Detecting Directionality in Random Fields Using the Monogenic Signal
This addresses the need for automated directionality analysis in image processing applications like object contour detection, but it is incremental as it builds on existing monogenic signal theory for a specific statistical modeling task.
The paper tackles the problem of detecting directional structures in images by proposing a measure based on the random monogenic signal to quantify directionality, enabling automatic classification of images as unidirectional or non-unidirectional with a determined threshold.
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.