Is pose-based pivot calibration superior to sphere fitting?

2017 ◽  
Author(s):  
Burton Ma ◽  
Niloofar Banihaveb ◽  
Joy Choi ◽  
Elvis C. S. Chen ◽  
Amber L. Simpson
Keyword(s):  
Sphere Fitting

scholarly journals Sphere Fitting with Applications to Machine Tracking

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 177
Author(s):  
Dror Epstein ◽  
Dan Feldman
Keyword(s):  
Pressure Control ◽  
Exact Match ◽  
Mechanical Pressure ◽  
Real World Data ◽  
Data Summarization ◽  
Technical Result ◽  
Multiplicative Factor ◽  
Pressure Control System ◽  
Sum Of Distances ◽  
Sphere Fitting

We suggest a provable and practical approximation algorithm for fitting a set P of n points in R d to a sphere. Here, a sphere is represented by its center x ∈ R d and radius r > 0 . The goal is to minimize the sum ∑ p ∈ P ∣ p − x − r ∣ of distances to the points up to a multiplicative factor of 1 ± ε , for a given constant ε > 0 , over every such r and x. Our main technical result is a data summarization of the input set, called coreset, that approximates the above sum of distances on the original (big) set P for every sphere. Then, an accurate sphere can be extracted quickly via an inefficient exhaustive search from the small coreset. Most articles focus mainly on sphere identification (e.g., circles in 2 D image) rather than finding the exact match (in the sense of extent measures), and do not provide approximation guarantees. We implement our algorithm and provide extensive experimental results on both synthetic and real-world data. We then combine our algorithm in a mechanical pressure control system whose main bottleneck is tracking a falling ball. Full open source is also provided.

scholarly journals New Objective Refraction Metric Based on Sphere Fitting to the Wavefront

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Mateusz Jaskulski ◽  
Andreí Martínez-Finkelshtein ◽  
Norberto López-Gil
Keyword(s):  
Pupil Size ◽  
Spherical Equivalent ◽  
Independent Dataset ◽  
Accurate Predictor ◽  
Equivalent Sphere ◽  
Wavefront Error ◽  
Variable Distance ◽  
The Mean ◽  
Similar Accuracy ◽  
Sphere Fitting

Purpose. To develop an objective refraction formula based on the ocular wavefront error (WFE) expressed in terms of Zernike coefficients and pupil radius, which would be an accurate predictor of subjective spherical equivalent (SE) for different pupil sizes.Methods. A sphere is fitted to the ocular wavefront at the center and at a variable distance,t. The optimal fitting distance,topt, is obtained empirically from a dataset of 308 eyes as a function of objective refraction pupil radius,r0, and used to define the formula of a new wavefront refraction metric (MTR). The metric is tested in another, independent dataset of 200 eyes.Results. For pupil radiir0≤2 mm, the new metric predicts the equivalent sphere with similar accuracy (<0.1D), however, forr0>2 mm, the mean error of traditional metrics can increase beyond 0.25D, and the MTR remains accurate. The proposed metric allows clinicians to obtain an accurate clinical spherical equivalent value without rescaling/refitting of the wavefront coefficients. It has the potential to be developed into a metric which will be able to predict full spherocylindrical refraction for the desired illumination conditions and corresponding pupil size.

Prosthetic Modeling of the Femoral Head Based on Reverse Method

2011 ◽  
Vol 88-89 ◽  
pp. 225-229
Author(s):  
Bin Liu ◽  
Zhi Huan Huang ◽  
Xin Fan ◽  
Hao Jie Li
Keyword(s):  
Femoral Head ◽  
New Method ◽  
Head Model ◽  
Spatial Motion ◽  
Spatial Dynamic ◽  
Data Points ◽  
Lunate Surface ◽  
Reverse Method ◽  
Fitting Model ◽  
Sphere Fitting

In this paper, a new method for reconstructing the model of the necrotic femoral head is presented. It can reconstruct the optimal femoral head prosthesis model utilizing the reverse technology. This new method not only affords a theoretical model for the accurate operation position fixing in orthopaedic clinic, but also provides an innovative practical means for the individualized manufacturing of artificial femoral head prosthesis.The femoral head is regarded as a sphere. Then, the femoral head's configuration is reconstructed by means of fitting using the data points on the unspoiled acetabulum lunate surface. A spatial dynamic analysis is implemented, it is proved that the sphere fitting model can well satisfy the spatial motion relation between the femoral head and the acetabulum. The experiment results show that this method can well reconstruct the femoral head model of the target patient.

scholarly journals Capturing Surface Complementarity in Proteins using Unsupervised Learning and Robust Curvature Measure

2021 ◽  
Author(s):  
Abhijit Gupta ◽  
Arnab Mukherjee
Keyword(s):  
Machine Learning ◽  
Biological Function ◽  
Current Approach ◽  
Curvature Measure ◽  
Shape Complementarity ◽  
Binding Partners ◽  
Fitting Method ◽  
Antigen Antibody ◽  
The Relationship ◽  
Sphere Fitting

The structure of a protein plays a pivotal role in determining its function. Often, the protein surface’s shape and curvature dictate its nature of interaction with other proteins and biomolecules. However, marked by corrugations and roughness, a protein’s surface representation poses significant challenges for its curvature-based characterization. In the present study, we employ unsupervised machine learning to segment the protein surface into patches. To measure the surface curvature of a patch, we present an algebraic sphere fitting method that is fast, accurate, and robust. Moreover, we use local curvatures to show the existence of “shape complementarity” in protein-protein, antigen-antibody, and protein-ligand interfaces. We believe that the current approach could help understand the relationship between protein structure and its biological function and can be used to find binding partners of a given protein.

