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Point based interactive image segmentation using multiquadrics splines

Multiquadrics (MQ) are radial basis spline function that can provide an efficient interpolation of data points located in a high dimensional space. MQ were developed by Hardy to approximate geographical surfaces and terrain modelling. In this paper we frame the task of interactive image segmentation as a semi-supervised interpolation where an interpolating function learned from the user provided seed points is used to predict the labels of unlabeled pixel and the spline function used in the semi-supervised interpolation is MQ. This semi-supervised interpolation framework has a nice closed form solution which along with the fact that MQ is a radial basis spline function lead to a very fast interactive image segmentation process. Quantitative and qualitative results on the standard datasets show that MQ outperforms other regression based methods, GEBS, Ridge Regression and Logistic Regression, and popular methods like Graph Cut,4 Random Walk and Random Forest.6