Knowing the shape and pose of objects of interest is critical information when planning robotic grasping and manipulation maneuvers. The ability to recover this information from objects for which the system has no prior knowledge is a valuable behavior for an autonomous or semiautonomous robot. This work develops and presents an algorithm for the shape and pose recovery of unknown objects using no a priori information. Using a monocular camera in an eye-in-hand configuration, three images of the object of interest are captured from three disparate viewing directions. Machine vision techniques are employed to process these images into silhouettes. The silhouettes are used to generate an approximation of the surface of the object in the form of a three dimensional point cloud. The accuracy of this approximation is improved by fitting an eleven parameter geometric shape to the points such that the fitted shape ignores disturbances from noise and perspective projection effects. The parametrized shape represents the model of the unknown object and can be utilized for planning robot grasping maneuvers or other object classification tasks. This work is implemented and tested in simulation and hardware. A simulator is developed to test the algorithm for various three dimensional shapes and any possible imaging positions. Several shapes and viewing configurations are tested and the accuracy of the recoveries are reported and analyzed. After thorough testing of the algorithm in simulation, it is implemented on a six axis industrial manipulator and tested on a range of real world objects: both geometric and amorphous. It is shown that the accuracy of the hardware implementation performs exceedingly well and approaches the accuracy of the simulator, despite the additional sources of error and uncertainty present.