Fun with TOMI : Part I
I believe that it's important for a clubfitter to understand his tools. This posting is about the TOMI, how it works, what the data it produces really means and how that data can be improved. There is a lot to tell about it and some of that information is very technical. I’ll try not to be too technical in this first posting.
According to the driver that came with the TOMI software it’s based on a VIMICRO ZC0301PLH. The VIMIRCO website (VIMICRO
) states it’s a USB 1.1 compatible webcam capable of streaming up to 30fps at VGA resolution. This webcam became available around 2005 and can support different CMOS image sensors. As I did not open it up it is unknown which CMOS chip it is using and at what resolution and speed (fps or frames per second) it is actually recording the swing. The video option in the TOMI software suggests it is using a 320x240 resolution when measuring the size of that video window.
The second part of the system is the marker unit or clip (transmitter)
which holds four infra-red leds. The arrangements of the leds are such that when an image (2D) is made from them it is possible to determine the 3D Pose of the marker unit. More background information can be found here http://en.wikipedia.org/wiki/3D_pose_estimation.
The third part is the TOMI software
I used the latest version (1.33) which was released around January 2008. This software is responsible for the calculations based on the images provides by the webcam. Those images contain only the four leds
, or move the head and keeping the marker at the same spot.
However as the axis of the shaft is parallel* to the marker and connected to the marker at a fixed and know distance we could use some math to determine were the tip of the shaft is when the position of the marker has been moved and/or rotated.
The manual states “Place the clip on the shaft with its base approximately 10 inches from the ground.”
Is that measured vertical from the ground or measured along the shaft? 10 inches from the top of the base or the bottom? And why “approximately”? If we do not place it at the same spot each and every time it’s obvious that that doesn't help to determine where the tip of the shaft is, especially because the system has no idea where the ground level is as it only sees the marker.
Because of these unknowns we have no idea which point the TOMI is actually calculating as the tip of the shaft.
Is it the green dot, the blue or the Red? Also note that all thee point are NOT in the sweetspot! What about a center shaft design?
Here we also followed the axis of the shaft. And if we would use the correct length in the calculation the tip of the shaft is the exactly in the sweetspot.
What about a design with an offset?
If we follow the axis of the shaft we are in front(!) of the clubhead.
Please remember these three examples while reading the following part.
The TOMI system doesn’t know when the impact really happened. It can’t see anything else then the four leds. It might be that the clubhead speed at impact slows down enough to clearly show the impact moment but I have included a speed chart at the end of this documents to show that impact doesn’t slow down the clubhead significant enough for the TOMI to use speed as an impact indication.
That leaves only one option for the TOMI to determine impact position and that is “calibration position”!
The following is what I assume it is doing but please note that there is no other option available for the TOMI system!
During the calibration procedure it measures\calculates a position, this position is possibly related to the 10 inch marker placement instruction. So during a 10 seconds calibration and with 30fps it gets 300 positions. When the calibration is finished it then calculates the average for the calibration point. This is a 3D point, it knows the position on the x-axis, height (y-axis) and depth (z-axis). It also knows the rotation of the marker at this calibration point. It will then assume that this point is also very close to a possible impact point. If it records a new position during the swing that is further to the right (on the x-axis) then the calibration point it can assume that that point crossed this virtual "finish-line". So when during the swing any data point is measured as passing the finish line then between that datapoint and the previous one the impact must have been taken place.
Imagine that the TOMI now indeed knows some virtual shaft tip position
The big yellow circle is the golf ball. The red line is the finish line, the black dot is the tip of the shaft for which its position is calculated by the TOMI software. The green line is the topline of the clubhead.
During the calibration period we place the sweetspot as close as possible to the ball and we cross the finish line at the exact same spot but with an open face and with the same three different clubhead designs as noted above.
In scenario A we have a centered shaft club head and at the moment we return to the calibration point we hit the ball with an open face. The system could report a center hit with an open face which is correct. However in scenario B we have also crossed the finish line with the calculated shaft tip but because of the design being a non-centered shaft only the tip of the shaft has crossed the finish line and there is still time for the golfer to close the face before the sweetspot will actually hit the ball.
Scenario C is the same as scenario B but now because of the extra offset there is even more time to close the face; it might be even possible to get it closed before really hitting the ball. If the offset would have been backwards the impact already happened before the virtual shaft tip crossed the finish line.
In both scenario B and C it is very unlikely that the reported face angle by the TOMI software is correct. The design of the head is important!
If you still with me till this point then remember the remarks about the height of the placement of the marker on the shaft and the trouble of finding the correct end of the shaft. Here are again three scenarios.
In these three scenarios we have three different “heights” for the shaft tip. Green is when the tip is measured too high. Blue when it’s correct and Red when too low.
Yellow is the ball, the red line is the finish line and the thick brown line is the shaft.
When hitting the ball with no shaft lean (scenario A) there is no problem with the error in the height. However in the B scenario’s with forward shaft lean we see that if the shaft tip height is calculated too high (B) we did not yet hit the ball and in scenario B II we already hit the ball before the TOMI assumed the crossing of the finish line!
The C Scenario with backward shaft lean show exactly the opposite. Too high (C) means we already hit the ball before the TOMI thinks we crossed the finish line and C II we did not hit the ball yet.
Combine the above scenarios with a calibration where you did not had the shaft in a 100% correct vertical position and all bets are off when and where the ball is when the calculated virtual shaft tip crossed the finish line!
In both scenario B and C it is very unlikely that the shaft angle at impact reported by the TOMI software is correct.
Conclusion: Head design determines what virtual position we are really measuring / calculating. As head design data can’t be entered into the TOMI system it’s unknown to the TOMI system where the sweetspot is. It can therefore not measure clubhead orientation or position.
Solution :
If we could enter the following information
A : The distance from the top led to the horizontal sweetspot line.
B : The distance from the sweetspot to the shaft axis line.
C : The LIE.
D : The offset, or distance from the sweetspot to the shaft axis.
Then that data could be used to calculate exactly where the sweetspot is in relation to the marker.
NOTE I: During calibration the ball must be placed as close to the sweetspot as possible, for every shot the ball should be placed on exact the same spot as it was during calibration.
NOTE II: The shaft must be held still and without any shaft lean during the complete calibration period.
I used the word “parallel” a few sentences back. But is the marker really parallel to the shaft? It is if you use a non-tappered part of the shaft to connect the marker on. But most shafts are tapered and that means that the marker is not parallel to the axis of the shaft.
Black is the tapered shaft en blue is the marker.
The error is not that big and depends on the size of the steps. For the putter I used in the tests the difference in step size was around 0.3mm so an error of 0.3 degrees which means we would miss the middle of the shaft at the tip with an error of around 1.5mm.
However there is a second issue with the shaft. Not all shafts have the same outside diameter. And it is important to know the exact position of the shaft rotation.
Above the image of the marker rotated from right to left on a vertical oriented shaft. As you can see the rotation is visible but the images also shows some displacement. The led on the top in the left image was measured as being on the x-axis position at 531.7mm and in the right image at 550.5 so a movement of 18.8mm where in reality it was not moved only rotated.
So without the correct information about the shaft diameter the software would report the club as being moved and rotated (red lines) and not as only being rotated (blue lines).
And lets not talk about the fact that this error also will influence speed calculations and might report the club as going across the finish line were in reality it still might not!
Conclusion: The TOMI system will report head displacement where it could be only rotated because the shaft information is not entered into the software. Also the tapered shape of the shaft introduces a (minor) error.
Solution: Shaft diameters at both positions where the marker is connected to the shaft should be entered into the software to overcome this issue.
I could continue explaining the consequences of the camera placement for the data or camera calibration for lens distortion or the frame-rate and resolution for the quality of the data or explaining the 4 inch impact zone but let me finish this first posting about the TOMI with some data.
4 swings were recorded with the TOMI and a high-speed camera (850nm Band Pass Filter) running at the same time. That camera was running at 75fps@640x480. With that camera also some calibration data was recorded.
During the calibration run a special rig was used to place the marker unit in a vertical position, laser aligned with the target.
The reported position relative to the camera is in mm, rotation in degrees. First values are the averages for 247 frames and the second line are the standard deviation values.
This shows good rather good precision for a marker based system using such a camera!
The following is the displacement recorded (mm) between each frame. Impact is around the 149 mark. Please note the rather stable data before the swing really begins. No "smoothing" filter was used on this data. It's the raw data
Below is the face angle rotation for the same swing.
And a close-up of face angle data just before and after impact.
When the sweetspot is at the impact position for this 240cm put it is moving around 18mm between frames. With the assumed 30fps for the TOMI the sweetspot for the TOMI would be moving at 45mm between frames!
With the face at impact closed -2.4degrees and closing more then 1degree between frames then again for those 30fps with the TOMI the face would be closing more then 2.5degree between frames!
In the 5 frames around the impact (2 frames before and 2 frames after) the Rate of Closure for this swing peaks at 102degrees/sec!
The first swing in the TOMI screenshot below is the same swing as shown above.
