Multiple acoustic source direction-of-arrival (DOA) estimation under reverberant and noisy environments is a fundamental yet challenging task. A promising solution to this challenge lies in the reliable detection of direct-path recordings, which can significantly improve source localization performance in such adverse conditions.In this paper, we introduce an approach based on the Householder transformation of the relative transfer function (RTF) vector. This method enables efficient identification of direct-path components in the time-frequency (TF) domain, while simultaneously providing instantaneous DOA estimates at each TF bin. We also demonstrate that the directional discrimination capability of the Householder transformation is governed by both spatial phase differences and the number of microphones, which highlights the need to consider a specific frequency band for both direct-path identification and source localization. Extensive experiments conducted on both simulated and real-world multi-channel recordings demonstrate the effectiveness of the proposed algorithm.