Stereo vision is a very useful, yet challenging technology for a wide variety of applications. One of the greatest challenges is meeting the computational demands of stereo vision applications that require real-time performance. The FPGA (Field Programmable Gate Array) is a readily-available technology that allows many stereo vision methods to be implemented while meeting the strict real-time performance requirements of some applications. Some of the best results have been obtained using non-parametric stereo correlation methods, such as the rank and census transform. Yet relatively little work has been done to study these methods or to propose new algorithms based on the same principles for improved stereo correlation accuracy or reduced resource requirements. This dissertation describes the sparse census and sparse rank transforms, which significantly reduce the cost of implementation while maintaining and in some case improving correlation accuracy. This dissertation also proposes the generalized census and generalized rank transforms, which opens up a new class of stereo vision transforms and allows the stereo system to be even more optimized, often reducing the hardware resource requirements. The proposed stereo methods are analyzed, providing both quantitative and qualitative results for comparison to existing algorithms. These results show that the computational complexity of local stereo methods can be significantly reduced while maintaining very good correlation accuracy. A hardware architecture for the implementation of the proposed algorithms is also described and the actual resource requirements for the algorithms are presented. These results confirm that dramatic reductions in hardware resource requirements can be achieved while maintaining high stereo correlation accuracy. This work proposes the multi-bit census, which provides improved pixel discrimination as compared to the census, and leads to improved correlation accuracy with some stereo configurations. A rotation-invariant census transform is also proposed and can be used in applications where image rotation is possible.