Digital volume correlation (DVC) is a computational tool used to measure a 3D displacement field between a pair of 3D images (from, for example, magnetic resonance imaging (MRI), computed tomography (CT), ultrasound, etc.). Studies in biomechanics have used DVC to quantify deformations in cells, tissues and organs, for the purpose of examining deformation and failure mechanisms, movement, and adaptation. The growing popularity of DVC has created increased demand for DVC algorithms that are computationally efficient, verified and validated. The goals of this project were to improve the efficiency of an existing DVC algorithm and to present a set of methods for robust verification and validation.
This dissertation first introduces DVC through a series of 1D examples that illustrates the use of optimization to find the displacement field that produces the best match between the pair of images. Different methods of regularization are explored. The concept of downsampling of the images is introduced as a way to promote faster convergence and a better image match.
In preparation for the move to 3D, the second part of the dissertation covers key concepts in 3D image acquisition and data preparation for the specific case of μCT imaging of human vertebrae. This section allows the reader to appreciate the use of DVC to enable study of failure mechanisms in the spine.
The third section addresses the DVC method for 3D images. A custom process is introduced that uses rigid registration of the images to obtain an initial guess for the displacement field. The effect of the quality of the initial guess is then explored using test displacement fields.
In the final section, new methods of verification and validation of DVC are presented. An “image-warping” code is presented that interpolates a given displacement field to every voxel of an image, producing a synthetic image. This code is used to warp one image of a pair that was analyzed by DVC, and the mismatch between the synthetic image and the second image of the pair is used to verify the success of the minimization. The image-warping code is also used to create synthetic images from artificial, “test” displacement fields of increasing complexity and realism as a tool for validating the accuracy of the DVC algorithm. Finally, an L-curve method is applied in order to fine tune selection of the regularization parameter.
Though the improvements to DVC presented here were developed for the study of failure mechanisms of the spine, there is opportunity for broader application. The 1D examples can be mimicked to understand the foundations and limitations of similar DVC algorithms. Downsampling can also help these alternative algorithms to increase computational efficiency and improve image matching. Furthermore, the verification and validation methods presented here model an approach that others could use as they seek to improve their own algorithms.
|18 January 2021
|Morgan, Elise F.
|Attribution-NoDerivatives 4.0 International, http://creativecommons.org/licenses/by-nd/4.0/
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