Recovery of a linear model parameter using three vanishing points from a single image of weak perspective projection

An essential role of model-based vision deals with the problem of solving for the values of all viewpoint and model parameters to be computed for the dimensions of an object for a three-dimensional (3-D) model. We propose a new method using only three vanishing points for recovering the dimensions of an object, its position, and the focal length of the camera from a single image of weak perspective projection. Our aim is to compute the dimension vector v of a model represented by the unit vector of objects from the image. The optimization of the dimension vector v for the object can be thus solved by the standard nonlinear optimization techniques with a multistart method that generates multiple starting points for the optimizer by sampling the parameter space uniformly. Experimental results demonstrate the dimension vector v of the proposed method for the 3-D model and show that the performance of the proposed method is better than the conventional. We also address that the actual dimensions of object from the image agree well with the simulated results from the single image of weak perspective projection.