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
Sachin Meena, Prakash Duraisamy, Kannappan Palniappan, and Guna Seetharaman, "Point based interactive image segmentation using multiquadrics splines," Proc. SPIE 10203, Pattern Recognition and Tracking XXVIII, 102030C (Presented at SPIE Defense + Security: April 12, 2017; Published: 1 May 2017); https://doi.org/10.1117/12.2263933.
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