Fuzzy connected object definition in images with respect to co-objects

Tangible solutions to practical image segmentation are vital to ensure progress in many applications of medical imaging. Toward this goal, we previously proposed a theory and algorithms for fuzzy connected object definition in n- dimensional images. Their effectiveness has been demonstrated in several applications including multiple sclerosis lesion detection/delineation, MR Angiography, and craniofacial imaging. The purpose of this work is to extend the earlier theory and algorithms to fuzzy connected object definition that considers all relevant objects in the image simultaneously. In the previous theory, delineation of the final object from the fuzzy connectivity scene required the selection of a threshold that specifies the weakest `hanging-togetherness' of image elements relative to each other in the object. Selection of such a threshold was not trivial and has been an active research area. In the proposed method of relative fuzzy connectivity, instead of defining an object on its own based on the strength of connectedness, all co-objects of importance that are present in the image are also considered and the objects are let to compete among themselves in having image elements as their members. In this competition, every pair of elements in the image will have a strength of connectedness in each object. The object in which this strength is highest will claim membership of the elements. This approach to fuzzy object definition using a relative strength of connectedness eliminates the need for a threshold of strength of connectedness that was part of the previous definition. It seems to be more natural since it relies on the fact that an object gets defined in an image by the presence of other objects that coexist in the image. All specified objects are defined simultaneously in this approach. The concept of iterative relative fuzzy connectivity has also been introduced. Robustness of relative fuzzy objects with respect to selection of reference image elements has been established. The effectiveness of the proposed method has been demonstrated using a patient's 3D contrast enhanced MR angiogram and a 2D phantom scene.

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