Micro tunnel excavation is limited to straight paths due to size constraints that prevent human entry through the jacking pipes. A compact, wide-angle system enables the measurement of enclosed spaces with complex paths. This paper proposes a 3D estimation method using a catadioptric imaging system, which consists of an omnidirectional camera and a single spherical mirror, to capture monocular images without relying on training data. The applicability of our method is demonstrated by measuring the geometry of a pipe designed to imitate a propulsion pipe used in tunnel excavation.