Bayesian analysis of object data using Top Space and Quotient Space models

47 mins 12 secs, 180.61 MB, iPod Video 480x270, 29.97 fps, 44100 Hz, 522.43 kbits/sec

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Description:	Dryden, I Wednesday 15th November 2017 - 09:45 to 10:30


Created:	2017-11-15 16:01
Collection:	Growth form and self-organisation
Publisher:	Isaac Newton Institute
Copyright:	Dryden, I
Language:	eng (English)


Abstract:	The analysis of object data is becoming common, where example objects under study include functions, curves, shapes, images or trees. Although the applications can be very broad, the common ingredient in all the studies is the need to deal with geometrical invariances. For the simple example of landmark shapes, one can specify a model for the landmark co-ordinates (in the Top Space) and then consider the marginal distribution of shape after integrating out the invariance transformations of translation, rotation and scale. An alternative approach is to optimize over translation, rotation and scale, and carry out modelling and analysis in the resulting Quotient Space. We shall discuss several examples, including functional alignment of growth curves via diffeomorphisms, molecule matching, and 3D face regression where translation and rotation are removed. Bayesian inference is developed and the Top space versus Quotient space approaches are compared.

Abstract:

The analysis of object data is becoming common, where example objects under study include functions, curves, shapes, images or trees. Although the applications can be very broad, the common ingredient in all the studies is the need to deal with geometrical invariances. For the simple example of landmark shapes, one can specify a model for the landmark co-ordinates (in the Top Space) and then consider the marginal distribution of shape after integrating out the invariance transformations of translation, rotation and scale. An alternative approach is to optimize over translation, rotation and scale, and carry out modelling and analysis in the resulting Quotient Space. We shall discuss several examples, including functional alignment of growth curves via diffeomorphisms, molecule matching, and 3D face regression where translation and rotation are removed. Bayesian inference is developed and the Top space versus Quotient space approaches are compared.

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