Abyssal-hill shape and orientation are related to the direction and spreading rate of paleo-spreading centers. Therefore analyzing abyssal-hill shape and trend is useful for constraining tectonic models of regions devoid of magnetic reversal anomalies. Detecting systematic changes of abyssal-hill shapes or trends, due to changes in spreading rate or direction, is not straightforward, which makes it difficult to determine appropriate regions over which to average abyssal-hill parameters. Often, however, detecting these systematic changes, where they occur, and the scale over which they occur, is of primary importance for tectonic reconstructions. We present a new method of abyssal-hill analysis that is based on the ridgelet transform, a relative of the two-dimensional wavelet transform. Our method is capable of locally estimating the width, azimuth, and root-mean-square (RMS) amplitude of abyssal-hill fabric and highlights changes in these parameters across a survey area, making it possible to identify regions created with a constant spreading rate and direction. We use three multibeam swaths, one crossing the Osbourn Trough in the southwest Pacific Basin, one crossing the East Pacific Rise, and one crossing the Mid-Atlantic Ridge, to demonstrate the utility and performance of our method.