A robust hit-or-miss transform for template matching applied to very noisy astronomical images

Abstract

The morphological Hit-or-Miss Transform (HMT) is a powerful tool for digital image analysis. Its recent extensions to grey level images have proven its ability to solve various template matching problems. In this paper we explore the capacity of various existing approaches to work in very noisy environments and discuss the generic methods used to improve their robustness to noise. We also propose a new formulation for a fuzzy morphological HMT which has been especially designed to deal with very noisy images. Our approach is validated through a pattern matching problem in astronomical images that consists of detecting very faint objects: low surface brightness galaxies. Despite their influence on the galactic evolution model, these objects remain mostly misunderstood by the astronomers. Due to their low signal to noise ratio, there is no automatic and reliable detection method yet. In this paper we introduce such a method based on the proposed hit-or-miss operator. The complete process is described starting from the building of a set of patterns until the reconstruction of a suitable map of detected objects. Implementation, running cost and optimisations are discussed. Outcomes have been examined by astronomers and compared to previous works. We have observed promising results in this difficult context for which Mathemat-

Adaptive Hit or Miss Transform

“…Template matching using the HMT is often not trivial for the case of binary images, and it is even more complicated for gray level images [17]. A specific object in the image can be extracted using the HMT with two structuring elements: one defines the object and another defines what is not the 1.…”

“…The HMT has most often been used for detecting a given pattern in a binary image (this problem is also called template matching) and has a number of different applications [17][18][19]. Two survey papers on HMT have been presented recently [20,21].…”

“…HMT relies on a pair of disjoint structuring elements, where one fits the foreground (object) and the other fits the background. The common approach to ensure robustness to variations in the shape or size of the sought pattern is to consider a set of structuring element pairs; a match is allowed if one of the pairs match the considered pattern [17]. Instead of using a limited, pre-defined set of structuring element pairs, we propose to use a single adaptive structuring element pair in order to limit the computation burden.…”

Fuzzy Hit-or-Miss Transform Using the Fuzzy Mathematical Morphology Based on T-norms

“…On the other hand, Soille [37] introduced two extensions for Hit-or-Miss: the so-called unconstrained HMT and the constrained HMT and he applied them to the analysis of topographic maps. A detailed account of these extensions can be found in [26,29]. Finally, some extensions of HMT to multivariate images have been recently proposed in [2,39,41] and see also [24] for a new conceptual view of the HMT.…”

“…We can highlight applications to document analysis [7]; template and pattern matching [4,19,33]; boundary and edge extraction [16,22]; face detection and localization [11,32]; medical image analysis [27,8]; building and vehicle detection [18,21,38]; satellite and astronomical image analysis [1,29,17] and analysis of geographic and topographic data [37,40]. But in many of these applications the hit-or-miss transform is used after preprocessing the image and performing a threshold to it.…”