I recorded an alignment at address of -0.1 (standard deviation 0.1)
Summary of the results
The TOMI system can’t measure the moment of impact. It can’t measure the correct sweetspot or clubhead orientation and direction. Because of these two issues the information it produces has large error margins.Description of the TOMI system
The TOMI consists of three parts, A PC webcamAccording to the driver that came with the TOMI software it’s based on a VIMICRO ZC0301PLH. The VIMIRCO website (VIMICRO
) states it’s a USB 1.1 compatible webcam capable of streaming up to 30fps at VGA resolution. This webcam became available around 2005 and can support different CMOS image sensors. As I did not open it up it is unknown which CMOS chip it is using and at what resolution and speed (fps or frames per second) it is actually recording the swing. The video option in the TOMI software suggests it is using a 320x240 resolution when measuring the size of that video window.The second part of the system is the marker unit or clip (transmitter)
which holds four infra-red leds. The arrangements of the leds are such that when an image (2D) is made from them it is possible to determine the 3D Pose of the marker unit. More background information can be found here http://en.wikipedia.org/wiki/3D_pose_estimation.
The third part is the TOMI software
I used the latest version (1.33) which was released around January 2008. This software is responsible for the calculations based on the images provides by the webcam. Those images contain only the four leds
Determining the 3D pose using the TOMI transmitter.
The Marker
It important to understand that this marker technique that the TOMI (and other systems) use will only measure the position and rotation of the marker, it doesn’t measure the clubhead or sweetspot. Only the marker. So it is possible to keep the head at the same position and move the rest of the club and thus the marker, or move the head and keeping the marker at the same spot.
However as the axis of the shaft is parallel* to the marker and connected to the marker at a fixed and know distance we could use some math to determine were the tip of the shaft is when the position of the marker has been moved and/or rotated.
The manual states “Place the clip on the shaft with its base approximately 10 inches from the ground.”
Is that measured vertical from the ground or measured along the shaft? 10 inches from the top of the base or the bottom? And why “approximately”? If we do not place it at the same spot each and every time it’s obvious that that doesn't help to determine where the tip of the shaft is, especially because the system has no idea where the ground level is as it only sees the marker.
Because of these unknowns we have no idea which point the TOMI is actually calculating as the tip of the shaft.
Is it the green dot, the blue or the Red? Also note that all thee point are NOT in the sweetspot! What about a center shaft design?
Here we also followed the axis of the shaft. And if we would use the correct length in the calculation the tip of the shaft is the exactly in the sweetspot.
What about a design with an offset?
Please remember these three examples while reading the following part.
The TOMI system doesn’t know when the impact really happened. It can’t see anything else then the four leds. It might be that the clubhead speed at impact slows down enough to clearly show the impact moment but I have included a speed chart at the end of this documents to show that impact doesn’t slow down the clubhead significant enough for the TOMI to use speed as an impact indication.
That leaves only one option for the TOMI to determine impact position and that is “calibration position”!
The following is what I assume it is doing but please note that there is no other option available for the TOMI system!
During the calibration procedure it measures\calculates a position, this position is possibly related to the 10 inch marker placement instruction. So during a 10 seconds calibration and with 30fps it gets 300 positions. When the calibration is finished it then calculates the average for the calibration point. This is a 3D point, it knows the position on the x-axis, height (y-axis) and depth (z-axis). It also knows the rotation of the marker at this calibration point. It will then assume that this point is also very close to a possible impact point. If it records a new position during the swing that is further to the right (on the x-axis) then the calibration point it can assume that that point crossed this virtual "finish-line". So when during the swing any data point is measured as passing the finish line then between that datapoint and the previous one the impact must have been taken place.
Imagine that the TOMI now indeed knows some virtual shaft tip position
The big yellow circle is the golf ball. The red line is the finish line, the black dot is the tip of the shaft for which its position is calculated by the TOMI software. The green line is the topline of the clubhead.
During the calibration period we place the sweetspot as close as possible to the ball and we cross the finish line at the exact same spot but with an open face and with the same three different clubhead designs as noted above.
In scenario A we have a centered shaft club head and at the moment we return to the calibration point we hit the ball with an open face. The system could report a center hit with an open face which is correct. However in scenario B we have also crossed the finish line with the calculated shaft tip but because of the design being a non-centered shaft only the tip of the shaft has crossed the finish line and there is still time for the golfer to close the face before the sweetspot will actually hit the ball.
Scenario C is the same as scenario B but now because of the extra offset there is even more time to close the face; it might be even possible to get it closed before really hitting the ball. If the offset would have been backwards the impact already happened before the virtual shaft tip crossed the finish line.
In both scenario B and C it is very unlikely that the reported face angle by the TOMI software is correct. The design of the head is important!
If you still with me till this point then remember the remarks about the height of the placement of the marker on the shaft and the trouble of finding the correct end of the shaft. Here are again three scenarios.
