Mixing
Parabola Equation from its trajectory points in a Video
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
I have a video of an object describing a ballistic trajectory (i.e. A ball being thrown)
The video is filmed with an angle and not orthogonally to the moving object, the camera is calibrated.
I am able to register the ball centres along the frames and extract the trajectory points.
Knowing all points and that the trajectory is a parabola, is there a way to recover the parabola plane and its equation?
conic-sections computer-vision
asked Jul 22 at 0:35
Brokenp17
11
add a comment |Â
up vote
0
down vote
favorite
I have a video of an object describing a ballistic trajectory (i.e. A ball being thrown)
The video is filmed with an angle and not orthogonally to the moving object, the camera is calibrated.
I am able to register the ball centres along the frames and extract the trajectory points.
Knowing all points and that the trajectory is a parabola, is there a way to recover the parabola plane and its equation?
conic-sections computer-vision
asked Jul 22 at 0:35
Brokenp17
11
Im not sure if i understand the problem completely but if you know at least 3 (x, y) coordinates of the parabola you can make a system of equations and solve.
– Shrey Joshi
Jul 22 at 2:03
Suppose i have domenica of the points in the trajectory in the Image. The Red trajectory is a parabola in real world, but since the Image is taken from an angle, It is not a parabola in the Image. From these Image coordinates, i want to extract the parabola equation.(i.stack.imgur.com/VVzBt.png)
– Brokenp17
Jul 23 at 9:28
Interesting problem. As you note, the trajectory in the image will not generally be a parabola—it will be hyperbolic unless the trajectory is parallel to the image plane. I suspect that you’ll have to use other cues in the scene, such as apparent ball size, to determine the trajectory plane uniquely. One you have that, back-mapping the data points to this plane is simple, and then you should be able to fit a parabola to the transformed points.
– amd
Aug 4 at 0:23
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a video of an object describing a ballistic trajectory (i.e. A ball being thrown)
The video is filmed with an angle and not orthogonally to the moving object, the camera is calibrated.
I am able to register the ball centres along the frames and extract the trajectory points.
Knowing all points and that the trajectory is a parabola, is there a way to recover the parabola plane and its equation?
conic-sections computer-vision
asked Jul 22 at 0:35
Brokenp17
11
I have a video of an object describing a ballistic trajectory (i.e. A ball being thrown)
The video is filmed with an angle and not orthogonally to the moving object, the camera is calibrated.
I am able to register the ball centres along the frames and extract the trajectory points.
Knowing all points and that the trajectory is a parabola, is there a way to recover the parabola plane and its equation?
conic-sections computer-vision
asked Jul 22 at 0:35
Brokenp17
11
asked Jul 22 at 0:35
Brokenp17
11
asked Jul 22 at 0:35
Brokenp17
11
asked Jul 22 at 0:35
Brokenp17
11
11
Im not sure if i understand the problem completely but if you know at least 3 (x, y) coordinates of the parabola you can make a system of equations and solve.
– Shrey Joshi
Jul 22 at 2:03
Suppose i have domenica of the points in the trajectory in the Image. The Red trajectory is a parabola in real world, but since the Image is taken from an angle, It is not a parabola in the Image. From these Image coordinates, i want to extract the parabola equation.(i.stack.imgur.com/VVzBt.png)
– Brokenp17
Jul 23 at 9:28
Interesting problem. As you note, the trajectory in the image will not generally be a parabola—it will be hyperbolic unless the trajectory is parallel to the image plane. I suspect that you’ll have to use other cues in the scene, such as apparent ball size, to determine the trajectory plane uniquely. One you have that, back-mapping the data points to this plane is simple, and then you should be able to fit a parabola to the transformed points.
– amd
Aug 4 at 0:23
add a comment |Â
Im not sure if i understand the problem completely but if you know at least 3 (x, y) coordinates of the parabola you can make a system of equations and solve.
– Shrey Joshi
Jul 22 at 2:03
Suppose i have domenica of the points in the trajectory in the Image. The Red trajectory is a parabola in real world, but since the Image is taken from an angle, It is not a parabola in the Image. From these Image coordinates, i want to extract the parabola equation.(i.stack.imgur.com/VVzBt.png)
– Brokenp17
Jul 23 at 9:28
Interesting problem. As you note, the trajectory in the image will not generally be a parabola—it will be hyperbolic unless the trajectory is parallel to the image plane. I suspect that you’ll have to use other cues in the scene, such as apparent ball size, to determine the trajectory plane uniquely. One you have that, back-mapping the data points to this plane is simple, and then you should be able to fit a parabola to the transformed points.
– amd
Aug 4 at 0:23
Im not sure if i understand the problem completely but if you know at least 3 (x, y) coordinates of the parabola you can make a system of equations and solve.
– Shrey Joshi
Jul 22 at 2:03
Im not sure if i understand the problem completely but if you know at least 3 (x, y) coordinates of the parabola you can make a system of equations and solve.
– Shrey Joshi
Jul 22 at 2:03
Suppose i have domenica of the points in the trajectory in the Image. The Red trajectory is a parabola in real world, but since the Image is taken from an angle, It is not a parabola in the Image. From these Image coordinates, i want to extract the parabola equation.(i.stack.imgur.com/VVzBt.png)
– Brokenp17
Jul 23 at 9:28
Suppose i have domenica of the points in the trajectory in the Image. The Red trajectory is a parabola in real world, but since the Image is taken from an angle, It is not a parabola in the Image. From these Image coordinates, i want to extract the parabola equation.(i.stack.imgur.com/VVzBt.png)
– Brokenp17
Jul 23 at 9:28
Interesting problem. As you note, the trajectory in the image will not generally be a parabola—it will be hyperbolic unless the trajectory is parallel to the image plane. I suspect that you’ll have to use other cues in the scene, such as apparent ball size, to determine the trajectory plane uniquely. One you have that, back-mapping the data points to this plane is simple, and then you should be able to fit a parabola to the transformed points.
– amd
Aug 4 at 0:23
Interesting problem. As you note, the trajectory in the image will not generally be a parabola—it will be hyperbolic unless the trajectory is parallel to the image plane. I suspect that you’ll have to use other cues in the scene, such as apparent ball size, to determine the trajectory plane uniquely. One you have that, back-mapping the data points to this plane is simple, and then you should be able to fit a parabola to the transformed points.
– amd
Aug 4 at 0:23
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Â
draft saved
draft discarded
Â
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2858988%2fparabola-equation-from-its-trajectory-points-in-a-video%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Im not sure if i understand the problem completely but if you know at least 3 (x, y) coordinates of the parabola you can make a system of equations and solve.
– Shrey Joshi
Jul 22 at 2:03
Suppose i have domenica of the points in the trajectory in the Image. The Red trajectory is a parabola in real world, but since the Image is taken from an angle, It is not a parabola in the Image. From these Image coordinates, i want to extract the parabola equation.(i.stack.imgur.com/VVzBt.png)
– Brokenp17
Jul 23 at 9:28
Interesting problem. As you note, the trajectory in the image will not generally be a parabola—it will be hyperbolic unless the trajectory is parallel to the image plane. I suspect that you’ll have to use other cues in the scene, such as apparent ball size, to determine the trajectory plane uniquely. One you have that, back-mapping the data points to this plane is simple, and then you should be able to fit a parabola to the transformed points.
– amd
Aug 4 at 0:23