MATLAB based Image PreProcessing and Digital Image Correlation of Objects in Liquid

The venerable digital image correlation (DIC) technique relies on a series of digital images to obtain the incremental displacement and strain field on the surface of a specimen. In a standard DIC procedure, the image recording system and the object are kept in the same medium i.e. images are taken while the object is deforming in air. There is a growing need, however, to extend the use of DIC for objects undergoing deformation while being completely submerged under a homogenous solution. In soft-tissue engineering, for instance, tests are required to be carried out inside an organ culture system or in a fluid nutrient medium that mimics the native physiologic environment of a tissue. Regardless of the type of image recording system, such as waterproof camera, there is always image distortion caused by refraction. This refraction induced image distortion is nonlinear and non-uniform and that current camera calibration algorithms used in DIC systems don't have the capability to correct the refraction-induced image distortion and would give a highly erroneous result. This paper presents a Matlab based approach that uses the localized direct linear transformation technique to restore the refracted image. Once an image is restored it can be passed onto a DIC algorithm to obtain the desired kinematic variables following the usual correlation technique. Keyword: Affine transformation, calibration-reconstruction, image distortion Introduction Measuring the deformation field of a liquid submerged body using digital image correlation (DIC), poses several unique obstacles to the investigator: these include the difficulty associated with placing the calibration grid in the liquids, insufficient illumination due to suspended particles, and image distortion by refraction. In standard DIC a rectangular calibration grid of known dimensions is positioned near the object to be deformed and a series of perspective images are acquired while changing the orientation of the grid. The system is then required to extract control points from the grid and match with known grid dimensions. Calibration in the context of three-dimensional stereovision is the process of determining the internal camera geometric and optical characteristics and/or the 3-D position and orientation of the camera frame relative to a certain world coordinate system [6]. A camera is considered calibrated if the principal distance, principal point offset and lens distortion parameters are known. The accuracy of the DIC system strongly depends on the accuracy of the camera calibration. Calibration of a DIC system while the calibration grid is submerged in a liquid is not always easy and attractive for several reasons: (a) the dispersion of light in liquid makes extraction of control points very difficult (b) in cloudy liquids, such as a soft tissue nutrient bath, the calibration algorithm will Proceedings of the SEM Annual Conference June 1-4, 2009 Albuquerque New Mexico USA ©2009 Society for Experimental Mechanics Inc. not be able to accurately reproduce camera parameters due to lack of image clarity (c) often it is not desirable to immerse a calibration grid inside fluid filled container due to test related restrictions such as the case of a sterile and sealed organ bath (d) finally there is always image distortion due to refraction of light. These drawbacks often limit the use of this novel technique in many areas of experimental mechanics particularly soft tissue engineering. Current commercially available DIC systems are primarily designed for use in applications where the deformation is measured in air and as such there is no clear provisions that extend the use of DIC to submerged bodies. In a typical lab setting it is possible, however, to mitigate some of the above problems by manipulating experimental conditions and using image processing software to obtain an accurate deformation measurement of a submerged body. The method presented in this paper makes full use of MATLAB's image processing tool box and Vic-3D correlation algorithm to obtain a whole-filed deformation measurement on a submerged specimen. Refraction-Induced Image Distortion One of the most serious obstacles to accurately quantify the deformation of a submerged body using DIC is image distortion caused by refraction. Refraction occurs at the liquid-air interface owing to density differences. Camera calibration and reconstruction algorithms used in standard DIC technique are based on affine transformation. Affine transformation is a linear conformal mapping where a uniform translation, rotation, scaling, and shearing is applied to every point on the image. A single closed form mathematical expression is applied to an entire image to calculate intrinsic calibration parameters. Image distortion induced by light refraction, however, are nonlinear and nonuniform and cannot be accurately corrected by a single expression. The collinearity condition does not hold in liquid, because of the refraction-induced image distortion. The later depends on the degree of refraction and this inturn depends on the density of the medium involved and the angle of incident ray. For a homogenous optically isotropic material, Snell's law provides [1]: