Trajectory calculation device, trajectory calculating method, and trajectory calculating program

1. A trajectory calculation device capable of calculating a trajectory of a moving object as a target jumping in three dimensions from information of a plurality of image frames captured by a monocular camera, comprising:

a detection unit that detects a specific point of the moving object from the plurality of image frames;

an existence straight line calculation unit that calculates an existence straight line connecting a three-dimensional position with respect to an image of the specific point captured in each of the image frames and a three-dimensional position of an optical center of a lens of the monocular camera;

a take-off point calculation unit that calculates a three-dimensional position of the specific point at a take-off point by calculating an amount of change related to a three-dimensional position of the specific point from information of the plurality of image frames that are consecutive and determining the take-off point where the moving object as the target takes off from the calculated amount of change;

a landing point calculation unit that calculates a three-dimensional position of the specific point at a landing point by calculating an amount of change related to a three-dimensional position of the specific point from information of the plurality of image frames that are consecutive and determining the landing point where the moving object lands from the calculated amount of change; and

a trajectory calculation unit that calculates the trajectory of the specific point in three dimensions from a positional relation of a curved line and the existence straight line wherein the curved line is capable of expressing a parabolic motion passing through the three-dimensional position of the specific point at the take-off point and the three-dimensional position of the specific point at the landing point and wherein the existence straight line connects the three-dimensional position of the optical center and the three-dimensional position with respect to the image of the specific point captured in each of the plurality of image frames after take-off and before landing of the moving object.

2. The trajectory calculation device according to claim 1 , wherein the take-off point calculation unit comprises:

means for calculating a three-dimensional position of the specific point at the take-off point by

calculating an amount of change related to a three-dimensional position of the specific point from information of the plurality of image frames that are consecutive in a chronological order of captured times and

determining the take-off point as the moving object takes off when the calculated amount of change is larger than a predetermined threshold value.

3. The trajectory calculation device according to claim 2 , wherein the landing point calculation unit comprises:

means for calculating a three-dimensional position of the specific point at the landing point by

calculating an amount of change related to a three-dimensional position of the specific point from information of the plurality of image frames that are consecutive in a reverse chronological order of captured times and

determining the landing point as the moving object lands when the calculated amount of change is larger than a predetermined threshold value.

4. The trajectory calculation device according to claim 3 , wherein the trajectory calculation unit comprises:

means for calculating the curved line as a trajectory of the specific point in three dimensions, wherein

the curved line is capable of expressing a parabolic motion passing through a three-dimensional position of the specific point at the take-off point and a three-dimensional position of the specific position at the landing point and

the curved line is calculated so as to minimize a sum of distances between the curved line and the existence straight line with respect to each of images of the specific point captured in the plurality of image frames after take-off of the moving object and before landing of the moving object.

5. The trajectory calculation device according to claim 3 , wherein the trajectory calculation unit comprises:

means for calculating the curved line as a trajectory of the specific point in three dimensions, wherein

the curved line is capable of expressing a parabolic motion passing through a three-dimensional position of the specific point at the take-off point and a three-dimensional position of the specific position at the landing point and

the curved line is calculated so as to minimize a sum of distances between a predicted position on the curved line at a time when capturing the specific point and the existence straight line with respect to an image of the specific point captured at the same time in one of the plurality of image frames, which are captured at times after take-off and before landing of the moving object.

6. The trajectory calculation device according to claim 2 , wherein the landing point calculation unit comprises:

means for calculating a three-dimensional position of the specific point by

calculating an amount of change related to a three-dimensional position of the specific point from information of the plurality of image frames that are consecutive in a chronological order of captured times after capturing the landing point;

acquiring time of capturing the moving object at an apex of jumping by determining the moving object reaches the apex of the jumping when the calculated amount turns from positive to negative or from negative to positive;

calculating an amount of change related to a three-dimensional position of the specific point from information of the plurality of image frames that are consecutive in a reverse chronological order of captured times starting from time when a period of time obtained by doubling a period of time from when capturing the take-off point to when capturing the moving object at the apex and by further adding a constant period of time thereto passes by from when capturing the take-off point; and

determining the landing point as the moving object lands when the calculated amount of change is larger than a predetermined threshold value.

7. The trajectory calculation device according to claim 6 , wherein the trajectory calculation unit comprises:

means for calculating the curved line as a trajectory of the specific point in three dimensions, wherein

the curved line is capable of expressing a parabolic motion passing through a three-dimensional position of the specific point at the take-off point and a three-dimensional position of the specific position at the landing point and

the curved line is calculated so as to minimize a sum of distances between the curved line and the existence straight line with respect to each of images of the specific point captured in the plurality of image frames after take-off of the moving object and before landing of the moving object.

8. The trajectory calculation device according to claim 6 , wherein the trajectory calculation unit comprises:

means for calculating the curved line as a trajectory of the specific point in three dimensions, wherein

the curved line is capable of expressing a parabolic motion passing through a three-dimensional position of the specific point at the take-off point and a three-dimensional position of the specific position at the landing point and

the curved line is calculated so as to minimize a sum of distances between a predicted position on the curved line at a time when capturing the specific point and the existence straight line with respect to an image of the specific point captured at the same time in one of the plurality of image frames, which are captured at times after take-off and before landing of the moving object.

9. The trajectory calculation device according to claim 2 , wherein the trajectory calculation unit comprises:

means for calculating the curved line as a trajectory of the specific point in three dimensions, wherein

the curved line is capable of expressing a parabolic motion passing through a three-dimensional position of the specific point at the take-off point and a three-dimensional position of the specific position at the landing point, and

the curved line is calculated so as to minimize a sum of distances between the curved line and the existence straight line with respect to each of images of the specific point captured in the plurality of image frames after take-off and before landing of the moving object.

