In many situations it is convenient to represent pictorial data in the form of contours. It may become necessary to compress such contour data for efficient storage and transmission. We present here a technique for achieving very high levels of compression of 2-D contours. The goal here is to represent each contour using a discrete set of representative points known as key points. A novel method of extracting the key points using wavelet transform is presented. The scheme exploits the properties of the high frequency coefficients to identify these points. Local peaks in the magnitude plot of high frequency coefficients are designated as key points and are identified using an efficient algorithm. The performance of the scheme is evaluated using multiple actual contours derived from weather radar reflectivity fields.