The Shape Collapse Problem in Image Registration

This paper investigates the shape collapse problem in nonrigid image registration. The shape collapse problem is the situation when an appendage of a deforming object does not overlap with the target shape and collapses to a set of zero measure during the registration process. The dual problem occurs when a new appendage grows out of the object to match the target shape. In both cases, the estimated correspondence between the source and target objects is often undesirable. The shape collapse problem is caused by deforming the moving image in the gradient direction of the similarity cost and affects both small and large deformation registration algorithms. Minimizing a registration cost function by following the similarity-cost gradient drives the registration to a local energy minimum and does not permit an increase in energy to ultimately reach a lower energy state. Furthermore, once an object collapses locally, it has zero measure under the similarity cost in this region and is permanently stuck in a local minimum. This paper presents a criterion for detecting image regions that will collapse if the similarity cost gradient direction is followed during optimization. This criterion is based on the skeletal points of the moving image in the symmetric difference of the original two binary images. Experimental results are presented that demonstrate that the shape collapse problem can be detected before registration.