Relation of Computed Tomography-Based Static Axial Radioulnar Incongruence Measurements under General Anaesthesia and Dynamic, In Vivo RUI during the Walk in Canine Elbow Joints with and without Medial Coronoid Process Disease

2021 ◽  
Author(s):  
Thomas Rohwedder ◽  
Peter Böttcher
Keyword(s):  
Computed Tomography ◽  
General Anaesthesia ◽  
Dynamic Change ◽  
Weight Bearing ◽  
3D Models ◽  
Coronoid Process ◽  
Control Group ◽  
Prospective Clinical Study ◽  
Sphere Fitting

Abstract Objective This study aimed to evaluate the correlation of static axial radioulnar incongruence (sRUI) measured under general anaesthesia with the real in vivo dynamic RUI (dRUI) during walking. Study design This was a prospective clinical study that included 6 sound elbows (5 dogs) and 7 medial coronoid process disease (MCPD) affected elbows (6 dogs). Materials and Methods Static axial radioulnar incongruence was measured using the sphere fitting technique on computed tomography-based three-dimensional (3D) models of radius and ulna. The in vivo pose of radius and ulna was derived from radiostereometric analysis during the walk and transferred onto previously calculated 3D models. Dynamic RUI was measured on those adjusted models using the sphere fitting technique, providing a measurement of RUI over time during walk. Results Mean sRUI was 0.2 mm (standard deviation [SD]: 0.30) in control and 1.4 mm (SD: 0.73) in elbow joints with MCPD; being significantly different (p = 0.0035; confidence interval [CI]: 0.4772–1.8824). Mean dRUI in controls (−0.4 mm; SD: 0.47) was significantly different (p = 0.0004; CI: 0.9918–2.5225) from dRUI in the affected elbows (1.4 mm; SD: 0.73). Comparison of sRUI and dRUI within each group showed difference in the control group (0.2 vs. −0.4 mm; p = 0.0138; CI: 0.1820–1.0014). In affected elbows, no difference between sRUI and dRUI was found (1.4 vs. 1.4 mm; p = 0.8963). Conclusion In normal elbow joints, sRUI does not represent the in vivo condition during weight bearing. Dynamic and slightly negative RUI occurs during loading (0.2 mm positive to −0.4 mm negative RUI). In MCPD affected elbows with sRUI, no dynamic change of RUI occurs during the walk.

scholarly journals A sphere fitting approach to determine the hip joint centre of the horse

2017 ◽  
Vol 13 (2) ◽  
pp. 113-118
Author(s):  
S. Valentin ◽  
C. Peham ◽  
R.R. Zsoldos ◽  
T.F. Licka
Keyword(s):  
Least Squares ◽  
Hip Joint ◽  
Ex Vivo ◽  
Femoral Condyle ◽  
Functional Method ◽  
Accurate Identification ◽  
Musculoskeletal Modelling ◽  
Joint Biomechanics ◽  
Sphere Fitting

Accurate identification of the hip joint centre (HJC) is crucial for the correct estimation of knee and hip joint loads and kinematics, which is particularly relevant in orthopaedic surgery and musculoskeletal modelling. Several methods have been described for calculation of the HJC in humans, however, no studies have used these methods in the horse despite a similar need for improved evaluation of hip joint biomechanics in rehabilitation and musculoskeletal modelling. This preliminary study uses the commonly used functional method (least-squares sphere fit) to determine the HJC in three equid cadavers. Bone pins with reflective markers attached were drilled into the tuber coxae (TC), tuber ischium (TI), tuber sacrale (TS), greater trochanter (GT), third trochanter (TT) and lateral femoral condyle (FC) of the uppermost limb of the cadavers positioned in lateral recumbency. Three repetitions of passive movements consisting of pro-and retraction, ab- and adduction and circumduction were performed. The HJC was calculated using a least-squares sphere fitting method and presented as a distance from the TC based on a percentage of the TC to TI vector magnitude. Mean (± standard deviation) of the HJC is located 52.4% (± 3.9) caudally, 0.2% (± 6.5) dorsally, and 19.8% (± 4.2) medially from the TC. This study is the first to quantify the HJC in horses ex vivo using a functional method. Further work (in vivo and imaging) is required to validate the findings of the present study.

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