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Augmented Statistical Shape Modeling for Orthopedic Surgery and Rehabilitation
Published in de Azevedo-Marques Paulo Mazzoncini, Mencattini Arianna, Salmeri Marcello, Rangayyan Rangaraj M., Medical Image Analysis and Informatics: Computer-Aided Diagnosis and Therapy, 2018
Bhushan Borotikar, Tinashe Mutsvangwa, Valérie Burdin, Enjie Ghorbel, Mathieu Lempereur, Sylvain Brochard, Eric Stindel, Christian Roux
In the previous version of IMCP by [36], the objects to be registered did not have size differences, since it was developed for intra-object registration. In the current SSM development pipeline, there was a big variation on the sizes of different scapulae and humeri. To remove the effect of size in the registration, the centroid size of each object was used to scale each object to unit size. Centroid size is the square root of the sum of squared distances of a set of landmarks, in this case vertices, from their centroid. Centroid size is used in geometric morphometrics because it is approximately uncorrelated with every shape variable, when landmarks are distributed around mean positions by independent noise of the same small variance at every vertex and in every direction. This ties in well with the concept of statistical shape analysis, where shape is the geometric information that is left after removing the effects of size, position and orientation. The Procrustes processes to follow remove the other effects of position and orientation/pose. The dataset is also initialized by aligning all instances using their main axes of inertia, as described earlier.
Two-Dimensional Measurements (Part 1)
Published in F. Brent Neal, John C. Russ, Measuring Shape, 2017
The most commonly used method for statistical shape analysis is generalized Procrustes analysis (GPA). For a series of points with coordinates (xi, yi), or in three dimensions (xi, yi, zi), translational variations are removed from the object by finding the mean values: x¯=∑xiny¯=∑yin
Foot shape analysis of professional American Football players
Published in Footwear Science, 2020
Statistical shape analysis is a technique to identify shape attributes that best represent a larger number of data sets based on a dimensionality reduction analysis, such as principal component analysis (PCA). PCA returns principal components (PCs), which indicate a new basis to best represent complex data, and their variances, which can be interpreted as the measure of the importance of each principal component. The PCs are ranked in descending order according to their variances, therefore, for example, the first PC is the most important basis (i.e. it describes the most shape variability).