Related papers: Two-chart Beltrami Optimization for Distortion-Con…
We address the problem of registering two surfaces, of which a natural bijection between them does not exist. More precisely, only a partial subset of the source surface is assumed to be in correspondence with a subset of the target…
In shape analysis, finding an optimal 1-1 correspondence between surfaces within a large class of admissible bijective mappings is of great importance. Such process is called surface registration. The difficulty lies in the fact that the…
In medical imaging, surface registration is extensively used for performing systematic comparisons between anatomical structures, with a prime example being the highly convoluted brain cortical surfaces. To obtain a meaningful registration,…
Registration, which aims to find an optimal one-to-one correspondence between different data, is an important problem in various fields. This problem is especially challenging when large deformations occur. In this paper, we present a novel…
Cortical surface registration is a fundamental tool for neuroimaging analysis that has been shown to improve the alignment of functional regions relative to volumetric approaches. Classically, image registration is performed by optimizing a…
Free-boundary diffeomorphism optimization, an important and widely occurring task in geometric modeling, computer graphics, and biological imaging, requires simultaneously determining a planar target domain and a locally bijective map with…
This paper presents a method to compute the {\it quasi-conformal parameterization} (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain $S$ onto a punctured disk $D_S$…
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…
This paper presents a novel shape prior segmentation method guided by the Harmonic Beltrami Signature (HBS). The HBS is a shape representation fully capturing 2D simply connected shapes, exhibiting resilience against perturbations and…
3D face registration is an important process in which a 3D face model is aligned and mapped to a template face. However, the task of 3D face registration becomes particularly challenging when dealing with partial face data, where only…
Over the past several decades, geometric mapping methods have been extensively developed and utilized for many practical problems in science and engineering. To assess the quality of geometric mappings, one common consideration is their…
Non-rigid cortical registration is an important and challenging task due to the geometric complexity of the human cortex and the high degree of inter-subject variability. A conventional solution is to use a spherical representation of…
Constrained Spherical Deconvolution (CSD) is widely used to estimate the white matter fiber orientation distribution (FOD) from diffusion MRI data. Its angular resolution depends on the maximum spherical harmonic order ($l_{max}$): low…
Many imaging problems can be formulated as mapping problems. A general mapping problem aims to obtain an optimal mapping that minimizes an energy functional subject to the given constraints. Existing methods to solve the mapping problems…
Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to…
Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is…
Deformable registration of magnetic resonance images between patients with brain tumors and healthy subjects has been an important tool to specify tumor geometry through location alignment and facilitate pathological analysis. Since tumor…
Diffeomorphic registration using optimal control on the diffeomorphism group and on shape spaces has become widely used since the development of the Large Deformation Diffeomorphic Metric Mapping (LDDMM) algorithm. More recently, a series…
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…
Cortical surface reconstruction (CSR) from MRI is key to investigating brain structure and function. While recent deep learning approaches have significantly improved the speed of CSR, a substantial amount of runtime is still needed to map…