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With the evolution of electronic devices, such as 3D cameras, addressing the challenges of text localization in 3D video (e.g., for indexing) is increasingly drawing the attention of the multimedia and video processing community. Existing methods focus on 2D video and their performance in the presence of the challenges in 3D video, such as shadow areas associated with text and irregularly sized and shaped text, degrades. This paper proposes the first approach that successfully addresses the challenges of 3D video in addition to those of 2D. It employs a number of innovations, among which, the first is the Generalized Gradient Vector Flow (GGVF) for dominant points detection. The second is the Wavefront concept for text candidate point detection from those dominant points. In addition, an Adaptive B-Spline Polygon Curve Network (ABS-Net) is proposed for accurate text localization in 3D videos by constructing tight fitting bounding polygons using text candidate points. Extensive experiments on custom (3D video) and standard datasets (2D video and scene text) show that the proposed method is practical and useful, and overall outperforms existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]