Principles of multivariate analysis: a user's perspective
Principles of multivariate analysis: a user's perspective
Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image analysis for the biological sciences
Image analysis for the biological sciences
Set-Valued Means of Random Particles
Journal of Mathematical Imaging and Vision
Automatic Interpretation and Coding of Face Images Using Flexible Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Averaging of Random Sets Based on Their Distance Functions
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Morphological Exploration of Shape Spaces
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Functional data analysis in shape analysis
Computational Statistics & Data Analysis
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Particles are random sets whose position and orientation areirrelevant. They are traditionally handled by calculating summariesof shape, such as compactness and elongation, or by defininglandmarks, whose positions are then subject to statistical analysis. Itwould be advantageous in many applications if shape variabilitycould be addressed without the need for landmarks. This paperproposes a way to do this. The first step is to definesimilarity/distance between shapes. This is done in terms of the areaof non-overlap between them, when they have been brought into theclosest possible alignment. The resulting distance matrix can thenbe treated by the methods of principal coordinate analysis. It isshown that this is equivalent to principal component analysis on thebinary sets in R^2 defined as the regions within the shapeoutlines. The method is illustrated by application to a set of carrotoutlines.