In modern research, the most studied step of stereo vision algorithms is the process of pixel correspondence, better known as stereo matching. As of now, researchers are attempting to integrate optimization techniques with stereo matching to improve stereo system performance. This paper seeks to provide an in-depth explanation of the stereo vision process in general and find value in the application of optimization techniques to stereo-matching algorithms. To analyze and implement a sound stereo vision algorithm as well as an optimized matching algorithm, scholarly sources involving stereo vision and optimization techniques were studied. After implementing a standard stereo-matching algorithm and an algorithm that involves a famous optimization technique known as Dynamic Programming, I found that there was a significant increase in both accuracy and efficiency in the depth estimates provided by the algorithm.