Technical Report: Endoscope Calibration and Derivation for Shape from Shading

(a) (b) (c) (d) (e) (f) (g) (h) Figure 1. Endoscope calibration setup: (a) geometric calibration (b-d) images of 5 × 4 checker board used for geometric calibration. (e) photometric calibration. (f-g) images of Macbeth color chart used for photometric calibration. The orthopedic endoscope has a single camera and one or more point light sources equipped at the tip of the scope. For this work, we use Stryker 344-71 arthroscope Vista (70 degree, 4mm), an oblique endoscope with two point light sources. The device is showed in Fig. 2. Unlike regular cameras with forward viewing, most current endoscopes are designed for oblique viewing with a tilt from the scope axis at the tip. The viewing direction can be changed by simply rotating the scope cylinder without having to move it. To increase flexibility of imaging in terms of focus and resolution, the lens system (in the cylinder) and the CCD plane (in the camera head) can be rotated with respect to one another (see Fig. 2 (b), 3 and 4 (a-b)). While they are desirable, these properties make the geometric calibration harder than in regular cameras. Yamaguchi et al. [4] calibrate an oblique scope using Tsai's model [3, 5], by attaching an optical marker to the camera head. However, since there can be a rotation between the head and the cylinder, their model is a complicated function of the rotation angle. Instead, we attach the marker on the scope cylinder and calibration turns out to be very simple. Still as an extension of Tsai's model, the geometric model illustrated in Fig. 3 can be written as: λp i = A · c T s · m T w · P w p i = R(θ) · (p i − cc) + cc (1)