ترغب بنشر مسار تعليمي؟ اضغط هنا

LSMAT Least Squares Medial Axis Transform

220   0   0.0 ( 0 )
 نشر من قبل Daniel Rebain
 تاريخ النشر 2020
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/or noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artifacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as the set of maximally inscribed spheres. We show how this definition can be formulated as a least squares relaxation where the transform is obtained by minimizing a continuous optimization problem. The proposed approach is inherently parallelizable by performing independant optimization of each sphere using Gauss-Newton, and its least-squares form allows it to be significantly more robust compared to traditional computational geometry approaches. Extensive experiments on 2D and 3D objects demonstrate that our method provides superior results to the state of the art on both synthetic and real-data.



قيم البحث

اقرأ أيضاً

61 - Barak Sober , David Levin 2016
In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes referred to as m anifold learning) assume that the scattered input data is lying on a lower dimensional manifold, thus the high dimensionality problem can be overcome by learning the lower dimensionality behavior. However, in real life applications, data is often very noisy. In this work, we propose a method to approximate $mathcal{M}$ a $d$-dimensional $C^{m+1}$ smooth submanifold of $mathbb{R}^n$ ($d ll n$) based upon noisy scattered data points (i.e., a data cloud). We assume that the data points are located near the lower dimensional manifold and suggest a non-linear moving least-squares projection on an approximating $d$-dimensional manifold. Under some mild assumptions, the resulting approximant is shown to be infinitely smooth and of high approximation order (i.e., $O(h^{m+1})$, where $h$ is the fill distance and $m$ is the degree of the local polynomial approximation). The method presented here assumes no analytic knowledge of the approximated manifold and the approximation algorithm is linear in the large dimension $n$. Furthermore, the approximating manifold can serve as a framework to perform operations directly on the high dimensional data in a computationally efficient manner. This way, the preparatory step of dimension reduction, which induces distortions to the data, can be avoided altogether.
Edge bundling methods can effectively alleviate visual clutter and reveal high-level graph structures in large graph visualization. Researchers have devoted significant efforts to improve edge bundling according to different metrics. As the edge bund ling family evolve rapidly, the quality of edge bundles receives increasing attention in the literature accordingly. In this paper, we present MLSEB, a novel method to generate edge bundles based on moving least squares (MLS) approximation. In comparison with previous edge bundling methods, we argue that our MLSEB approach can generate better results based on a quantitative metric of quality, and also ensure scalability and the efficiency for visualizing large graphs.
Ubiquitous in eukaryotic organisms, the flagellum is a well-studied organelle that is well-known to be responsible for motility in a variety of organisms. Commonly necessitated in their study is the capability to image and subsequently track the move ment of one or more flagella using videomicroscopy, requiring digital isolation and location of the flagellum within a sequence of frames. Such a process in general currently requires some researcher input, providing some manual estimate or reliance on an experiment-specific heuristic to correctly identify and track the motion of a flagellum. Here we present a fully-automated method of flagellum identification from videomicroscopy based on the fact that the flagella are of approximately constant width when viewed by microscopy. We demonstrate the effectiveness of the algorithm by application to captured videomicroscopy of Leishmania mexicana, a parasitic monoflagellate of the family Trypanosomatidae. ImageJ Macros for flagellar identification are provided, and high accuracy and remarkable throughput are achieved via this unsupervised method, obtaining results comparable in quality to previous studies of closely-related species but achieved without the need for precursory measurements or the development of a specialised heuristic, enabling in general the automated generation of digitised kinematic descriptions of flagellar beating from videomicroscopy.
Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these functions are extremely concise, but their impleme ntation in real code is tedious, especially when optimized for real-time performance on modern GPUs in interactive applications. In this work, we propose a new language, Opt (available under http://optlang.org), for writing these objective functions over image- or graph-structured unknowns concisely and at a high level. Our compiler automatically transforms these specifications into state-of-the-art GPU solvers based on Gauss-Newton or Levenberg-Marquardt methods. Opt can generate different variations of the solver, so users can easily explore tradeoffs in numerical precision, matrix-free methods, and solver approaches. In our results, we implement a variety of real-world graphics and vision applications. Their energy functions are expressible in tens of lines of code, and produce highly-optimized GPU solver implementations. These solver have performance competitive with the best published hand-tuned, application-specific GPU solvers, and orders of magnitude beyond a general-purpose auto-generated solver.
Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider LSD under the Bayesian framework and we introduce a flexible Gaussian Process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results. We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا