A computer-implemented method, comprising: receiving, by a computing system, first and second frames of a video that was captured by a camera; identifying, by the computing system and using the first and second frames of the video, a mathematical transformation that indicates movement of the camera with respect to a scene captured by the video from when the first frame was captured to when the second frame was captured; generating, by the computing system, a modified mathematical transformation by modifying the mathematical transformation so that the mathematical transformation is less representative of movement that began recently; generating, by the computing system using the mathematical transformation and the modified mathematical transformation, a second mathematical transformation that is able to be applied to the second frame to stabilize the second frame; identifying, by the computing system, an anticipated distortion that would be present in a stabilized version of the second frame resulting from application of the second mathematical transformation to the second frame, based on a difference between: (i) an amount of distortion in the horizontal direction resulting from application of the second mathematical transformation to the second frame, and (ii) an amount of distortion in the vertical direction resulting from application of the second mathematical transformation to the second frame; determining, by the computing system, an amount by which to reduce a stabilizing effect that results from application of the second mathematical transformation to the second frame, based on a degree to which the anticipated distortion exceeds an acceptable change in distortion that was calculated from distortion in multiple frames of the video that preceded the second frame; and generating, by the computing system, the stabilized version of the second frame by applying the second mathematical transformation to the second frame, where a stabilizing effect of applying the second mathematical transformation to the second frame has been reduced based on the determined amount by which to reduce the stabilizing effect, wherein the second frame is a frame of the video that immediately follows the first frame of the video, wherein the mathematical transformation that indicates movement of the camera includes a homography transform matrix, and wherein modifying the mathematical transformation includes applying a lowpass filter to the homography transform matrix. receiving, by a computing system, first and second frames of a video that was captured by a camera; identifying, by the computing system and using the first and second frames of the video, a mathematical transformation that indicates movement of the camera with respect to a scene captured by the video from when the first frame was captured to when the second frame was captured; generating, by the computing system, a modified mathematical transformation by modifying the mathematical transformation so that the mathematical transformation is less representative of movement that began recently; generating, by the computing system using the mathematical transformation and the modified mathematical transformation, a second mathematical transformation that is able to be applied to the second frame to stabilize the second frame; identifying, by the computing system, an anticipated distortion that would be present in a stabilized version of the second frame resulting from application of the second mathematical transformation to the second frame, based on a difference between: (i) an amount of distortion in the horizontal direction resulting from application of the second mathematical transformation to the second frame, and (ii) an amount of distortion in the vertical direction resulting from application of the second mathematical transformation to the second frame; (i) an amount of distortion in the horizontal direction resulting from application of the second mathematical transformation to the second frame, and (ii) an amount of distortion in the vertical direction resulting from application of the second mathematical transformation to the second frame; determining, by the computing system, an amount by which to reduce a stabilizing effect that results from application of the second mathematical transformation to the second frame, based on a degree to which the anticipated distortion exceeds an acceptable change in distortion that was calculated from distortion in multiple frames of the video that preceded the second frame; and generating, by the computing system, the stabilized version of the second frame by applying the second mathematical transformation to the second frame, where a stabilizing effect of applying the second mathematical transformation to the second frame has been reduced based on the determined amount by which to reduce the stabilizing effect, wherein the second frame is a frame of the video that immediately follows the first frame of the video, wherein the mathematical transformation that indicates movement of the camera includes a homography transform matrix, and wherein modifying the mathematical transformation includes applying a lowpass filter to the homography transform matrix.