If you need it, I can produce a video demo of it.

Chas Tennis wrote:

In your example, is the analyst manually identifying the blurry ball images and placing a marker?  So that with given a set of sparse markers with some missing frames a track is to be placed?

Yes. For cases when the video quality is insufficient and can't be improved.
It wouldn't be a track in the same sense as the track tool though, just a curve spanning multiple frames.

What doesn't satisfy me entirely with rebuilding the curve from chronological order, is that it will be very specific to this type of problem. Wouldn't be able to connect dots on the same image for example, while that might be useful in some other instances.
I can't think of a simpler way to express the order in which the curve should be built…

No good answer here.  Don't take literally as this is just to see what might be useful -

Disregard sensor scanning artifacts such as rolling shutter or interlaced scanning that may put a ball image in one frame or the next and make the frame time uncertain. ?  Scanning artifacts are unique for each model camera and probably each recording. 

The analyst could trace the complete smeared image of the ball as best can be done to produce a small line.   These ball smears would be inaccurate and appear as little straight lines at best.  These smears are part of the trajectory.

A ball flying around the court would always fall under gravity and be subject to aerodynamic accelerations due to its spin.

Vz = Vzo - gt + az(V)t
Vx = Vxo + ax(V)t
Vy = Vyo + ay(V)t

Where Vz is the vertical velocity, Vx and Vy are velocity components in two other orthogonal directions.  Vzo, Vxo,Vyo are initial velocity components at time t = 0. V is the magnitude of velocity that produces the aerodynamic forces.  az,ax,ay are components of the aerodynamic acceleration vector - slowing air resistance and spin/Magnus force which, I guess, is always perpendicular to the trajectory. t is time

Gravity works on Vz so that the trajectory always curves downward.   If you had a ball smear, a small straight line, how would it proceed to a later ball smear?  It would always bend downward from just extending the straight line of the earlier ball smear.

The spins and aerodynamic forces, which can be in any direction, are unknown. 

Vertical Z - Gravity + Aerodynamic Forces - For tennis and probably all other sports where ball spin curves the trajectory, I'd say that gravity is considerably the larger force.  I can't think of any sport with a spinning ball that in level flight would rise up against gravity due to aerodynamic forces.  Exceptions?  For connecting the ball smears ignore aerodynamic forces at first or research the magnitude of spin effects for the sport.   

Horizontal X & Y-  = 0 Gravity + Some Unknown Aerodynamic Forces

Bounces - the ball smear has to be associated with the right trajectory before or after the bounce. 

FYI - Paper on the kick serve with its spin, aerodynamic and bounce issues.  http://twu.tennis-warehouse.com/learnin … kserve.php

The discussion has been in terms of an x,y,z coordinate system.   The location of the ball has to be translated into its position in the camera's frame. A camera locates the angle of the light source in relation to its pointing axis.  The 3D space of the squash court has to be projected onto the 2D camera sensor.  Think of a pin hole camera in order to see how the projection works (forget the lens except that the pin hole is placed at the focal length of the lens).

This stuff has probably been researched for the tennis line calling video system, Hawk-Eye.

http://en.wikipedia.org/wiki/Hawk-Eye

In your example, is the analyst manually identifying the blurry ball images and placing a marker?  So that with given a set of sparse markers with some missing frames a track is to be placed?

Yes. For cases when the video quality is insufficient and can't be improved.
It wouldn't be a track in the same sense as the track tool though, just a curve spanning multiple frames.

What doesn't satisfy me entirely with rebuilding the curve from chronological order, is that it will be very specific to this type of problem. Wouldn't be able to connect dots on the same image for example, while that might be useful in some other instances.
I can't think of a simpler way to express the order in which the curve should be built…

In your example, is the analyst manually identifying the blurry ball images and placing a marker?  So that with given a set of sparse markers with some missing frames a track is to be placed?

The ball is going too fast for the camera it was filmed with, so on some frames it's so blurred it's not visible at all. The trajectory tool, even in full manual mode, cannot really be used because of this.
Putting some cross markers doesn't really do what I need, as it doesn't nicely show the ball trajectory.

I think what would be nice is a way to reconstruct a curve from a set of sparse points. A sort of "connect the dots" feature. That would work even if the points sequence misses several frames in a row.
One way to do it would be to connect the markers by chronological order. (Triggered by a right click menu on any marker maybe). For example it could connect all the markers of a specific color, so as to allow several such reconstructed lines in the same sequence.
Another way would be to have a dedicated tool maybe.

Please add your input.
Did you ever found yourself in similar situation ? What do you think would be a sensible way to handle it ?