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Interpolating and approximating moving frames using B-splines

Ma Lizhuang, Jiang Zhongding, C.K.Y. Tony
Proceedings the Eighth Pacific Conference on Computer Graphics and Applications  
We present a method to interpolate the moving frame homogeneously using B-splines.  ...  The error caused by approximation and interpolation is given and shown to be controllable.  ...  In this paper, we present a method to interpolate the original and the three coordinate axis of the moving frame homogeneously by B-splines.  ... 
doi:10.1109/pccga.2000.883937 dblp:conf/pg/MaCJ00 fatcat:y4ofkrbupvg2bbrckylzb2aave

Sweeping Surface Generated by a Class of Generalized Quasi-cubic Interpolation Spline [chapter]

Benyue Su, Jieqing Tan
2007 Lecture Notes in Computer Science  
function without calculating control points inversely as in the cases of B-spline and Bézier methods or solving equation system as in the case of cubic polynomial interpolation spline.  ...  In this paper we present a new method for the model of interpolation sweep surfaces by the C 2 -continuous generalized quasicubic interpolation spline.  ...  On the other hand, in order to avoid a sharp acceleration of moving frame, we can use the chord length parametrization in the generalized quasi-cubic interpolation spline.  ... 
doi:10.1007/978-3-540-72586-2_6 fatcat:tg62epfogvhbbaeot2gf5mvx6a

Robust real-time segmentation of images and videos using a smooth-spline snake-based algorithm

F. Precioso, M. Barlaud, T. Blu, M. Unser
2005 IEEE Transactions on Image Processing  
This paper deals with fast image and video segmentation using active contours.  ...  A parametric active contour method based on B-Spline interpolation has been proposed in [26] to highly reduce the computational cost, but this method is sensitive to noise.  ...  (a) Frame 10. (b) Frame 20. (c) Frame 30. (d) Frame 40. Fig. 11 . 11 Smoothing spline to smooth contours. (a) Initial sequence. (b) Interpolation = 0 and = 20. (c) Approximation = 0:3 and = 0.  ... 
doi:10.1109/tip.2005.849307 pmid:16028555 fatcat:clxjtyysezg43cetwvq7zoiiqy

Minimizing the Distortion of Affine Spline Motions

Dae-Eun Hyun, Bert Jüttler, Myung-Soo Kim
2002 Graphical Models  
This paper proposes a simple approach to the affine motion interpolation problem, where an affine spline motion is generated that interpolates a given sequence of affine keyframes and satisfies approximately  ...  An affine spline motion is first generated so as to interpolate the given keyframes; after that, it is progressively refined via knot insertion and degree elevation into an optimal affine motion by an  ...  Acknowledgements This work was supported in part by the Korean Ministry of Information and Communication (MIC) under the University Basic Research Program in the year of 1999.  ... 
doi:10.1006/gmod.2002.0569 fatcat:jnjfar5375hltpyiweubuw5qym

Representation Method of the Moving Object Trajectories by Interpolation with Dynamic Sampling

Jin-Hwal Lee, Kee-Sung Lee, Geun-Sik Jo
2013 2013 International Conference on Information Science and Applications (ICISA)  
In the experiment result, we found that Cubic Spline Interpolation method is able to save up to 80 percent of annotation size with 15 frames annotation and below.  ...  In this study, we experiment the Cubic Spline Interpolation annotation method in order to reduce annotation size for stable or uncertainty cause by the object movement.  ...  CONCLUSION AND FUTURE WORKS In this study, Cubic Spline Interpolation method was proposed in order to interpolate the time interval and to represent uncertainty of a moving object.  ... 
doi:10.1109/icisa.2013.6579375 dblp:conf/icisa/LeeLJ13 fatcat:bijxk2mnc5egfhkkez7zrls5eu

Continuous body 3-D reconstruction of limbless animals

Qiyuan Fu, Thomas W. Mitchel, Jin Seob Kim, Gregory S. Chirikjian, Chen Li
2021 Journal of Experimental Biology  
Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely-used cubic B-spline interpolation  ...  Limbless animals such as snakes, limbless lizards, worms, eels, and lampreys move their slender, long body in three dimensions to traverse diverse environments.  ...  Acknowledgements We thank Henry Astley, Bob Full and Rajat Mittal for discussion; Sean Gart for providing snake step traversal experimental data for accuracy comparison with B-spline; and Henry Astley  ... 
doi:10.1242/jeb.220731 pmid:33536306 fatcat:td3id3uhhbei3lmsy54blefqnm

A new method for video data compression by quadratic Bézier curve fitting

Murtaza Ali Khan
2010 Signal, Image and Video Processing  
The input points are approximated using quadratic Bézier least square fitting. The output data consists of quadratic Bézier control points and difference between original and fitted data.  ...  The method can be applied to 1-D space like luminance and chrominance components separately or 3-D color spaces such as RG B and Y C b C r .  ...  Contour data compression method using Curvature Scale Space technique and Hermite curves is proposed by [15] . Proposed method of [8] uses multilevel B-Splines to approximate scattered data.  ... 
doi:10.1007/s11760-010-0165-9 fatcat:opdgc7nuu5hjpmtznapjkeslpm

Pixel timing correction in time-lapsed calcium imaging using point scanning microscopy

