Detecting Directionality in Random Fields Using the Monogenic Signal

TL;DR

This paper introduces a novel measure based on the monogenic signal to quantify and classify the directionality of structures in random fields, enabling automatic detection of unidirectional patterns in images.

Contribution

It proposes a new measure of directionality using the monogenic signal and provides a method for automatic classification of random fields as unidirectional or not.

Findings

The measure effectively distinguishes between isotropic, anisotropic, and unidirectional fields.

A threshold for classification is derived from the statistical properties of the monogenic signal.

The approach works on finite-size sample images for practical applications.

Abstract

Detecting and analyzing directional structures in images is important in many applications since one-dimensional patterns often correspond to important features such as object contours or trajectories. Classifying a structure as directional or non-directional requires a measure to quantify the degree of directionality and a threshold, which needs to be chosen based on the statistics of the image. In order to do this, we model the image as a random field. So far, little research has been performed on analyzing directionality in random fields. In this paper, we propose a measure to quantify the degree of directionality based on the random monogenic signal, which enables a unique decomposition of a 2D signal into local amplitude, local orientation, and local phase. We investigate the second-order statistical properties of the monogenic signal for isotropic, anisotropic, and unidirectional random fields. We analyze our measure of directionality for finite-size sample images, and determine a threshold to distinguish between unidirectional and non-unidirectional random fields, which allows the automatic classification of images.