This paper introduces a fast Central Processing Unit (CPU) implementation of geodesic morphological operations using stream processing. In contrast to the current state-of-the-art, that focuses on achieving insensitivity to the filter sizes with efficient data structures, the proposed approach achieves efficient computation of long chains of elementary $3 \times 3$ filters using multicore and Single Instruction Multiple Data (SIMD) processing. In comparison to the related methods, up to $100$ times faster computation of common geodesic operators is achieved in this way, allowing for real-time processing (with over $30$ FPS) of up to $1500$ filters long chains, applied on $1024\times 1024$ images. In addition, the proposed approach outperformed GPGPU, and proved to be more efficient than the comparable streaming method for the computation of morphological erosions and dilations with window sizes up to $183\times 183$ in the case of using char and $27\times27$ when using double data types.