Automated Registration of Three-Dimensional Knee Implant Models to Fluoroscopic Images using Lipschitzian Optimization

This paper describes an automated method for registering three-dimensional models of metallic knee implants to single-plane radiographic images. We develop a pyramidal approach that identifies the correct pose by matching decreasing dilations of an edge-detected image with the silhouette of an implant model. The location of the similarity function's minimum is found using a novel optimization routine that combines the DIRECT (Dividing Rectangles) algorithm with properties of the Lipschitz constant specific to the registration metric. Depending on the implant type, this technique reliably converges under maximum displacements of approximately 25 to 55 millimeters for translation components and 25 to 55 degrees for Euler angles. The method proves to be robust to noise from bones and soft tissue. After an initial guess for the first image in the sequence, subsequent frames can be automatically registered from the optimum pose in the previous image. Once optimized, the poses from the better-performing femoral implants can be used to create an image mask and slightly increase tibial registration success while maintaining automation.