Construction of Neuroanatomical Shape Complex Atlas from 3D Brain MRI

Abstract. This paper proposes a novel technique for constructing a neuroanatomical shape complex atlas using an information geometry framework. A shape complex is a collection of shapes in a local neighborhood. We represent the boundary of the entire shape complex using the zero level set of a distance function S(x). The spatial relations between the different anatomical structures constituting the shape complex are captured via the distance transform. We then leverage the well known relationship between the stationary state wave function ψ(x) of the Schr¨odinger equation − 2 2 ψ + ψ = 0 and the eikonal equation S = 1 satisfied by any distance function S(x). This leads to a one-to-one map between ψ(x) and S(x) and allows for recovery of S(x) from ψ(x) through an explicit mathematical relationship. Since the wave function can be regarded as a square-root density function, we are able to exploit this connection and convert shape complex distance transforms into probability densi...

• Type: Journal
• Year: 2010
• Where: MICCAI
• Authors: Ting Chen, Anand Rangarajan, Stephan J. Eisenschenk, Baba C. Vemuri
• Keywords: Atlas, Medical Imaging, MICCAI 2010, Shape Complex, Square-root Density Functions