Shape analysis via inconsistent surface registration
This work addresses shape analysis for anatomical surfaces, offering a novel method to overcome limitations in traditional and advanced mapping techniques, though it is domain-specific and incremental in its approach.
The paper tackles the problem of shape analysis for anatomical surfaces by developing a framework that uses inconsistent surface registration to automatically detect relevant parts and find optimal landmark-matching alignments without assuming global correspondence, resulting in effective shape classification demonstrated on Platyrrhine molars.
In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometrics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid surface mapping methods rely on a strong assumption of the global consistency of two surfaces. From a practical point of view, given two anatomical surfaces with prominent feature landmarks, it is more desirable to have a method that automatically detects the most relevant parts of the two surfaces and finds the optimal landmark-matching alignment between those parts, without assuming any global 1-1 correspondence between the two surfaces. Our method is capable of solving this problem using inconsistent surface registration based on quasi-conformal theory. It further enables us to quantify the dissimilarity of two shapes using quasi-conformal distortion and differences in mean and Gaussian curvatures, thereby providing a natural way for shape classification. Experiments on Platyrrhine molars demonstrate the effectiveness of our method and shed light on the interplay between function and shape in nature.