Abstract
This paper proposes the method of the pose determination of the 3-D polyhedral object from a single perspective image based on the known 3-D prototype model. For the pose determination from the 2-D perspective image, we must know the correspondence of vertices and the parameter for the coordinate transformation between the 3-D prototype model and the 3-D reconstructed model from the 2-D perspective image. Generally there is hopefully only one transformation of the coordinate between the 3-D prototype model and the reconstructed model. Therefore the parameters of the coordinate transformation, which we calculate between each surface chosen from 3-D prototype model and 3-D reconstructed model at will, have just the same value. We make use of this property, and search the correspondence of vertices and the parameter of the coordinate transformation.
First we assume to match a surface of prototype model with one of 2-D projective image, reconstruct the 3-D coordinate of vertices on 2-D projective image and determine the parameter between them. Next, we calculate the parameter within the permission limit to the error obtained from pairing the surface and look for the primary parameter with the most number of the corresponding points. Then the optimal parameter is calculated from the primary parameter using the quasi-Newton method so that the square distance error between the point of 2-D perspective image and its corresponding point of the reconstructed model on the image plane is minimized. Therefore we can obtain the 3-D location of the 2-D image using the optimal parameter.
Using the above theory, we make the experiment on the pose determination of 2-D image based on the 3-D prototype model using the real image. The application of the object recognition is also shown and the proposed theory in the paper is able to be applied effectively in the field of the robot vision.
