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

The 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.

Multivariate Medians for Image and Shape Analysis

Having been studied since long by statisticians, multivariate medianconcepts found their way into the image processing literature in thecourse of the last decades, being used to construct robust and efficientdenoising filters for multivariate images such as colour images but alsomatrix-valued images.Based on the similarities between image and geometric data as results ofthe sampling of continuous physical quantities, it can be expected that theunderstanding of multivariate median filters for images provides a startingpoint for the development of shape processing techniques.This paper presents an overview of multivariate median concepts relevantfor image and shape processing. It focusses on their mathematical principlesand discusses important properties especially in the context of imageprocessing.