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We present a technique for the automatic adaptation of a deformable model's elastic parameters within a Kalman filter framework for shape estimation applications. The novelty of the technique is that the model's elastic parameters are not constant, but spatio-temporally varying. The variation of the elastic parameters depends on the distance of the model from the data and the rate of change of this distance. Each pass of the algorithm uses physics-based modeling techniques to iteratively adjust both the geometric and the elastic degrees of freedom of the model in response to forces that are computed from the discrepancy between the model and the data. By augmenting the state equations of an extended Kalman filter to incorporate these additional variables, we are able to significantly improve the quality of the shape estimation. Therefore, the model's elastic parameters are always initialized to the same value and they are subsequently modified depending on the data and the noise distribution. We present results demonstrating the effectiveness of our method for both two-dimensional and three-dimensional data.