Robust non-rigid surface matching and its application to scoliosis modelling

Research Doctorate - Doctor of Philosophy (PhD)With the advancement of digital photogrammetry techniques, development of digital surface topographies becomes easier and straightforward, leading to more desirable applications in the medical field. The potential application of digital photogrammetry to the medical field is expected to be able to manipulate and analyse the surface data, which in many cases requires comparisons with previously derived data for the purpose of identifying surface change. A potential application in the medical field may result from the extensive use of surface topographies of back shapes to monitor scoliosis. A new spatial data manipulation tool in the form of a non-rigid surface matching algorithm with new parameters has been investigated, aimed at replacing the classical least squares 3D surface matching approach which allows positional fit rather than shape fit. A computer program has been written to implement the matching algorithm. So far, the analysis of shape change to identify scoliotic progress has not been satisfactorily solved. As a contribution to this task, the capacity of the non-rigid matching algorithm to find the match and simultaneously model the scoliotic deformities has been assessed. A complete complete review of the advantages and disadvantages of the classical surface matching algorithm has been analysed and presented in this work. Current constraints faced in the scoliosis modelling and monitoring has been discussed as the preparation for designing the new matching algorithm. The main conclusion of this review is that the surface matching is a feasible tool for solving the modelling and monitoring constraints faced by the researchers. Various surface matching algorithms with different objective functions and transformation procedure have been investigated. This investigation serves the purpose to determine the optimal transformation objective function and transformation procedure that is best to be implemented in the proposed non-rigid surface matching algorithm. Four different surface matching algorithms based on a rigid transformation, involving six unknown parameters have been developed and compared. These four algorithms are Modified Iterative Closest Point (MICP), Least Z Difference (LZD), Combined ICP-LZD, and Least Normal Distance Difference (LNDD). LNDD was chosen as the required transformation objective function and transformation procedure due to its simplicity, efficiency and the accuracy of the resulting calculation. This selection is supported by the studies carried out by Schenk (2000) where the outcome is matched with the result reported here. The scoliosis data sets are automatically matched by a least squares non-rigid matching algorithm involving nine unknown parameters with three scales and six shears. The effectiveness of this algorithm comes from its ability to match the deformed surface to the un-deformed surface and detect the deformation magnitude. This non-rigid matching algorithm has been trialled using models with predictable topographic deformation. There is evidence that surface deformities can be modelled. In addition, to demonstrate the capability of this new non-rigid matching algorithm in scoliosis modelling, the author has performed experimental comparison with classical rigid matching algorithm using four different scoliosis data sets. The non-rigid matching algorithm returned r.m.s. values which were improved by about 10% for all data. Analysis indicates that this new non-rigid matching algorithm has proven to be a very successful tool and is an improvement on the classical approach. The new parameters are able to model and delineate the possible shape changes caused by scoliosis. Scaling factor can be interpreted as the dilation caused by natural growth (seen noise) in all three direction, while shearing parameters can be used to depict the deformation caused by scoliosis. The results show that this new non-rigid algorithm not only assures the best positional fit but also the best shape fit. This research is among the first using non-rigid transformation for surface matching without control points. Finally, the matching accuracy and robustness is improved by integrating Least Trimmed Squares (LTS) into the non-rigid matching algorithm. This robust algorithm is called Trimmed Least Normal Distance Difference (TrLNDD). The TrLNDD is able to detect local deformation covering up to 50% of the surfaces being matched, the highest value reported in the literature. Improvement of about 79% of r.m.s. value can be detected indicating LTS estimator is highly desirable to be integrated into existing matching algorithm in detecting the surface deformation. True scoliotic change can be revealed by eliminating the unseen noise (outliers) by using the TrLNDD algorithm