Related papers: Tooth morphometry using quasi-conformal theory
In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometrics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid…
Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obtain a diffeomorphism between shapes that minimizes angular…
We present results of a long-term team collaboration of mathematicians and biologists. We focus on building a mathematical framework for the shape space constituted by a collection of homologous bones or teeth from many species. The…
This is a commentary on Teichm{\"u}ller's paper Unter-suchungen{\"u}ber konforme und quasikonforme Abbildungen (Inves-tigations on conformal and quasiconformal mappings) published in 1938. The paper contains fundamental results in conformal…
The study of shapes is one of the most fundamental problems in life sciences. Although numerous methods have been developed for the morphometry of planar biological shapes over the past several decades, most of them focus solely on either…
We define a universal Teichm\"uller space for locally quasiconformal mappings whose dilatation grows not faster than a certain rate. Paralleling the classical Teichm\"uller theory, we prove results of existence and uniqueness for extremal…
In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…
We present a new and simple proof of Teichm\"uller-Wittich-Belinskii's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point. Known proofs gave separate estimates for the radial and angular…
In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two…
Surface mapping plays an important role in geometric processing. They induce both area and angular distortions. If the angular distortion is bounded, the mapping is called a {\it quasi-conformal} map. Many surface maps in our physical world…
Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability…
Image landmark detection aims to automatically identify the locations of predefined fiducial points. Despite recent success in this field, higher-ordered structural modeling to capture implicit or explicit relationships among anatomical…
Given a surface of infinite topological type, there are several Teichm\"uller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the…
With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…
Craniofacial profile is one of the anatomical causes of obstructive sleep apnea(OSA). By medical research, cephalometry provides information on patients' skeletal structures and soft tissues. In this work, a novel approach to cephalometric…
The type problem is the problem of deciding, for a simply connected Riemann surface, whether it is conformally equivalent to the complex plane or to the unit dic in the complex plane. We report on Teichm{\"u}ller's results on the type…
In derivational morphology, what mechanisms govern the variation in form-meaning relations between words? The answers to this type of questions are typically based on intuition and on observations drawn from limited data, even when a wide…
One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Raw images are in the form of triangulated surfaces and the first step is to create a standardised…
Temporal imaging of biological epithelial structures yields shape data at discrete time points, leading to a natural question: how can we reconstruct the most likely path of growth patterns consistent with these discrete observations? We…
We present a framework for shape matching in computational anatomy allowing users control of the degree to which the matching is diffeomorphic. This control is given as a function defined over the image and parameterises the template…