into the parametric plane, where the parameters r and θ of the line are shown in Fig.3(a). A straight line in the image plane corresponds to a point in the parametric plane. During the transformation, the number of pixels falling into each parametric coordinate is counted as shown in Fig.3(b). The highest vote of pixels in the parametric plane corresponds to the longest line in the image plane. With the estimator given in Eq.(4), the where abouts of the line can be predicted and Hough transformation is necessaryonly in that region to get the details of the line. Thus the extraction is much faster enabling real-time operations and avoids detecting false targets.
r = xcos(θ) ＋ ysin(θ). (1)
4. Estimator
In order to compensate the delay caused by image processing and to find the where abouts of the cable in the next image frame, the following estimator is introduced. The motion parameters of the object of interest can be derived with the pin-hole camera model shown in Fig.4. A point P projects into a point p in the image plane with image coordinates (x,y) given by;
x=Xs/Zs, and y=Ys/Zs. (2)
The perspective projection and the focal length is assumed to be unity. If the vehicle moves in a static environment with a translational velocity T and with an angular velocity R with respect to the vehicle frame, then the velocity of point P can be derived as;
By taking the time derivatives of the expressions for x and y and using Eqs.(2) and (3), we obtain Eq.(4) which is used as the motion estimator in the proposed tracking algorithms
5. 2D to 3D Transformation
To generate the control commands of the UUV, it is necessary to know the position of the cable with respect to the vehicle's coordinates. In the experiment discussed, the camera position is kept constant relative to the vehicle.
Fig.4:Image and vehicle coordinate systems.
(Where Tx - Sway, Ty - Heave, Tz - Surge, Rx - Pitch, Ry - Yaw, Rz - Roll)
