There is a Quillen equivalence between the model category presenting Lurie's $\infty$-operads (which are inner fibrations $\mathcal{C}\to\mathrm{N}(\mathbf{F})$ satisfying certain conditions) and the model category of dendroidal sets. On the other hand, in his paper on operator categories and topological operads (http://arxiv.org/abs/1302.5756), Barwick proves that there is an equivalence of $\infty$-categories between complete Segal $\Phi$-operads and $\infty$-operads over $\Phi$ for a perfect operator category $\Phi$.

This provides a zig-zag of Quillen equivalences between Barwick's complete Segal $\Phi$-operads and dendroidal sets when $\Phi$ is the perfect operator category $\mathbf{F}$. Is there a direct construction of a Quillen equivalence between these two models (namely, complete Segal operads and dendroidal sets) for $\infty$-operads?