A Comparative Study on Discrete Shmaliy Moments and Their Texture-Based Applications

Abstract

In recent years, discrete orthogonal moments have attracted the attention of the scientific community because they are a suitable tool for feature extraction. However, the numerical instability that arises because of the computation of high-order moments is the main drawback that limits their wider application. In this article, we propose an image classification method that avoids numerical errors based on discrete Shmaliy moments, which are a new family of moments derived from Shmaliy polynomials. Shmaliy polynomials have two important characteristics: one-parameter definition that implies a simpler definition than popular polynomial bases such as Krawtchouk, Hahn, and Racah; a linear weight function that eases the computation of the polynomial coefficients. We use IICBU-2008 database to validate our proposal and include Tchebichef and Krawtchouk moments for comparison purposes. The experiments are carried out through 5-fold cross-validation, and the results are computed using random forest, support vector machines, naïve Bayes, and k-nearest neighbors classifiers.

Novel Integer Shmaliy Transform and New Multiparametric Piecewise Linear Chaotic Map for Joint Lossless Compression and Encryption of Medical Images in IoMTs

“…The discrete Shmaliy polynomials (SPs) are a type of discrete orthogonal polynomial. SPs have a simpler definition than other discrete orthogonal polynomials (Tchebichef, Krawtchouk, Hahn, Dual Hahn, and Racah) due to their independence from local parameters and their linear weight function [41]. Only few works in the literature use SPs as basis kernel for defining discrete Shmaliy transforms.…”

“…The discrete Shmaliy transform (DST), commonly known as discrete Shmaliy moments (DSMs), is increasingly used in signal and image analysis, including signal and image reconstruction [42], texture classification [41], and bio-signal zero-watermarking [43]. The 2D DST of the order (n,m) is calculated by using the following formula:…”

What is new in computer vision and artificial intelligence in medical image analysis applications

“…González et al (75), based on previous papers (76,77), introduced and validated Shmaliy orthogonal moments as a statistical textural descriptor, and its performance is compared to the DOMs. This statistical textural descriptor is based on overlapping square windows and assure numerical stability.…”

“…The general scheme of classification is depicted in Figure 8. This proposal and its detailed description have been published previously for CRC (78) and HMs (73,75) with state-of-art results at the time of publication. Recently, with the spread of neural networks, some papers (79,80) have worked on these databases using CNNs, e.g., Kather et al image datasets, ordered chronologically.…”

Applications of Discrete Shmaliy Moments on the Quantitative Analysis of Multitarget Compounds Based on the Chemical Spectra

“…They applied the DSM to signal analysis, particularly to signal reconstruction, and proved the effectiveness of the DSM as a new feature descriptor in one dimension. Later, Germán González explored the use of the DSM as 2D texture descriptors and showed that the DSM has the same capability for texture description as other classical discrete polynomial bases …”