The theoretical development and numerical implementation of image registration methods for high resolution images. These problems involve modeling pixel motion, least-squares finite element solutions to optical flow formulations, iterative solutions to large scale linear systems, large scale nonlinear optimization, and parallel computing.
The goal of this research is to accurately and efficiently register 4D computed tomography lung images. In order to do so, three issues must be taken into account. First, lungs are compressible. Second, 4D CT images are noisey. Finally, 4D CT images are very large.
The image shown below (reference image) has been warped by a known displacement field (also shown below) according to the mass conservation law. The result is a second target image (not shown). The goal is to recover the pixel displacement field by performing image registration on the reference and target image.
2% random noise was added to the reference and target images, then three different registration methods were applied.
The standard (Horn and Schunck) optical flow solution is incorrect because it is based on a constant pixel intensity assumption. Put another way, the optical flow method assumes the material in the image is incompressible. The compressible optical flow solution is based on the conservation of mass assumption but fails due to the image noise. Finally, our Combined Compressible Local-Global optical flow method, which is based on the conservation of mass and is also robust to noise, recovers the correct answer.
The goal is to register images where the pixel displacements are large. This is a known problem for registration methods that require accurate finite difference approximations to image derivatives, such as Horn and Schunck optical flow.
The square in the two images above has moved a significant distance. Below are the results produced by registering the images with Horn and Schunck optical flow (left) and our Large Displacement Optical Flow (right) approach.
The Horn and Schunck optical flow result is inaccurate due to poor finite difference approximations to image derivatives brought on by large pixel displacements. Our Large Displacement Optical Flow approach, though still dependant on finite differences, creates synthetic image data in order to capture the large pixel displacements with pleasing results.
