scholarly journals New Methods and Novel Framework for HypersurfaceCurvature Determination and Analysis

2021 ◽  
Vol 22 (1-2) ◽  
pp. 11-20
Author(s):  
Jacob D. Hauenstein ◽  
Timothy S. Newman
Keyword(s):  
Ground Truth ◽  
Dimensional Manifold ◽  
Accuracy Analysis ◽  
Volumetric Data ◽  
3 Dimensional ◽  
New Methods ◽  
Synthetic Test ◽  
Method Accuracy

New methods for hypersurface (that is, 3-dimensional manifold) curvature determination in volumetric data areintroduced. One method is convolution-based. Another method is spline-based. Method accuracy is also analyzed,with that analysis involving comparison of the methods with each other as well as against two existing convolution-based methods. The accuracy analysis utilizes a novel framework that enables curvature determination methodaccuracy analysis via dynamically generated synthetic test datasets formed from continuous trivariate functions.Such functions enable accuracy analysis versus ground truth. The framework is also described here.

scholarly journals Hand-Held Stereovision System for Image Updating in Open Spine Surgery

2020 ◽  
Vol 19 (4) ◽  
pp. 461-470
Author(s):  
Xiaoyao Fan ◽  
Maxwell S Durtschi ◽  
Chen Li ◽  
Linton T Evans ◽  
Songbai Ji ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Spine Surgery ◽  
Surgical Navigation ◽  
Image Data ◽  
Ground Truth ◽  
Acquisition Time ◽  
Fiducial Markers ◽  
Image Pair ◽  
3 Dimensional ◽  
Surgical Field

Abstract BACKGROUND Image guidance in open spinal surgery is compromised by changes in spinal alignment between preoperative images and surgical positioning. We evaluated registration of stereo-views of the surgical field to compensate for vertebral alignment changes. OBJECTIVE To assess accuracy and efficiency of an optically tracked hand-held stereovision (HHS) system to acquire images of the exposed spine during surgery. METHODS Standard midline posterior approach exposed L1 to L6 in 6 cadaver porcine spines. Fiducial markers were placed on each vertebra as “ground truth” locations. Spines were positioned supine with accentuated lordosis, and preoperative computed tomography (pCT) was acquired. Spines were re-positioned in a neutral prone posture, and locations of fiducials were acquired with a tracked stylus. Intraoperative stereovision (iSV) images were acquired and 3-dimensional (3D) surfaces of the exposed spine were reconstructed. HHS accuracy was assessed in terms of distances between reconstructed fiducial marker locations and their tracked counterparts. Level-wise registrations aligned pCT with iSV to account for changes in spine posture. Accuracy of updated computed tomography (uCT) was assessed using fiducial markers and other landmarks. RESULTS Acquisition time for each image pair was <1 s. Mean reconstruction time was <1 s for each image pair using batch processing, and mean accuracy was 1.2 ± 0.6 mm across 6 cases. Mean errors of uCT were 3.1 ± 0.7 and 2.0 ± 0.5 mm on the dorsal and ventral sides, respectively. CONCLUSION Results suggest that a portable HHS system offers potential to acquire accurate image data from the surgical field to facilitate surgical navigation during open spine surgery.

scholarly journals Evaluation of Automatic Facial Wrinkle Detection Algorithms

2020 ◽  
Vol 6 (4) ◽  
pp. 17
Author(s):  
Remah Mutasim Elbashir ◽  
Moi Hoon Yap
Keyword(s):  
Gabor Filter ◽  
Ground Truth ◽  
Jaccard Similarity ◽  
Skin Changes ◽  
Detection Algorithms ◽  
New Methods ◽  
Facial Wrinkle ◽  
Similarity Indices ◽  
The Face ◽  
Enhancement Method

Facial wrinkles (considered to be natural features) appear as people get older. Wrinkle detection is an important aspect of applications that depend on facial skin changes, such as face age estimation and soft biometrics. While existing wrinkle detection algorithms focus on forehead horizontal lines, it is necessary to develop new methods to detect all wrinkles (vertical and horizontal) on whole face. Therefore, we evaluated the performance of wrinkle detection algorithms on the whole face and proposed an enhancement technique to improve the performance. More specifically, we used 45 images of the Face Recognition Technology dataset (FERET) and 25 images of the Sudanese dataset. For ground truth annotations, the selected images were manually annotated by the researcher. The experiments showed that the method with enhancement performed better at detecting facial wrinkles when compared to the state-of-the-art methods. When evaluated on FERET, the average Jaccard similarity indices were 56.17%, 31.69% and 15.87% for the enhancement method, Hybrid Hessian Filter and Gabor Filter, respectively.

Correlation based swarm trackers for 3-dimensional manifold mesh formation

2009 ◽  
Author(s):  
Charles Casey ◽  
Laurence G. Hassebrook ◽  
Priyanka Chaudhary
Keyword(s):  
Dimensional Manifold ◽  
3 Dimensional

scholarly journals The Long-Time Behavior of the Ricci Tensor under the Ricci Flow

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Christian Hilaire
Keyword(s):  
Ricci Flow ◽  
Ricci Tensor ◽  
Closed Manifold ◽  
Time Behavior ◽  
Dimensional Manifold ◽  
Long Time Behavior ◽  
Bounded Curvature ◽  
3 Dimensional ◽  
Long Time ◽  
Uniformly Bounded

We show that, given an immortal solution to the Ricci flow on a closed manifold with uniformly bounded curvature and diameter, the Ricci tensor goes to zero as . We also show that if there exists an immortal solution on a closed 3-dimensional manifold such that the product of the curvature and the square of the diameter is uniformly bounded, then this solution must be of type III.

scholarly journals Accurate localization of linear probe electrodes across multiple brains

2020 ◽  
Author(s):  
Liu D Liu ◽  
Susu Chen ◽  
Michael N Economo ◽  
Nuo Li ◽  
Karel Svoboda
Keyword(s):  
Ground Truth ◽  
Brain Structures ◽  
Brain Regions ◽  
Brain Atlas ◽  
3 Dimensional ◽  
Accurate Localization ◽  
Large Numbers ◽  
Linear Probe ◽  
Electrode Localization ◽  
Recording Electrodes

AbstractRecently developed silicon probes have large numbers of recording electrodes on long linear shanks. Specifically, Neuropixels probes have 960 recording electrodes distributed over 9.6 mm shanks. Because of their length, Neuropixels probe recordings in rodents naturally span multiple brain areas. Typical studies collate recordings across several recording sessions and animals. Neurons recorded in different sessions and animals have to be aligned to each other and to a standardized brain coordinate system. Here we report a workflow for accurate localization of individual electrodes in standardized coordinates and aligned across individual brains. This workflow relies on imaging brains with fluorescent probe tracks and warping 3-dimensional image stacks to standardized brain atlases. Electrophysiological features are then used to anchor particular electrodes along the reconstructed tracks to specific locations in the brain atlas and therefore to specific brain structures. We performed ground-truth experiments, in which motor cortex outputs are labelled with ChR2 and a fluorescence protein. Recording from brain regions targeted by these outputs reveals better than 100 μm accuracy for electrode localization.

scholarly journals Three-Filters-to-Normal: An Accurate and Ultrafast Surface Normal Estimator

2020 ◽  
Author(s):  
Rui Fan ◽  
Hengli Wang ◽  
Bohuan Xue ◽  
Huaiyang Huang ◽  
Yuan Wang ◽  
...  
Keyword(s):  
Large Scale ◽  
Median Filter ◽  
Ground Truth ◽  
Depth Image ◽  
Range Data ◽  
3 Dimensional ◽  
Depth Images ◽  
Mesh Model ◽  
Surface Normal ◽  
Synthetic Datasets

