In this paper, we propose two new algorithms for high quality motion estimation in high definition digital videos. Both algorithms are based on the use of random features that guarantee robustness to avoid dropping into a local-minimum. The first algorithm was developed from a simple two stage approach where a random stage is complemented by a greedy stage in a very simple fashion. The second algorithm is based on a more refined class of algorithms called Memetic Network Algorithms where each instance of the search may exchange information with its neighbour instances according to some rules that control the information flow. The proposed algorithms were implemented and tested exclusively with high definition sequences against well known fast algorithms like Diamond Search and Three Step Search. The results show that our algorithms can outperform other algorithms in quality yielding an increment in complexity that may be amortized if resources for a parallel execution are available. Additionally, we provide further evidence that fast algorithms do not perform well in high definition.