprocessing analysis workflows on simulation data often generate a large number of images from the raw data, many of which are then compared to each other or to specified reference images. In this image-comparison scenario, image quality assessment (IQA) measures are quite useful, and the Structural Similarity Index (SSIM) continues to be a popular choice. However, generating large numbers of images can be costly, and plot-specific (but data independe…
The Structural Similarity Index (SSIM) is generally considered to be a milestone in the recent history of Image Quality Assessment (IQA). Alas, SSIM's accepted development from the product of three heuristic factors continues to obscure it's real underlying simplicity. Starting instead from a symmetric-antisymmetric reformulation we first show SSIM to be a contrast or visibility function in the classic sense. Furthermore, the previously enigmatic structural covariance is revealed to be the difference of variances. The second step, eliminating the intrinsic quadratic nature of SSIM, allows a ne…
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of easy-to-understand basic geometric structures was shown. As a result of the analysis of these structures it was proposed to enrich the classical PCA. In particular, it was proposed a new criterion for the selection of important principal components and a new algorithm for clustering primary variables by their level of similarity to the principal components. Vi…
While a set of covariance matrices corresponding to different populations are unlikely to be exactly equal they can still exhibit a high degree of similarity. For example, some pairs of variables may be positively correlated across most groups, while the correlation between other pairs may be consistently negative. In such cases much of the similarity across covariance matrices can be described by similarities in their principal axes, the axes defined by the eigenvectors of the covariance matrices. Estimating the degree of across-population eigenvector heterogeneity can be helpful for a variet…
A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent to the Gini PCA. It is also proven that the dimensionality reduction based on the generalized Gini correlation matrix, that relies on city-block distances, is robust to outliers. Monte Carlo simulations and an application on cars data (with outliers) show the robustness of the Gini PCA and provide different interpretations of the results compared with the var…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs should map to similar pairs of outputs. However, the operation of these networks (and of similar networks) requires a fixed-point iteration to determine the output corresponding to a given input, which means that dynamics must operate on a faster time scale than the variation of the input. Further, during these fast dynamics such networks typically "disable" l…
Generative models and inferential autoencoders mostly make use of $\ell_2$ norm in their optimization objectives. In order to generate perceptually better images, this short paper theoretically discusses how to use Structural Similarity Index (SSIM) in generative models and inferential autoencoders. We first review SSIM, SSIM distance metrics, and SSIM kernel. We show that the SSIM kernel is a universal kernel and thus can be used in unconditional and conditional generated moment matching networks. Then, we explain how to use SSIM distance in variational and adversarial autoencoders and uncond…
The importance of Image quality assessment (IQA) is ever increasing due to the fast paced advances in imaging technology and computer vision. Among the numerous IQA methods, Structural SIMilarity (SSIM) index and its variants are better matched to the perceived quality of the human visual system. However, SSIM methods are insufficiently sensitive, when images contain low information, where the important information only occupies a low proportion of the image while most of the image is noise-like, which is common in scientific data. Therefore, we propose two new IQA methods, InTensity Weighted …
INESC TEC（INESC TEC（葡萄牙系统与计算机工程技术研究所））；Faculty of Sciences of the University of Porto（波尔图大学理学院）
Blood vessel segmentation is one of the most studied topics in computer vision, due to its relevance in daily clinical practice. Despite the evolution the field has been facing, especially after the dawn of deep learning, important challenges are still not solved. One of them concerns the consistency of the topological properties of the vascular trees, given that the best performing methodologies do not directly penalize mistakes such as broken segments and end up producing predictions with disconnected trees. This is particularly relevant in graph-like structures, such as blood vessel trees, …