Over the past decade, significant efforts have been made to improve the trade-off between speed and accuracy of surface normal estimators (SNEs). This paper introduces an accurate and ultrafast SNE for structured range data. The proposed approach computes surface normals by simply performing three filtering operations, namely, two image gradient filters (in horizontal and vertical directions, respectively) and a mean/median filter, on an inverse depth image or a disparity image. Despite the simplicity of the method, no similar method already exists in the literature. In our experiments, we created three large-scale synthetic datasets (easy, medium and hard) using 24 3-dimensional (3D) mesh models. Each mesh model is used to generate 1800--2500 pairs of 480x640 pixel depth images and the corresponding surface normal ground truth from different views. The average angular errors with respect to the easy, medium and hard datasets are 1.6 degrees, 5.6 degrees and 15.3 degrees, respectively. Our C++ and CUDA implementations achieve a processing speed of over 260 Hz and 21 kHz, respectively. Our proposed SNE achieves a better overall performance than all other existing computer vision-based SNEs. Our datasets and source code are publicly available at: sites.google.com/view/3f2n.

scholarly journals Three-Filters-to-Normal: An Accurate and Ultrafast Surface Normal Estimator

2020 ◽  
Author(s):  
Rui Fan ◽  
Hengli Wang ◽  
Bohuan Xue ◽  
Huaiyang Huang ◽  
Yuan Wang, ◽  
...  
Keyword(s):  
Large Scale ◽  
Median Filter ◽  
Ground Truth ◽  
Depth Image ◽  
Range Data ◽  
3 Dimensional ◽  
Depth Images ◽  
Mesh Model ◽  
Surface Normal ◽  
Synthetic Datasets

Over the past decade, significant efforts have been made to improve the trade-off between speed and accuracy of surface normal estimators (SNEs). This paper introduces an accurate and ultrafast SNE for structured range data. The proposed approach computes surface normals by simply performing three filtering operations, namely, two image gradient filters (in horizontal and vertical directions, respectively) and a mean/median filter, on an inverse depth image or a disparity image. Despite the simplicity of the method, no similar method already exists in the literature. In our experiments, we created three large-scale synthetic datasets (easy, medium and hard) using 24 3-dimensional (3D) mesh models. Each mesh model is used to generate 1800--2500 pairs of 480x640 pixel depth images and the corresponding surface normal ground truth from different views. The average angular errors with respect to the easy, medium and hard datasets are 1.6 degrees, 5.6 degrees and 15.3 degrees, respectively. Our C++ and CUDA implementations achieve a processing speed of over 260 Hz and 21 kHz, respectively. Our proposed SNE achieves a better overall performance than all other existing computer vision-based SNEs. Our datasets and source code are publicly available at: sites.google.com/view/3f2n.

scholarly journals The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
J. A. Helayël-Neto ◽  
Alireza Sepehri ◽  
Tooraj Ghaffary
Keyword(s):  
Modified Gravity ◽  
Dimensional Space ◽  
Main Idea ◽  
Big Bang ◽  
Space Time ◽  
Dimensional Manifold ◽  
3 Dimensional ◽  
Dimensional Space Time ◽  
The Big Bang ◽  
Chern Simons

It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.

scholarly journals Poincare's conjecture and the homeotopy group of a closed, orientable 2-manifold

1974 ◽  
Vol 17 (2) ◽  
pp. 214-221 ◽  
Author(s):  
Joan S. Birman
Keyword(s):  
Dimensional Manifold ◽  
3 Dimensional ◽  
Dimension 2 ◽  
Poincare Conjecture ◽  
Simply Connected

In 1904 Poincaré [11] conjectured that every compact, simply-connected closed 3-dimensional manifold is homeomorphic to a 3-sphere. The corresponding result for dimension 2 is classical; for dimension ≧ 5 it was proved by Smale [12] and Stallings [13], but for dimensions 3 and 4 the question remains open. It has been discovered in recent years that the 3-dimensional Poincaré conjecture could be reformulated in purely algebraic terms [6, 10, 14, 15] however the algebraic problems which are posed in the references cited above have not, to date, proved tractable.

Sign in / Sign up

Export Citation Format

Share Document