Calibration of Endoscope’s Geometry and Photometry

(a) Geometric calibration setup. (b-d) Images of 5 x 4 checker board used for geometric calibration.

(e) Photometric calibration setup. (f-g) Images of Macbeth color chart used for photometric calibration.

ABSTRACT

Camera geometric calibration, as an important step in endoscope related applications, mostly based on Tsai’s model has been addressed in several. However, most of these methods deal with the forward-viewing endoscope except that of Yamaguchi et al. Due to the constraints of the small incision, the range of the movement of such a tool is restricted thus the field of view is very small. In order to view sideways, oblique scope has been designed to have a tilted viewing direction, and a wider viewing field could be reached by rotating the scope cylinder. Yamaguchi et al. first modeled and calibrated the oblique scope. They formulate the rotation parameter of the scope cylinder as other external parameters in Tsai’s camera model. They use two extra transformations to compensate the rotation µ of the lens system and still of the camera head. Their model successfully compensates the rotation effect but requires five additional parameters and the model is complicated. We propose an alternative approach to simplify the calibration. We attach an optical marker to the scope cylinder instead of the camera head, with a newly designed coupler. As a result our camera model is much simpler and we only need to estimate one additional parameter.

Camera photometric calibration, another important process in illumination related applications, is performed to find the relationship between the image irradiance and image intensity for the camera. This relationship is called the camera response function. Traditional photometric calibration recovers only the camera response function by changing the camera’s exposure time. Compared with regular cameras, it is hard to control the exposure time for endoscope, and the light spatial distribution can be anisotropy. Based on our knowledge, no photometric calibration method has been introduced to endoscope, which is however necessary and important for illumination based visualization applications such as shape-from-shading. Therefore we develop a method to calibrate all these unknown parameters simultaneously.

PUBLICATIONS

“A Full Geometric and Photometric Calibration Method for Oblique-viewing Endoscope”

Chenyu Wu, Srinivasa G. Narasimhan, Branislav Jaramaz

To appear in International Journal of Computer Aided Surgery, 2009.

[PDF]

“An easy calibration for oblique-viewing endoscopes”

Chenyu Wu, Branislav Jaramaz

IEEE International Conference on Robotics and Automation (ICRA’08), Pages 1424-1429, 19-23 May 2008, Pasadena, CA

[PDF]

“Endoscope Calibration and Derivation for Shape from Shading”

Chenyu Wu, Srinivasa G. Narasimhan, Branislav Jaramaz

Tech. Report CMU-RI-TR-07, Robotics Institute, Carnegie Mellon University, Dec, 2007

[PDF]

VDIEOS

	Geometric Calibration (WMV)
	Photometric Calibration (WMV)

PICTURES (click on thumbnails to enlarge images)

	Stryker 344-71 arthroscope Vista (70 degree, 4mm): an oblique endoscope consists of a scope cylinder with a lens and point light sources at the tip (the tip has a tilt from the scope cylinder), a camera head that captures video images, and a light source device that supports the illumination. Scope cylinder is connected to the camera head via a coupler. This connection is flexible such that you can rotate either the scope cylinder or the camera head separately, or rotate them together.
	The geometric model of endoscope based on a tracking system. A new coupler is designed to mount an optical marker to the scope cylinder which ensures that the transformation from scope (marker) coordinates O2 to the lens system (camera) coordinates O3 is fixed. World coordinates O1 is defined by the optical tracker. Two optical markers are attached to the coupler and camera head separately in order to compute the rotation angle in between.
	This shows a comparison between Yamaguchi et al.’s system and ours. In Yamaguchi et al.’s system, the camera head is tracked such that the transformation from the marker to the lens system is not fixed but depends on the rotation angle. Let the marker coordinates as a reference, the lens system is rotated around the scope cylinder about the rotation angle, but the image plane (that is in the camera head) remains the same. They use two additional transformations to describe the effect of rotation, so their model becomes complicated. Moreover, they need to calibrate the axis of both the scope cylinder and the lens system by using another optical maker attached to the scope cylinder. Based on our observation, it is possible to simplify the model if we fix the transformation between the marker and the lens system. We design a coupler that enables the mounting of the optical marker onto the scope cylinder. Then we set the marker coordinates as a reference, the lens system is fixed. The rotation only affects the image plane since the camera head is rotated around the cylinder (reference). And the image plane only rotates around the principal point. Since the principal point is an intrinsic parameter, we only need to estimate the rotation angle. As a result, we come up with a very simple model (see details in the text).
	Illustration of the relationship between the rotation angle and two markers’ coordinates. (O1 is attached to the scope cylinder and O2 is attached to the camera head. A indicates the position of O2 when the rotation angle = 0 and B indicates the position of O2 given a rotation angle. Given any point Pr in O2, its trace with the rotation of the camera head is a circle in Marker 1’s coordinates O1. It moves from position P^Ai to P^Bi in Marker 1’s coordinates O1. This circle is also on the plane perpendicular to the axis of scope cylinder. O is the center of the circle.
	Endoscopes used in the experiments. (a) Smith & Nephew video arthroscope – autoclavable SN-OH 272589 (30 degree, 4mm). (b) Stryker 344-71 arthroscope Vista (70 degree, 4mm).
	Images used for geometric calibration (1) and photometric calibration (2-3). Row 2-3 show different light intensities and Column a-c show different albedos on a color-checker.

Last Update: September 2009