Mahalanobis Distance Based Iterative Closest Point | Mads Fogtmann Hansen, Morten Rufus Blas, Rasmus Larsen
| | Abstract | An important prior task in statistical shape modeling and in feature extraction from shapes is finding the best rigid transformations which register the shapes to each other, and establishing point correspondence between the shapes. Establishing point correspondence from e.g. biological shapes is often a manual and tedious task, which requires expert knowledge.
A common automatic approach is the iterative closest point (ICP) algorithm which iterates between the steps: (i) match target points to reference points using minimum distance at the current transformation (ii) update pose parameters by minimizing the sum of squared distances between the matches. Unfortunately, ICP with the Euclidian distance metric (ICP-E) will often produce suboptimal results as it is unable to handle unequal uncertainty among points.
This paper proposes an extension to standard ICP which uses the Mahalanobis distance (ICP-M) to align a set of shapes. Thus, assigning an anisotropic independent Gaussian noise to each point class.
Initially, the covariance matrices are set to the identity matrix, and all shapes re aligned to a randomly selected shape (equivalent to ICP-E). From this point he algorithm iterates between the steps: (a) obtain mean shape and new stimates of the covariance matrices from the aligned shapes, (b) align shapes to the mean shape. The superiority of ICP-M compared with ICP-E in recovering the underlying correspondences is demonstrated. | | Type | Conference paper [With referee] | | Conference | Spie - Medical Imaging | | Year | 2007 Month February | | BibTeX data | [bibtex] | | IMM Group(s) | Image Analysis & Computer Graphics |
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