10. The trajectory calculation device according to claim 2 , wherein the trajectory calculation unit comprises:

means for calculating the curved line as a trajectory of the specific point in three dimensions, wherein

the curved line is capable of expressing a parabolic motion passing through a three-dimensional position of the specific point at the take-off point and a three-dimensional position of the specific position at the landing point and

the curved line is calculated so as to minimize a sum of distances between a predicted position on the curved line at a time when capturing the specific point and the existence straight line with respect to an image of the specific point captured at the same time in one of the plurality of image frames, which are captured at times after take-off and before landing of the moving object.

11. The trajectory calculation device according to claim 1 , wherein the trajectory calculation unit comprises:

means for calculating the curved line as a trajectory of the specific point in three dimensions, wherein

the curved line is capable of expressing a parabolic motion passing through a three-dimensional position of the specific point at the take-off point and a three-dimensional position of the specific point at the landing point and

the curved line is calculated so as to minimize a sum of distances between the curved line and the existence straight line with respect to each of images of the specific point captured in the plurality of image frames after take-off and before landing of the moving object.

12. The trajectory calculation device according to claim 1 , wherein the trajectory calculation unit comprises:

means for calculating the curved line as a trajectory of the specific point in three dimensions, wherein

the curved line is capable of expressing a parabolic motion passing through a three-dimensional position of the specific point at the take-off point and a three-dimensional position of the specific position at the landing point and

the curved line is calculated so as to minimize a sum of distances between a predicted position on the curved line at a time when capturing the specific point and the existence straight line with respect to an image of the specific point captured at the same time in one of the plurality of image frames, which are captured at times after take-off and before landing of the moving object.

13. A trajectory calculation method of calculating a trajectory of a moving object as a target jumping in three dimensions from information of a plurality of image frames captured by a monocular camera, comprising the steps of:

detecting a specific point of the moving object from the plurality of image frames;

calculating an existence straight line connecting a three-dimensional position with respect to an image of the specific point captured in each of the image frames and a three-dimensional position of an optical center of a lens of the monocular camera;

calculating a three-dimensional position of the specific point at a take-off point by calculating an amount of change related to a three-dimensional position of the specific point from information of the plurality of image frames that are consecutive and determining the take-off point where the moving object takes off from the calculated amount of change;

calculating a three-dimensional position of the specific point at a landing point by calculating an amount of change related to a three-dimensional position of the specific point from information of the plurality of image frames that are consecutive and determining the landing point where the moving object lands from the calculated amount of change; and

calculating the trajectory of the specific point in three dimensions from a positional relation of a curved line and the existence straight line wherein the curved line is capable of expressing a parabolic motion passing through the three-dimensional position of the specific point at the take-off point and the three-dimensional position of the specific point at the landing point and wherein the existence straight line connects the three-dimensional position of the optical center and the three-dimensional position with respect to the image of the specific point captured in each of the plurality of image frames after take-off and before landing of the moving object.

14. A trajectory calculation device capable of calculating a trajectory of a moving object as a target jumping in three dimensions from information of a plurality of image frames captured by a monocular camera, comprising:

an input device capable of inputting the information of the plurality of image frames;

an output device capable of outputting the trajectory;

a memory capable of storing the information of the plurality of image frames; and

a central processing unit capable of controlling the trajectory calculation device, wherein the central processing unit is operable to:

detect a specific point of the moving object from the image frames;

calculate an existence straight line connecting a three-dimensional position of the specific point captured in each of the image frames and a three-dimensional position of an optical center of a lens of the monocular camera;

calculate an amount of change related to three-dimensional positions of images of the specific point from information of the consecutive image frames;

determine a take-off point where the moving object takes off based on the calculated amount of change;

calculate a three-dimensional position of the specific point at the take-off point;

calculate an amount of change related to three-dimensional positions of images of the specific point from information of the consecutive image frames;

determine a landing point where the moving object lands based on the calculated amount of change;

calculate a three-dimensional position of the specific point at the landing point; and

calculate the trajectory of the specific point in three dimensions from a positional relation of a curved line and the existence straight line wherein the curved line is capable of expressing a parabolic motion passing through the three-dimensional position of the take-off point and the three-dimensional position of the landing point and wherein the existence straight line connects the three-dimensional position of the optical center and the three-dimensional position with respect to the image of the specific point captured in each of the plurality of image frames after take-off and before landing of the moving object.

15. The trajectory calculation device according to claim 14 , wherein the curved line is calculated so as to minimize a sum of distances between the curved line and the existence straight line with respect to the specific point captured in each of the image frames.

16. The trajectory calculation device according to claim 14 , wherein the curved line is calculated so as to minimize a sum of distances between a predicted position on the curved line at a time when capturing the specific point and the existence straight line with respect to the specific point captured at the same time in one of the plurality of image frames, which are captured at times after take-off and before landing of the moving object.

17. The trajectory calculation device according to claim 14 , wherein the curved line is represented by

x ( t )= m/k x v x0 (1− e−k x t /m )+ x 0

y ( t )= m/k y v y0 (1− e−k y t /m )+ y 0

z ( t )= m/k z ( v z0 +m/k z g )(1− e−k z t /m )− m/k z gt+z 0

wherein t is time, m is mass, g is gravitational acceleration, v is velocity, and k is viscosity coefficient.