Dimitri Boiroux, Yoshihiko Oke, Fumikazu Miwakeichi, Yoshitaka Oku
2014 Journal of Neuroscience Methods  
We present and compare three interpolation methods (linear, Lanczos and cubic B-spline). We test these methods on a simulated network of coupled bursting neurons at different framerates.  ...  h i g h l i g h t s • Point scanning introduces a delay between image pixels when used at frequencies below 10 Hz. • The time delays can be corrected by using temporal interpolation. • Real two-photon  ...  Acknowledgements This study was supported by JST Strategic Japanese-German Cooperative Program in Computational Neuroscience and Grantin-Aid for Scientific Research from the Japan Society for Promotion  ... 
doi:10.1016/j.jneumeth.2014.08.008 pmid:25128722 fatcat:4xpe4puq3vghjiqecuvfc73ehq

B-Spline Active Contour with Handling of Topology Changes for Fast Video Segmentation

Frederic Precioso, Michel Barlaud
2002 EURASIP Journal on Advances in Signal Processing  
In this paper we propose to use a regular B-Spline parametric method to provide a fast and accurate segmentation. • Our B-Spline interpolation is based on a fixed number of points 2 j depending on the  ...  This results in improving both smoothness and accuracy. Then we show some experiments on real video sequences.  ...  In this paper, we propose a fast parametric method using B-Spline interpolated active contour.  ... 
doi:10.1155/s1110865702203121 fatcat:y3yrr3d7wbgalgo43vyw64goi4

Interactive Multiresolution Editing of Arbitrary Meshes

Seungyong Lee
1999 Computer graphics forum (Print)  
The result of the interpolation is mapped back to the editing area and then used to update the mesh. We adopt harmonic maps for the embedding and multilevel B-splines for the interpolation.  ...  The basic idea is to embed an editing area of a mesh onto a 2D rectangle and interpolate the user-specified editing information over the 2D rectangle.  ...  The author also owes thanks to Junho Kim and Kyuman Jeong for help with implementation and examples.  ... 
doi:10.1111/1467-8659.00329 fatcat:rbexhw2sv5e6ric74xx4mfcl4m

On-line Cartesian trajectory control of mechanisms along complex curves

Zhaoxue Yang, Edward Red
1997 Robotica (Cambridge. Print)  
Non -Uniform Rational B -Spline ( NURBS ) To define a rational B-spline , we make use of the homogeneous coordinate .  ...  Given the interpolated frame in Cartesian space , inverse kinematics are used to determine the joint values , speeds , and accelerations .  ...  as where u is the parameter , and N i ,k ( u ) is the B-spline basis function .  ... 
doi:10.1017/s0263574797000301 fatcat:sa4smtbi5vh6dgjubcji76wvxu

AN AUTOMATED ALGORITHM FOR APPROXIMATION OF TEMPORAL VIDEO DATA USING LINEAR B´EZIER FITTING

Murtaza Ali Khan
2010 The International Journal of Multimedia & Its Applications  
This paper presents an efficient method for approximation of temporal video data using linear Bezier fitting.  ...  For a given sequence of frames, the proposed method estimates the intensity variations of each pixel in temporal dimension using linear Bezier fitting in Euclidean space.  ...  Linear Bezier is most efficient and simple than other types curves e.g., quadratic/cubic Bezier curves, Natural cubic spline, B-spline, Cardinal spline etc.  ... 
doi:10.5121/ijma.2010.2207 fatcat:jcor7jqpbfhtph3xvdctnonjli

Verbs and adverbs: multidimensional motion interpolation

C. Rose, M.F. Cohen, B. Bodenheimer
1998 IEEE Computer Graphics and Applications  
Finally, we would like to thank the reviewers and Jessica Hodgins, whose suggestions helped strengthen this article.  ...  We would also like to thank the Interactive Media Productions group at Microsoft for contributing their time, equipment, and motion-capture expertise.  ...  Our technique, using radial B-splines, requires O(n) examples to establish the baseline approximation and O(n 3 ) to compute the resulting answer.  ... 
doi:10.1109/38.708559 fatcat:c4ff4yfif5f6pl6ckctdkh45sa

Smooth invariant interpolation of rotations

F. C. Park, Bahram Ravani
1997 ACM Transactions on Graphics  
The resulting rotation curve is easy to compute, invariant with respect to fixed and moving reference frames, and also approximately minimizes angular acceleration.  ...  We present an algorithm for generating a twice-differentiable curve on the rotation group SO(3) that interpolates a given ordered set of rotation matrices at their specified knot times.  ...  ACKNOWLEDGMENTS We wish to acknowledge In-Gyu Kang for debugging the multiple point algorithm, and generating all the simulation results and figures.  ... 
doi:10.1145/256157.256160 fatcat:jn3xlzwohjexdfa5rrczse73ga

Image Stabilization with Model-Based Tracking for Beating Heart Surgery

Gerhard Kurz, Uwe D. Hanebeck
2012 CURAC Jahrestagung  
As an alternative, using a teleoperated robot for compensating the heart motion has been proposed.  ...  Based on correspondences obtained by motion tracking, image stabilization is considered as a scattered data interpolation problem.  ...  We thank Evgeniya Ballmann for her work on physics-based motion compensation and Szabolcs Pa ´li for his contributions to the in-vivo experiment. References  ... 
dblp:conf/curac/KurzH12 fatcat:ppd6e6wqrnfuvoyt63w56rgjya
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