Robust Object Detection in Colour Images Using a Multivariate Percentage Occupancy Hit-or-Miss Transform

Stephen Marshall,Henry White,Adrian Evans,Fraser Macfarlane,Benjamin Perret,Paul Murray

doi:10.1515/mathm-2020-0111

Abstract

AbstractThe extension of Mathematical Morphology to colour and multivariate images is challenging due to the need to define a total ordering in the colour space. No one general way of ordering multivariate data exists and, therefore, there is no single, definitive way of performing morphological operations on colour images. In this paper, we propose an extension to mathematical morphology, based on reduced ordering, specifically the morphological Hit-or-Miss Transform which is used for object detection. The reduced ordering employed transforms multivariate observations to scalar comparisons allowing for an order to be derived and for both flat and non-flat structuring elements to be used. We also compare other definitions of the Hit-or-Miss Transform and test alternative colour ordering schemes presented in the literature. Our proposed method is shown to be intuitive and outperforms other approaches to multivariate Hit-or-Miss Transforms. Furthermore, methods of setting the parameters of the proposed Hit-or-Miss Transform are introduced in order to make the transform robust to noise and partial occlusion of objects and, finally, a set of design tools are presented in order to obtain optimal values for setting these parameters accordingly.

Highlights

Mathematical Morphology (MM), first introduced and formalised by Matheron [25] and Serra [37, 38] and later extended by Heijmans [13], is a fundamental set of non-linear image processing techniques
We first compare our Multiple Dimensional Percentage Occupancy Hit-or-Miss Transform (MDPOHMT) to an existing greyscale Hit-or-Miss Transform (HMT) in order to highlight the need for a generalisation to colour and multivariate imagery in order to better distinguish between objects of interest
We compare our approach with other colour HMTs and investigate the benefits of the noise robustness offered by using Percentage Occupancy (PO)

Summary

Introduction

Mathematical Morphology (MM), first introduced and formalised by Matheron [25] and Serra [37, 38] and later extended by Heijmans [13], is a fundamental set of non-linear image processing techniques. MM applies the mathematical concepts of set theory, lattice theory, in order to study the shape, or morphology, of objects in various image analysis tasks such as object detection, edge detection, segmentation and image de-noising [32, 41]. The Hit-or-Miss Transform (HMT) is a useful tool in MM and is often used for detecting objects based on their size and shape. In common with many other MM operators, the definition of the HMT was originally Open Access.

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