Mask-Based Second-Generation Connectivity and Attribute Filters

Abstract

Abstract-Connected filters are edge-preserving morphological operators, which rely on a notion of connectivity. This is usually the standard 4 and 8-connectivity, which is often too rigid since it cannot model generalized groupings such as object clusters or partitions. In the set-theoretical framework of connectivity, these groupings are modeled by the more general second-generation connectivity. In this paper, we present both an extension of this theory, and provide an efficient algorithm based on the Max-Tree to compute attribute filters based on these connectivities. We first look into the drawbacks of the existing framework that separates clustering and partitioning and is directly dependent on the properties of a preselected operator. We then propose a new type of second-generation connectivity termed mask-based connectivity which eliminates all previous dependencies and extends the ways the image domain can be connected. A previously developed Dual-Input Max-Tree algorithm for area openings is adapted for the wider class of attribute filters on images characterized by second-generation connectivity. CPU-times for the new algorithm are comparable to the original algorithm, typically deviating less than 10 percent either way.

Component-Trees and Multivalued Images: Structural Properties

“…From an applicative point of view, component-trees have been involved in the development of several image processing and analysis techniques. Most of them are devoted to filtering or segmentation [8], [14], [15], [16], [17]. Other applications have also been considered, for instance, image registration [7], [18], image retrieval [19], [20], image classification [21], interactive visualisation [22], multithresholding [23] or document binarisation [24].…”

“…If this property is verified, we say that Ω is connected. Several (similar, and sometimes equivalent [35]) ways can be considered to define connectivity: from the standard notions of topology [36], [37]; from the notions of paths in digital/discrete spaces [38], [39], [40]; or even by morphological definitions of connectivity [41], [42], [43], [16].…”

Segmentation of Complex Images Based on Component-Trees: Methodological Tools

“…As mentioned above, component-trees have been considered for the development of image segmentation methods, mainly in the field of (bio)medical imaging, and in particular for: dermatological data [10], wood micrographs [6], cerebral MRI [4], CT/MR angiography [19], or confocal microscopy [12].…”

“…It has to be noticed that their use is often only devoted to one specific step of the segmentation (marker selection in [4]), or to perform filtering [19,12], i.e. to remove "useless" parts of the processed image, leading to a superset of an actual segmentation.…”

“…Thanks to efforts devoted to its efficient computation [2,14,7,11,8] or its use in complex knowledge handling procedures [15], component-trees have been considered for the design of various kinds of grey-level image processing methods, including image filtering and segmentation [5,6,17,12,16,10], video segmentation [14], image registration [7], image compression [14], or image retrieval [9,1].…”