Measuring ball spin using the ball's logo.
Most will probably not want to use specially marked balls so we have developed the Bcam system to use the standard ball logo on the ball to measure ball spin and spin axis.
New logo matching end detection.
An issue with measuring ball spin using the ball's logo is that the correct matching ends of the logo must be detected in order to correctly measure the amount of rotation within the time frame..
i.e. if one end of the logo is found in image 1 then that same end has to found in image 2. Failing to do this can result in very different ball spin rate measurements.
The above two images show a ball spinning at a rate of 8321 rpm. We know this because the amount of rotation within the 1 ms frame delay was 149.78 degrees.
And we only know the correct amount of rotation because the Letter "C" in the Calloway logo has been detected correctly in both frames. This is shown by the two red cross hairs over the letter "C".
Without this new "Matching logo end detection" feature, the CP image processing may well get the ends mixed up and then a totally different amount of rotation will be measured
(i.e. 30.22 degrees here) and thus a totally different and false ball spin rate will be calculated. (Note that the two sets of images are from the same shot.)
As can be seen from the above two images, the letter "C" in the Calloway logo has not been detected in image 2 (i.e. there's a green cross hair on the "C" instead of a red cross hair).
And thus a false spin rate measurement was calculated (i.e. 1678 rpm instead of the real 8321 rpm).
It should be noted that not all ball logos have a dominant end and thus it may be required to use a black magic marker or black ink pen to accent one end of the logo.
Note that measuring ball spin using the logo (or any marked balls like those with About Golf systems) is the only way a camera method of ball spin detection is able to do this in real time. i.e. without a long 2 to 4 second or so lag time (SkyTrak / GC2 etc).
While radar systems (Trackman, FlightScope etc) require metallic dots be applied to the ball and the ball be placed with the dot facing upwards.
Quantum F and FB Setup
Side Spin and spin axis detection
Note that in reality a ball cannot have both back spin and side spin at the same time. In reality a ball has only spin and spin axis.
Never-the-less, a theoretical side spin rate can be measured by the amount of horizontal rotation within a certain time period.
And a back spin rate can be measured by the amount of vertical rotation within a certain time period.
Side spin theory
Side spin is imparted on the ball by the club face striking the ball with a relative-to-club-path face angle that is not square - i.e. open or closed.
This open or closed club face relative to the club path will cause the ball's backspin rotation axis to shift off center.
The above image shows ball spin without any side spin and 0 degree spin axis. The red line represents a line or logo on the ball.
If the Bcam is overhead mounted (Top View), then the line will only move backwards in each frame if there is no side spin and the line will have the same angle in each frame.
This backward movement is vertical rotation and is used to measure the back spin.
If the Bcam is mounted at floor level (for a side view) and there is no side spin, the red line will continue to rotate around the initial center of rotation
and the amount of rotation within a certain time period is used to calculate the back spin rate in rpm.
The "ref frame" is a frame of the stationary ball on the ground or tee before being struck.
The above image shows ball spin with side spin.
If the Bcam is overhead mounted (Top View), then the line angle will have changed from the initial image of the ball on the ground or tee
to a different angle after launch. This change in angle within a certain time frame is used to calculate the amount of side spin in rpm.
If the Bcam is side mounted (side view), then the line will be seen as rotating around a different axis compared to the initial axis the line was on when on the ground or tee.
We use this shift in spin axis to then calculate the side spin rotation in rpm.
Spin axis theory
Note that spin axis is never always on one plane. i.e. spin axis can have both a vertical and horizontal component to it. Thus spin axis is a 3D value.
So when you see a launch monitor displaying a spin axis of 4 degrees left or right, it is not known whether this value is on the vertical or horizontal plane.
As the real spin axis value can only described by a mathematical 3D vector - which most average golfers will have difficulty comprehending - it is simplified by reducing it to just the one plane.
Just like side spin: it's not real but we can at least grasp its meaning.
Bcam side view images
The above shows real balls - viewed from the side - with a back spin rotation and rotation axis shift.
Side spin can then be converted to spin axis.
Note that both the single camera Bcam and dual camera Bcam Pro are both using reference frames now. i.e. images of the ball on the ground or tee are automatically captured.
Bcam overhead view images
The above images are from the Bcam when mounted overhead.
Bcam overhead mounted images
Left: frame 2 of full shot with 3 wood - Right: frame 1 of ball on mat hitting position
Left: frame 2 of open faced 3 wood. Right: Composite of frames 1 and 2.
VisTrak Quantum physics : Spin rate and spin axis theory
Measuring spin rate from an overhead camera system
A little math is required to deduce the spin rate from the circle arc measured from the rotating and shifting key point pattern on the ball.
Knowing the circle arc length (i.e. the vertical shift of the key point pattern on the ball as viewed from above) and the radius of the ball, the arc central angle can be calculated.
This arc central angle is the rotation in degrees (or radians) for a given time between the two frames (1 ms) and from this, the spin rate can be calculated.
VisTrak LX ball spin detection
Ball spin detection without ball markings stages
In order to detect ball spin from balls that don't feature any markings, the above ball image process stages have to first be performed.
Stage 1 is the dimple edge detection in gray scales (completed)
Stage 2 is the conversion of the edge detection gray scale image to a binary (just black and white) image. (completion expected this weekend).
Stage 3 is to detect the dimple centers. (around 10 days to complete)
Stage 4 is to rotate/shift and match the two image dimple patterns in order to determine the amount of rotation within the frame time period and thus the spin rate. (50% complete)
Stage 5 is Testing, adjustments and modifications.
GSA Golf tracking systems that measure ball spin without ball markings
VisTrak Quantum C
All ceiling mounted 3 camera ball and club tracking system.
Detecting ball spin from ceiling mounted cameras that look down on the ball, requires a different approach.
When looking down on the ball, back spin rotation will appear as image shift downwards and not as regular rotation as when the cameras are viewing the ball from the side.
As the ball is spherical, images of the dimple patterns are distorted as the ball rotates, so that direct dimple pattern matching of two images of the ball will not be possible.
The above method solves this problem by projecting the ball's 3D spherical surface onto a 2D UV map so that dimple spin patterns are not distorted during the rotation
and thus can be located and matched.
As we are only seeing a small arc of the rotation, camera frame timing must be very fast. Currently, a frame time of 0.2 ms or 200 micro seconds is being used.
Using two individual hi-resolution cameras that only grab 1 image of the ball each, we can set the frame timing to be as fast as we want.
At a 1 milli-second frame time, the dual camera system has the equivalent of a 1000 fps camera and at 0.2 ms, the camera system will have
the equivalent of a 5000 frames per second camera.
Not bad for a low cost system we think.
The Quantum C will undoubtedly be our best selling system by far and it's price -
compared to the competition that are in the $10,000 to $20,000 range - should ensure that it dominates the market.
Data captured: Ball spin and spin axis, ball speed, LA and path, club face, club speed and path with swing video playback .
Estimated release date : October 15 2020.
VisTrak Quantum F and Quantum FB
Quantum F and Quantum FB
A combination of ceiling and floor mounted cameras
Development of new ball spin detection of balls without markings for the Quantum C is underway.
The real image size of the ball is huge when using the Quantum C 48mm lenses.
The above shows two images of a ball after dimple edge detection and conversion to a binary image using two separate frames.
i.e. the edge detection filter process is run separately for each frame.
The second ball image is of the ball after it has been rotated by 45 degrees
An image matching and rotation process of the two frames is run until a close match is found.
i.e. we start out at 0 degrees and go through all 360 degrees, noting the number of pixels in the images that match for every 1 degree of rotation and store this matching value into a table.
We then just search through the 360 element table for the closest match - which will then tell us the amount of rotation the ball has made within the 1 ms frame time.
From this, the spin rate is calculated.
Using this method, stage 3 - dimple center detection - will not be required.
September 9 11:00 am
Ball spin detection without ball markings
Stage 2 - gray scale dimple edge conversion to binary dimple pattern completed.
The conversion itself was actually very simple.
Far more time was spent creating a smother gray scale dimple edge image which is now a composite of 12 segments - 8 around the sides and 4 in the center.
Stage 3 - dimple center detection - is going to be quite a challenge but I'm confident I'll have this completed by the weekend.
Then it's off to the races : image matching to determine rotation and thus spin rate.
White paper quote:
Although the small depression parts on a golf ball surface, which are called dimples, may appear to be regular, they actually have slight irregularity in their sizes and arrangement
in order to improve aerodynamic characteristics for, for example, better stability of flight or longer flight distance.
This is true for any real golf balls, as far as the authors know, because completely regular dimples offer poor aerodynamic performance.
Bcam side mounted images
Left: 9 iron shot using spin dots on ball ---------------------- Right: White head driver using line marking on ball