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Recently, Greg\'orio and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of…
Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
We present a method for nonrigid registration of 2-D geometric shapes. Our contribution is twofold. First, we extend the classic chamfer-matching energy to a variational functional. Secondly, we introduce a meshless deformation model that…
We propose several cost functions for registration of shapes encoded with Euclidean and/or non-Euclidean information (unit vectors). Our framework is assessed for estimation of both rigid and non-rigid transformations between the target and…
We present an implementation of a new approach to diffeomorphic non-rigid registration of medical images. The method is based on optical flow and warps images via gradient flow with the standard $L^2$ inner product. To compute the…
We present an unsupervised data-driven approach for non-rigid shape matching. Shape matching identifies correspondences between two shapes and is a fundamental step in many computer vision and graphics applications. Our approach is designed…
Image registration is the basis for many applications in the fields of medical image computing and computer assisted interventions. One example is the registration of 2D X-ray images with preoperative three-dimensional computed tomography…
In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space…
Registration is a fundamental task in medical image analysis which can be applied to several tasks including image segmentation, intra-operative tracking, multi-modal image alignment, and motion analysis. Popular registration tools such as…
Registering an object shape to a sequence of point clouds undergoing non-rigid deformation is a long-standing challenge. The key difficulties stem from two factors: (i) the presence of local minima due to the non-convexity of registration…
Establishing voxelwise semantic correspondence across distinct imaging modalities is a foundational yet formidable computer vision task. Current multi-modality registration techniques maximize hand-crafted inter-domain similarity functions,…
Multiview point cloud registration is a fundamental task for constructing globally consistent 3D models. Existing approaches typically rely on feature extraction and data association across multiple point clouds; however, these processes…
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…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
Registration is widely used in image-guided therapy and image-guided surgery to estimate spatial correspondences between organs of interest between planning and treatment images. However, while high-quality computed tomography (CT) images…
Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains…