- Series
- Job Candidate Talk
- Time
- Thursday, January 23, 2020 - 3:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Nina Miolane – Stanford University – nmiolane@stanford.edu – https://www.ninamiolane.com/
- Organizer
- Yao Yao
The advances in bioimaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, statistical analyses in biomedical research are poised to incorporate more shape data. This leads to the question: how do we define quantitative descriptions of shape variability from images?
Mathematically, landmarks’ shapes, curve shapes, or surface shapes can be seen as the remainder after we have filtered out the corresponding object’s position and orientation. As such, shape data belong to quotient spaces, which are non-Euclidean spaces.
In this talk, I introduce “Geometric statistics”, a statistical theory for data belonging to non-Euclidean spaces. In the context of shape data analysis, I use geometric statistics to prove mathematically and experimentally that the “template shape estimation” algorithm, used for more than 15 years in biomedical imaging and signal processing, has an asymptotic bias. As an alternative, I present variational autoencoders (VAEs) and discuss the accuracy-speed trade-off of these procedures. I show how to use VAEs to estimate biomolecular shapes from cryo-electron microscopy (cryo-EM) images. This study opens the door to unsupervised fast (cryo-EM) biological shape estimation and analysis.