For decades, fuzzy spatial relations have demonstrated their utility and effectiveness for visual reasoning, including semantic annotation and object recognition. However, a major issue is that they often involve fuzzy morphological operators 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 acceptable 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 and the Parallel Reverse (PR) algorithms. Reverse is an exact and efficient algorithm for the fuzzy dilation operator and PR combines the Reverse algorithm exactness with efficient usage of modern-processor multiple cores using OpenMP. Using SIMD extensions to enhance Parallel Reverse, 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 highlight the contribution of the SIMD instructions, an extensive benchmark was carried out on two datasets of natural and artificial images.