A nonparametric approach to 3D shape analysis from digital camera images – II

ABSTRACT

With the wide availability of digital cameras and high quality smart phone cameras the world is awash in digital images. These cameras are most often uncalibrated meaning that one does not have knowledge of the internal camera parameters, such as focal length and optical center, nor information about the external camera parameters which describe the location of the camera relative to the imaged scene. In the absence of additional information about the scene one cannot parse out many common types of geometric information. For instance, one cannot calculate distances between points or angles between lines. One can, however, determine the lesser known projective shape of a scene. Projective shape data do not lie in Euclidean space ${\mathbb{R}}^p$. This presents special challenges since the overwhelming majority of statistical methods are for data in ${\mathbb{R}}^p$. Furthermore, we consider 3D projective shapes of contours extracted from digital camera images which lie in an infinite-dimensional projective shape space and as such presents an especially novel environment for doing statistics. We develop a novel nonparametric hypothesis testing method for the mean change from matched sample contours. Our methodology is applied to the two-sample problem for 3D projective shapes of contours extracted from digital camera images.

KEYWORDS:

• Extrinsic means
• infinite-dimensional data
• neighborhood hypothesis test
• nonparametric bootstrap

Acknowledgements

The authors are grateful to the associate editor and the referees, who helped us improve the quality of the manuscript. In particular, at their suggestion, as future research, one may consider images of leaves from a different tree species, and develop a two-sample test for comparing their contours, by using a related methodology for two-sample test for mean 3D projective shapes of contours.

Disclosure statement

No potential conflict of interest was reported by the authors.