# CSE 190a Project Report: Golf Club Head Tracking

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4 Figure 7. The upswing and downswing are processed separately, after obtaining the transition frame either automatically or from the user. Each part of the swing is fit with a polar curve using a RANSAC-like process. The inliers of each of the models are then used to estimate the trajectory as another polar function in time. Figure 6. The green segments correspond to GOOD segments when there are any, and the red ones correspond to the best BAD segments. The white dots indicate the club head hypothesis in each frame. These hypotheses are used in the next phase to estimate polynomials that describe the swing trajectory in time and space. the club, we guess that the club head in each frame is the endpoint of the segment furthest from this reference point. Figure 6 shows results from hypothesis generation. It is worth discussing the differences in our approach compared to that of [3]. Our approach to generating hypotheses diverges from theirs after we compute motion masks. Whereas their approach allows multiple hypotheses per frame, we try to choose the best segment as the single hypothesis for a given frame. In their paper, they discuss issues with inaccurate candidate hypotheses, and they try to improve them in a couple of ways. First, they eliminate segments that correspond to physically impossible club positions. Second, they try to improve some hypotheses that are too short by extending them in either direction by using color information. In contrast, our approach to choosing the best BAD segment (based on slope and position) corresponds loosely to removing physically impossible hypotheses. Our approach employs no means for extending segments, however; we have observed that there are typically enough accurate hypotheses along the club head trajectory so as not to warrant it. 4. Trajectory Estimation The second major component is taking the club head hypotheses and estimating a model for them in time and space. For this, we follow the approach taken in [3]. The pipeline for this component is summarized in Figure Transition Identification We first need to identify which frames correspond to the upswing and which to the downswing. [3] evaluates the average y coordinate over time to conclude where the transition between upswing and downswing occurs. We use a slightly different approach. We consider the change in slope of hypotheses in consecutive frames, and we look for places where the derivative is zero, since the club must come to a stop when transitioning. Out of the candidate frames with zero (or close to it) derivative, we use an error metric to guess which is the transition. The error metric includes proximity to the middle of the video and use of GOOD segments over BAD. We have found our approach to identifying the transition to be fragile, however, so it might be worth trying the approach taken in [3]. As a temporary solution, we ask the user to provide the frame in which the transition from upswing to downswing occurs Computing Space Models Once we have the transition, we process the upswing and downswing frames independently. As empirically determined in [3], we seek to fit a 4th degree polar curve to the upswing hypotheses and a 6th degree polar curve to the downswing ones. For this we convert all hypotheses from Cartesian to polar coordinates, but we use the standard direction of the θ axis, unlike the one used in [3]. We use a RANSAC approach to estimating these curves by randomly sampling a subset of hypotheses. The sample size is two more than the parameters of the polynomial (five points for the upswing and seven points for the downswing) to overconstrain the curve to prevent unstable behavior. For each randomly selected subset of points, their least squares fit is computed. Once these parameters are computed, each hypothesis is checked to see if it is within some error threshold away from the value predicted by the curve. This process is repeated many times, and the model with the highest number of inliers is selected. Figure 8 shows the trajectories estimated on both parts of a swing. The results vary on our set of sample videos. The

6 applications to golf instruction and to animating a golfer s swing. To produce a 3D estimate, additional camera angles are needed. In addition to the face-on angle we have been dealing with, the down-line (directly behind the golfer on the target line) and up-line (directly in front of golfer on the target line) are the other two popular camera angles for golf swing instruction and analysis. To demonstrate the additional information provided by the down-line angle, for instance, in Figure 11 we show three different positions at the top of the swing from the face-on and down-line angles. Figure 10. The best model return by guiding RANSAC with the four superdelegates the extreme hypotheses in every direction, whose votes count for more than the other points. although each sample contains the four extreme points, the best model does not necessarily fit each of these points well; it is simply more likely that it will. This approach does in fact improve the quality of the best model on most videos, but there are still some with undesirable results. The last way in which we guide RANSAC towards a better solution builds upon the previous one. Not only do we require RANSAC to use the extreme points in computing models, we also give more weight to them when they agree with a model. We consider the extreme points to be superdelegates because when they agree with a model, they have more influence over whether the model will be kept than all other points that agree with the model. The danger in biasing RANSAC in these two ways is that the popular vote solution computed by random consensus may be overturned in favor of a model that is possibly overfit to these four extreme points. However, on the set of sample videos we have used, this guided RANSAC approach produces consistently acceptable results. Figure 10 shows one such result. We have run the early stages of our pipeline motion detection and line segment detection on videos from these two perspectives, and the quality of the line segments we have observed are encouraging. We leave it to future work to identify which end of the segments correspond to the club head and how to estimate the motion of these club head hypotheses as functions of time and space Computing Time Models Once we have estimated the magnitude of the club head as functions of angle, we then estimate the angle of the club head as functions of time. As in [3], we use the inliers for each of these curves to compute the least squares fits for the desired time models. Examples of complete spatiotemporal models can be found on the project website. 5. Additional Camera Angles The approach we have described produces a 2D estimation of the golf swing. What we would like to produce, however, is an estimation of the swing in 3D. Having a complete representation of the swing in space would be useful for Figure 11. Three different positions at the top of the backswing. Although they look similar from the face-on view, the downline view reveals significant differences. Thus, analyzing additional perspectives is crucial for constructing 3D trajectory models. Note: the images for the face-on and down-line view were taken separately, while the golfer re-enacted the same positions.

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