Elastic map: interactive image segmentation using a few seed-points
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Over the past two decades interactive methods for clinical and biomedical image segmentation have been investigated since the pioneering work of Live-Wire, Live-Lane  and Intelligent Scissors . Fully automatic image segmentation is essential for quantitative analysis but remains an unsolved problem, so user driven interactive methods continue to be a powerful alternative when extremely precise segmentation is required. However, manual methods although routinely used are tedious, time-consuming, expensive, inconsistent between experts and error prone. In semi-supervised interactive segmentation the goal is for the user to provide a small amount of partial information or hints for an automatic algorithm to use in order to produce accurate boundaries suitable for the user. The coupled interaction between the user provided input and the semi-supervised segmentation algorithm should be minimal and robust. Commonly used drawing tools for interactive segmentation interfaces include active contour or boundary drawing, scribbles to identify foreground and background regions, and rectangles to outline the object of interest. But interactive segmentation using a sparse set of seed-points has not been widely investigated. In this work we investigate the use of sparse seed point-based for interactive image segmentation task. We have also proposed a new regression based framework, making use of Elastic Body Splines (EBS) to perform interactive image segmentation. Elastic Body Splines belonging to the family of 3D splines were recently introduced to capture tissue deformations within a physical model-based approach for non-rigid biomedical image registration . ElasticMap model the displacement of points in a 3D homogeneous isotropic elastic body subject to forces. We propose a novel extension of using elastic body splines for interactive learning-based figure-ground segmentation. The task of interactive image segmentation, with user provided foreground-background labeled seeds or samples, is formulated as learning a spatially dependent interpolating pixel classification function that is then used to assign labels for all unlabeled pixels in the image. The spline function we chose to model the semisupervised pixel classifier is the ElasticMap which can use sparse point-scribble input from the user and has a closed form solution. Experimental results demonstrate the applicability of the EBS approach for image segmentation. The ElasticMap method for interactive foreground segmentation uses on an average just four to six labeled pixels as input from the user. Using such sparsely labeled information the proposed EBS method produces very accurate results with an average accuracy consistently exceeding 95 percent on three different benchmark datasets and outperforms eleven other popular interactive image segmentation methods.