Bronchoscopy is a major step in lung cancer staging. To perform bronchoscopy, the physician uses a procedure plan, derived from a patient's 3D computed-tomography (CT) chest scan, to navigate the bronchoscope through the lung airways. Unfortunately, physicians vary greatly in their ability to perform bronchoscopy. As a result, image-guided bronchoscopy systems, drawing upon the concept of CT-based virtual bronchoscopy (VB), have been proposed. These systems attempt to register the bronchoscope's live position within the chest to a CT-based virtual chest space. Recent methods, which register the bronchoscopic video to CT-based endoluminal airway renderings, show promise but do not enable continuous real-time guidance. We present a CT-video registration method inspired by computer-vision innovations in the fields of image alignment and image-based rendering. In particular, motivated by the Lucas-Kanade algorithm, we propose an inverse-compositional framework built around a gradient-based optimization procedure. We next propose an implementation of the framework suitable for image-guided bronchoscopy. Laboratory tests, involving both single frames and continuous video sequences, demonstrate the robustness and accuracy of the method. Benchmark timing tests indicate that the method can run continuously at 300 frames/s, well beyond the real-time bronchoscopic video rate of 30 frames/s. This compares extremely favorably to the ≥ 1 s/frame speeds of other methods and indicates the method's potential for real-time continuous registration. A human phantom study confirms the method's efficacy for real-time guidance in a controlled setting, and, hence, points the way toward the first interactive CT-video registration approach for image-guided bronchoscopy. Along this line, we demonstrate the method's efficacy in a complete guidance system by presenting a clinical study involving lung cancer patients.