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Video stabilization is used to eliminate unwanted shakiness in video caused by movement of the camera. This can be achieved by estimating the motion of the camera, filtering out the high frequency components in the motion path and warping the video frames in order to compensate for the motion. In this paper, an adaptive parameterization technique is proposed to define the characteristics of the filter used to eliminate high frequency components in the motion path. Scale Invariant Feature Transform (SIFT) is used to extract the features from each video frame. A string of transformation matrices is used to represent the motion of the camera. For any frame that has to be stabilized, only a few frames in the local neighborhood are considered to calculate the required amount of motion compensation. The high-frequency components in camera motion are eliminated using a zero-mean Gaussian filter. The variance of the Gaussian filter that defines the amount of smoothening is computed automatically from the camera motion path. This is based on the observation that the variation in the individual components in the transformation matrices correlates with the amount of instability in the video. The proposed approach has been found to be effective irrespective of the presence of moving objects in the video.