On Modelling and Understanding Image Manifolds

Crynodeb

Images of objects (e.g. a rotating teapot, views from a camera mounted on a robot, an actor illuminated from different positions on a hemisphere, etc.) which vary between them by some controlled parameter tend not to be randomly located in the space of all possible w×h pixel images. Instead, with each pixel comprising of c colour components, each image forms one w×h×c dimensional position vector, in a space commonly referred to as image space. Instead of these images being randomly located, small changes in the sampling parameters normally produce neighbouring images in image space. This in turn can form structures, such as curves, surfaces, or more generally manifolds in image space. These are not novel, and commonly referred to as image manifolds in the literature. To date studies of image manifolds have been limited in both scope and application. This work presents an investigation of some of the features of 28 specific collections of images from a diverse range of sources, which potentially form image manifolds. We investigate several properties of these image manifolds — their general shape, and curvature. Image manifolds are well known not to be simple linear structures, instead, as we see in our study they are highly complex shapes. The main contribution of this work however, is a study of two novel approaches to numerical modelling of these image manifolds. Given the highly curved nature of image manifolds, which our investigation into the specific datasets confirmed, our approach is based upon extended versions of two techniques (NURBS and PDE Surfaces) typically used in the field of computer graphics to model curves and surfaces in 3-D space. Our approach is to construct exact geometric models, in image space, of the underlying image manifolds. The number of sample images required to adequately represent the appearance of an object or environment is a complex function of the subject itself. We show that it is possible to produce acceptable (depending on the application, which we discuss briefly), compact representations of objects and environments using our models. Furthermore we show that an awareness of simple geometric properties can improve the construction of such models, by focusing on improving the model in higher curved areas

Dyddiad Dyfarnu	26 Maw 2010
Iaith wreiddiol	Saesneg
Sefydliad Dyfarnu	Prifysgol Aberystwyth
Goruchwyliwr	Fred Labrosse (Goruchwylydd) & Mark Neal (Goruchwylydd)