In these three scenarios we have three different “heights” for the shaft tip. Green is when the tip is measured too high. Blue when it’s correct and Red when too low.
Yellow is the ball, the red line is the finish line and the thick brown line is the shaft.
When hitting the ball with no shaft lean (scenario A) there is no problem with the error in the height. However in the B scenario’s with forward shaft lean we see that if the shaft tip height is calculated too high (B) we did not yet hit the ball and in scenario B II we already hit the ball before the TOMI assumed the crossing of the finish line!
The C Scenario with backward shaft lean show exactly the opposite. Too high (C) means we already hit the ball before the TOMI thinks we crossed the finish line and C II we did not hit the ball yet.
Combine the above scenarios with a calibration where you did not had the shaft in a 100% correct vertical position and all bets are off when and where the ball is when the calculated virtual shaft tip crossed the finish line!
In both scenario B and C it is very unlikely that the shaft angle at impact reported by the TOMI software is correct.
Conclusion: Head design determines what virtual position we are really measuring / calculating. As head design data can’t be entered into the TOMI system it’s unknown to the TOMI system where the sweetspot is. It can therefore not measure clubhead orientation or position.
Solution :
If we could enter the following information
A : The distance from the top led to the horizontal sweetspot line.
B : The distance from the sweetspot to the shaft axis line.
C : The LIE.
D : The offset, or distance from the sweetspot to the shaft axis.
Then that data could be used to calculate exactly where the sweetspot is in relation to the marker.
NOTE I: During calibration the ball must be placed as close to the sweetspot as possible, for every shot the ball should be placed on exact the same spot as it was during calibration.
NOTE II: The shaft must be held still and without any shaft lean during the complete calibration period.
I used the word “parallel” a few sentences back. But is the marker really parallel to the shaft? It is if you use a non-tappered part of the shaft to connect the marker on. But most shafts are tapered and that means that the marker is not parallel to the axis of the shaft.
Black is the tapered shaft en blue is the marker.
The error is not that big and depends on the size of the steps. For the putter I used in the tests the difference in step size was around 0.3mm so an error of 0.3 degrees which means we would miss the middle of the shaft at the tip with an error of around 1.5mm.
However there is a second issue with the shaft. Not all shafts have the same outside diameter. And it is important to know the exact position of the shaft rotation.
Above the image of the marker rotated from right to left on a vertical oriented shaft. As you can see the rotation is visible but the images also shows some displacement. The led on the top in the left image was measured as being on the x-axis position at 531.7mm and in the right image at 550.5 so a movement of 18.8mm where in reality it was not moved only rotated.
So without the correct information about the shaft diameter the software would report the club as being moved and rotated (red lines) and not as only being rotated (blue lines).
And lets not talk about the fact that this error also will influence speed calculations and might report the club as going across the finish line were in reality it still might not!
Conclusion: The TOMI system will report head displacement where it could be only rotated because the shaft information is not entered into the software. Also the tapered shape of the shaft introduces a (minor) error.
Solution: Shaft diameters at both positions where the marker is connected to the shaft should be entered into the software to overcome this issue.
I could continue explaining the consequences of the camera placement for the data or camera calibration for lens distortion or the frame-rate and resolution for the quality of the data or explaining the 4 inch impact zone but let me finish this first posting about the TOMI with some data.
4 swings were recorded with the TOMI and a high-speed camera (850nm Band Pass Filter) running at the same time. That camera was running at 75fps@640x480. With that camera also some calibration data was recorded.
During the calibration run a special rig was used to place the marker unit in a vertical position, laser aligned with the target.
The reported position relative to the camera is in mm, rotation in degrees. First values are the averages for 247 frames and the second line are the standard deviation values.
This shows good rather good precision for a marker based system using such a camera!
The following is the displacement recorded (mm) between each frame. Impact is around the 149 mark. Please note the rather stable data before the swing really begins. No "smoothing" filter was used on this data. It's the raw data
Below is the face angle rotation for the same swing.
And a close-up of face angle data just before and after impact.
When the sweetspot is at the impact position for this 240cm put it is moving around 18mm between frames. With the assumed 30fps for the TOMI the sweetspot for the TOMI would be moving at 45mm between frames!
With the face at impact closed -2.4degrees and closing more then 1degree between frames then again for those 30fps with the TOMI the face would be closing more then 2.5degree between frames!
In the 5 frames around the impact (2 frames before and 2 frames after) the Rate of Closure for this swing peaks at 102degrees/sec!
The first swing in the TOMI screenshot below is the same swing as shown above.
I recorded an alignment at address of -0.1 (standard deviation 0.1)