For decades, fuzzy spatial relations have demonstrated their utility and effectiveness for visual reasoning, including se- mantic annotation and object recognition. However, a major issue is that they often involve fuzzy morphological opera- tors that are compute-intensive leading to long latency in the relation evaluation. As a result, approximate methods have been proposed to compute some relations in an accept- able time, but they are not as generic as the fuzzy dilation or do not make the most of modern computing architectures. In this paper, we introduce the Reverse algorithm, an exact and efficient algorithm for the fuzzy dilation operator, and Parallel Reverse (PR), which combines the Reverse algorithm exactness with efficient usage of modern processors multiple cores and vectorization using OpenMP and SIMD extensions. Based on these modern processors features, PR128 (AVX), PR256 (AVX2), and PR512 (AVX512) are faster than the state- of-the-art approximate methods while remaining generic and exact. To demonstrate the performance of PR and high- light the contribution of the SIMD instructions, an extensive benchmark was carried out on two datasets of natural and artificial images.