Model-based positional estimation method

Abstract

A model-based method is described which defines a rigid transformation between two co-ordinate systems that reduces the accuracy requirements on the quality of the data-set (including, but not restricted to, the error in the acquisition process, and the number and spread of the points) measured in one of the two co-ordinate systems by identifying a set of remote correspondences that are used to bind the convergence process. The method can be used in minimal-access orthopaedic surgery to improve the accuracy of limb registration. Specific instances include femoral registration, by estimating the functional centre of the hip joint in both co-ordinate systems to be co-registered, and tibial registration, using the ankle centre as a distant set of paired correspondences. Accuracy can be measured in a variety of ways, including, but not restricted to, evaluating the mis-alignment between the two co-registered objects.

1 .- 13 . (canceled) 
   
   
       14 . A method of registering a measurement co-ordinate system to a model co-ordinate system, comprising:
 (a) measuring in the measurement co-ordinate system the location of a plurality of points within a local region, each said point having a corresponding model point location within the model co-ordinate system; and   (b) fitting the measured points to the corresponding model points subject to the constraint of one or more correspondences between the measurement and model co-ordinate systems at a location remote from the local region.   
   
   
       15 . A method as claimed in  claim 14  in which the fitting comprises minimizing an error measure between the measured points and the model points. 
   
   
       16 . A method as claimed in  claim 14  in which the correspondence comprises a common remote point in the measurement and model co-ordinate systems. 
   
   
       17 . A method as claimed in  claim 16  in which the fitting is carried out leaving a distance between the local region and the remote point as a free variable. 
   
   
       18 . A method as claimed in  claim 16  in which the correspondence comprises an axis which is constrained to extend from the local region to the common remote point. 
   
   
       19 . A method as claimed in  claim 18  in which the axis extends from a centroid of the measured points to the said common remote point. 
   
   
       20 . A method as claimed in  claim 18  in which the fitting is carried out leaving an angle of rotation of the measured points about the axis as a free variable. 
   
   
       21 . A method as claimed in  claim 18  in which the fitting is carried out leaving a rotation angle of the axis about the remote point as a free variable. 
   
   
       22 . A method as claimed in  claim 14  in which the model points are points on a model bone, and in which the measured points are points on a physical bone. 
   
   
       23 . A method as claimed in  claim 22  in which the correspondence comprises a common remote point in the measurement and model co-ordinate systems, and in which the remote point is the center of a joint of the bone. 
   
   
       24 . A method as claimed in  claim 23  in which the joint center is measured in the measurement co-ordinate system by moving the bone about the joint. 
   
   
       25 . A method as claimed in  claim 22  in which the correspondence comprises an axis which is constrained to extend from the local region to the common remote point and in which the said axis is an axis of a joint of the bone. 
   
   
       26 . A method as claimed in  claim 22  in which the bone is a femur, tibia, humerus, radius or ulna.